Encyclopædia Britannica, Ninth Edition/Clocks

by Edmund Beckett

CLOCKS

THE origin of clock work is involved in great obscurity. I Notwithstanding the statements by many writers that clocks, horologia, were in use so early as the 9th century, and that they were then invented by an archdeacon of Verona, named Pacificus, there appears to be no clear evidence that they were machines at all resembling those which have been in use for the last five or six centuries. But it may be inferred from various allusions to horologia, and to their striking spontaneously, in the 12th century, that genuine clocks existed then, though there is no surviving description of any one until the 13th century, when it appears that a horologiuni was sent by the sultan of Egypt in 1 232 to the Emperor Frederick II. " It resembled a celestial globe, in which the sun, moon, and planets moved, being impelled by weights and wheels, so that they pointed out the hour, day, and night with cer tainty." A clock was put up in a former clock tower at Westminster with some great bells in 1288, out of a fine imposed on a corrupt chief-justice, and the motto Discite justiliam, moniti, inscribed upon it. The bells were sold or rather, it is said, gambled away, by Henry VIII. In 1292 one is mentioned in Canterbury Cathedral as costing 30. And another at St Albans, by R. Wallingford the abbot in 1326, is said to have been such as there was not in all Europe, showing various astronomical phenomena. A description of one in Dover Castle with the date 1348 on it was published by the late Admiral Smyth, P.R.A.S., in 1851, and the clock itself was exhibited going, in the Scientific Exhibition of 1876. In the early editions of this Encyclopaedia there was a picture of a very similar one, made by De Vick for the French king Charles V. about the same time, much like our common clocks of the last century, exeept that it had a vibrating balance, but no spring, instead of a pendulum, for pendulums were not invented till three centuries after that.

Fig.—1. Section of House Clock.

The general construction of the going part of all clocks, except large or turret clocks, which we shall treat separ ately, is substantially the same, and fig. 1 is a section of any ordinary house clock. B is the barrel with the rope coiled round it, generally 16 times for the 8 days ; the barrel is fixed to its arbor K, which is prolonged into the winding square coming up to the face or dial of the clock ; the dial is here shown as fixed either by small screws x, or by a socket and pin z, to the prolonged pillars p, p, which (4 or 5 in number) connect the plates or frame of the clock together, though the dial is commonly, but for no good reason, set on to the front plate by another set of pillars of its own. The great wheel G rides on the arbor, and is connected with the barrel by the ratchet R, the action of which is shown more fully in fig 1 4. The intermediate wheel r in this drawing is for a purpose which will be de scribed hereafter, and for the present it may be considered as omitted, and the click of the ratchet R as fixed to the great wheel. The great wheel drives the pinion c which is called the centre pinion, on the arbor of the centre whee.1 C, which goes through to the dial, and carries the long, or minute-hand; this wheel always turns in an hour, and the great wheel generally in 12 hours, by having 12 times as many teeth as the centre pinion. The centre wheel drives the " second wheel " D by its pinion d, and that again drives the scape-wheel E by its pinion e. If the pinions d and e have each 8 teeth or leaves (as the teeth of pinions are usually called), C will have 64 teeth and D 60, in a clock of which the scape-wheel turns in a minute, so that the seconds hand may be set on its arbor prolonged to the dial. A represents the pallets of the escapement, which will be described presently, and their arbor a goes through a large hole in the back plate near F, and its back pivot turns in a cock OFQ screwed on to the back plate. From the pallet arbor at F descends the crutch F/, ending ic the /or/;/, which embraces the pendulum F, so that as the pendulum vibrates, the crutch and the pullets necessarily vibrate with it. The pendulum is hung by a thin spring S from the cock Q, so that the bending point of the spring may be just opposite the end of the pallet arbor, and the edge of the spring as close to the end of that arbor aa possible a point too frequently neglected.

We may now go to the front (or left hand) of the clock, and describe the dial or " motion-work." The minute hand fits on to a squared end of a brass socket, which is fixed to the wheel M, and fits close, but not tight, on the pro longed arbor of the centre wheel. Behind this wheel is a bent spring which is (or ought to be) set on the same arbor with a square hole (not a round one as it sometimes is) in the middle, so that it must turn with the arbor; the wheel is pressed up against this spring, and kept there, by a cap and a small pin through the end of the arbor. The consequence is, that there is friction enough between the spring .and the wheel to carry the hand round, but not enough to resist a moderate push with the finger for the purpose of altering the time indicated. This wheel M, which is sometimes called the minute-wheel, but is better called the hour-wheel as it turns in an hour, drives another wheel N, of the same number of teeth, which has a pinion attached to it; and that pinion drives the twelve-hour tcheel H, which is also attached to a large socket or pipe carrying the hour hand, and riding on the former socket, or rather (in order to relieve the centre arbor of that extra weight) on an intermediate socket fixed to the bridge L, which is screwed to the front plate over the hour-wheel M. The weight W, which drives the train and gives the impulse to the pendu lum through the escapement, is generally hung by a catgut line passing through a pulley attached to the weight, the other end of the cord being tied to some convenient place in the clock frame or seat-board, to which it is fixed by screws through the lower pillars. It has usually been the practice to make the case of house clocks and astronomical clocks not less than 6 feet high ; but that is a very unnecessary waste of space and materials ; for by either diminishing the size of the barrel, or the number of its turns, by increasing the size of the great wheel by one-half, or hanging the weights by a treble instead of a double line; a case just long enough for the pendulum will also be long enough for the fall of the weights in 7? or 8 days. Of courso the weights have to be increased in the same ratio, and indeed ratharmore, to overcome the increased friction; but that is of no consequence.

Pendulum.

The claim to the invention of the pendulum, like the claim to most inventions, is disputed ; and we have no intention of trying to settle it. It was, like many other discoveries and inventions, probably made by various persons independently, and almost simul taneously, when the state of science had become ripe for it. The discovery of that peculiarly valuable property of the pendulum called isochronism, or the disposition to vibrate different arcs in very nearly the same time (provided the arcs are none of them large), is commonly attributed to Galileo, in the well-known story of his being struck with the isochronism of a chandelier hung by a long chain from the roof of the church, at Florence. And Galileo s son appears as a rival of Avicenna, Huyghens, Dr Hooke, and a London clockmaker named Harris, for the honour of having first applied the pendulum to regulate the motion of a clock train, all in the early part of the 17th century. Be this as it may, there seems little doubt that Huyghens was the first who mathematically investi gated, and therefore really knew, the true nature of those properties of the pendulum which may now be found explained in any mathe matical book on mechanics. He discovered that if a simple pen dulum (i.e., a weight or lob consisting of a single point, and hung by a rod or string of no weight) can be made to describe, not a circle, but a cycloid of which the string would be the radius of cur vature at the lowest point, all its vibrations, however large, will be performed in the same time. For a little distance near the bottom, the circle very nearly coincides with the cycloid ; and hence it is that, for small arcs, a pendulum vibrating as usual in a circle is nearly enough isochronous for the purposes of horology ; more espe cially when contrivances are introduced either to compensate for the variations of the arc, or, better still, to destroy them altogether, by making the force on the pendulum so constant that its arc may never sensibly vary.

The difference between the time of any small arc of the circle an any arc of the cycloid varies nearly as the square of the circular arc ; and again, the difference between the times of any two smal and nearly equal circular arcs of the same pendulum, varies nearly as the arc itself. If a, the arc, is increased by a small amount da, the pendulum, will lose IQSOOada seconds a day, which is rather more than 1 second, if a is 2 (from zero) and da is 10 , since the numerical value of 2 is 035. If the increase of arc is considerable, t will not do to reckon thus by differentials, but we must take the difference of time for the day as 5400 (a, 2 a 2 ), which will be j ist seconds if a ? 2 and a t 6. For many years it wag thought of great importance to obtain cycloidal vibrations of clock pendulums, ind it was done by making the suspension string or spring vibrate Between cycloidal checks, as they were called. But it was in time discovered that all this is a delusion, first, because there is and can be no such thing in reality as a simple pendulum, and cycloidal cheeks will only make a simple pendulum vibrate isochronously ; secondly, because a very slight error in the form of the cheeks (as Huyghens himself discovered) would do more harm than the circular error uncorrected, even for an arc of 1 0, which is much larger than the common pendulum arc ; thirdly, because there was always some friction or adhesion between the cheeks and the string ; and fourthly (a reason which applies equally to all the isochronous contrivances since invented), because a common clock escapement itself generally tends to produce an error exactly opposite to the circular error, or to make the pendulum vibrate quicker the farther it swings ; and therefore the circular error is actually useful for the purpose of helping to counteract the error due to the escapement, and the clock goes better than it would with, a simple pendulum, describing the most perfect cycloid. At the same time, the thin spring by which pendulums are always suspended, except in some French clocks where a silk string is used (a very inferior plan), causes the pendulum to deviate a little from circular and to approxi mate to cycloidal motion, because the bend does not take place at one point, but is spread over some length of the spring.

The accurate performance of a clock depends so essentially on the pendulum, that we shall go somewhat into detail respecting it. First then, the time of vibration depends entirely on the length of the pendulum, the effect of the spring being too small for considera tion until we come to differences of a higher order. But the time does not vary as the length, but only as the square root of the length ; i.e., a pendulum to vibrate two seconds must be four- times as long as a seconds pendulum. The relation between the time of vibration and the length of a pendulum is expressed thus : t TT/-, where t is the time in seconds, it the well-known symbol for 3 141 59, the ratio of the circumference of a circle to ita diameter, I the length of the pendulum, and g the force of gravity at the latitude where it is intended to vibrate. This letter g, in the latitude of London, is the symbol for 32 2 feet, that being the velocity (or number of feet per second) at which a body is found by experiment to be moving at the end of the first second of its fall, being necessarily equal to twice the actual number of feet it has fallen in that second. Consequently, the length of a pendulum to beat seconds in London is 39 14 inches. But the same pendulum carried to the equator, where the force of gravity is less, would lose 2J minutes a day.

The seconds we are here speaking of are the seconds of. a common clock indicating mean solar time. But as clocks are also required for sidereal time, it may be as well to mention the proportions between a mean and a sidereal pendulum. A sidereal day is the interval between two successive transits over the meridian of a place by that imagin ary point in the heavens called T, the first point of Aries, at the intersection of the equator and the ecliptic ; and there is one more sidereal day than there are solar days in a year, since the earth has to turn more than once round iii space before the sun can coma a second time to the meridian, on account of the earth s own motion in its orbit during the day. A sidereal day or hour is shorter than a mean solar one in the ratio of 99727, and consequently a sidereal pendulum must be shorter than a mean time pendulum in the squaro of that ratio, or in the latitude of London the sidereal seconds pen dulum is 38 87 inches. As we have mentioned what is or 24 o clock by sidereal time, we may as well add, that the mean day is also reckoned in astronomy by 24 hours, and not from midnight as in civil reckoning, but from the following noon ; thus, what wo call 11 A.M. May 1 in common life is 23 h. April 30 with astronomers.

It must be remembered that the pendulums whose lengths _we have been speaking of are simple pendulums ; and as that is a thing which can only exist in theory, the reader may ask how the length of a real pendulum to vibrate in any required time is ascertained. In every pendulum, that is to say, in every body hung so as to be capable of vibrating freely, there is a certain point, always some where below the centre of gravity, which possesses these remarkable properties that if the pendulum were turned upside down, and set vibrating about this point, it would vibrate in the same time as before, and moreover, that the distance of this point from the point of suspension is exactly the length of that imaginary simple pendulum which would vibrate in the same time. This point is therefore , called the centre of oscillation. The rules for finding it by calcula-

tbn are too complicated for ordinary use, except in bodies of certain simple and regular forms ; but they are fortunately not requisite in practice, because in all clock pendulums the centre of oscillation is only a short distance below the centre of gravity of the whole pendulum, and generally so near to the centre of gravity of the bob in fact a little above it that there is no difficulty in making a pendulum for any given time of vibration near enough to the proper length at once, and then adjusting it by screwing the bob up or down until it is found to vibrate in the proper time.

Revolving or Conical Pendulum.

Thus far we have been speaking of vibrating pendulums but now useu universally, in all but some interior foreign clocks, which have strings instead, is a thin and short spring, with one end let into the top of the pendulum, and the other screwed between two luiu me lujj vi uic peuuiuum, iinu uie inner screwed ueiwecn two chops ot metal with a pin through them, which rests firmly in n nick in the cock which carries the pendulum as shown in fig. 2 a little farther on ; and the steadiness of this cock, and its firm Qxing to a wall, are essential to the accurate performance of the rlnc V. Tlio thinner flip Qnrinrr flip 1^o<fnT. -rn^t-i.!*./! ff isMii*cr> if lilUS I UT We nave uccll suettmiig ui iuianii^ ^/CUILIUIUUO , L>uii the notice of pendulums would be incomplete without some allusion to revolving or conical pendulums, as they are called, because they describe a cone in revolving. Such pendulums are used where a continuous instead of an intermittent motion of the clock train is required, as in the clocks for keeping an equatorial telescope directed to a star, by driving it the opposite way to the motion of the earth, to whose axis the axis on which the telescope turns is made parallel. Clocks with such pendulums may also be used in bedrooms by persons who cannot bear the ticking of a common clock. The pendulum, instead of being hung by a flat spring, is hung by a thin piece of piano-forte wire ; and it should be under stood that it has no tendency to twist on its own axis, and so to twist off the wire, as may be apprehended ; in fact, it would require some extra force to make it twist, if it were wanted to do so. The time of revolution of such a pendulum may be easily ascertained as follows : Let Z be its length ; a the angle which it makes with the vertical axis of the cone which it describes ; w the angular velocity ; then the centrifugal force ? u> 2 ? sin. a ; and as this is the force which keeps the pendulum away from the vertical, it must balance the force which draws it to the vertical, which is g tan. a : and therefore / 2 ? the angular velocity, or the angle de- v/ i cos. 6 scribed in a second of time ; and the time of complete revolution through the angle 360 or 2w is^?2ir^/L2L ; that is to say, the time of revolution of a pendulum of any given length is less than the time of a double oscillation of the same pendulum, in the proportion of the cosine of the angle which it makes with the axis of revolution to unity.

A rotary pendulum is kept in motion by the train of the clock ending in a horizontal wheel with a vertical axis, from which pro jects an arm pressing against a spike at the bottom of the pendu lum ; and it has this disadvantage that any inequality in the force of the train, arising from variations of friction or any other cause, is immediately transmitted to the pendulum ; whereas it will be seen that in several kinds of escapements which can be applied to a vibrating pendulum, the variations of force can be rendered nearly or quiteinsensible. And it is a mistake to imagine that there is any self-correcting power in a conical pendulum analogous to that of the governor of a steam-engine ; for that apparatus, though it is a couple of conical pendulums, has also a communication by a system of levers with the valve which supplies the steam. _ The governor apparatus has itself been applied to telescope-driving clocks, with a lever ending in a spring which acts by friction on some revolving plate in the clock, increasing the friction, and so diminishing the force as the balls of the governor fly out farther under any increase in the force . And with the addition of some connection with the hand of the observer, by which the action can be farther moderated, the motion can be made sufficiently uniform for that purpose.

Various other contrivances have been invented for producing a continuous clock-motion. The great equatorial telescope at Green wich is kept in motion by a kind of water clock called in books on hydrostatics Barker s Mill, in which two horizontal pipes branching out from a vertical tubular axis have each a hole near their ends on opposite sides, from which water flows, being poured constantly into the tubular axis, which revolves on a pivot, resistance of the air to the water issuing from the holes drives the mill round, and there are means of regulating it. Another plan is to connect a clock train having a vibrating pendulum with another clock havin" a conical pendulum by one of the lower wheels in the train, with a spring connection ; the telescope is driven by the revolving clock train, and the other pendulum keeps it sufficiently in order, though allowing it to expatiate enough for each beat ot the pendulum The more complicated plan of Wagner of I ans described in Sir E. Beckett s Rudimentary Treatise on Clocks and JFatches and Bdls does not appear to have ever come i and therefore it is now omitted.

Pendulum Suspension.

The suspension of the pendulum on what are called like those of a scale-beam, has often been advocated. But it may do well enough for short experiments, in which th iiii.iv in me LUIIV nuivii lituTieH uiu pciKimuiii as snown in rig. z a little farther on ; and the steadiness of this cock, and its firm Gxing to a wall, are essential to the accurate performance of the clock. The thinner the spring the better ; provided, of course, it is strong enough to carry the pendulum without being bent beyond its elasticity, or bent short ; not that there is much risk of that in practice. Pendulum springs are much oftener too thick than too thin ; and it is worth notice that, independently of their greater effect on the natural time of vibration of the pendulum, thick and narrow springs are more liable to break than thin nnd broad ones of the same strength. It is of great importance that the spring should be of uniform thickness throughout its breadth ; and the bottom of the chops which carry it should be exactly horizontal ; otherwise the pendulum will swing with a twist, as they may he often seen to do in ill-made clocks. If the bottom of the chops is left sharp, where they clip the spring, it is very likely to break there ; and therefore the sharp edges should be taken off.

The bob of the pendulum used to be generally made in the shape of a lens, with a view to its passing through the air with the least resistance. But after the importance of making the bob heavy was discovered, it became almost necessary to adopt a form of more solid content in proportion to its surface. A sphere has beOn occa sionally used, but it is not a good shape, because a slight error in the place of the hole for the rod may make a serious difference in the amount of weight on each side, and give the pendulum a ten dency to twist in motion. The mercurial jar pendulum suggested the cylindrical form, which is now generally adopted for astronomical clocks, and in the best turret clocks, with a round top to prevent any bits of mortar or dirt falling and resting upon it, which would alter the time ; it also looks better than a flat-topped cylinder. There is no rule to be given for the weight of pendulums. It will be shown hereafter that, whatever escapement may be used, the errors due to any variation of force are expressed in fractions which inva riably have the weight and the length of the pendulum in the denominator, though some kind of escapements require a heavy pendulum to correct their errors much less than others. And as a heavy pendulum requires very little more force to keep it in motion than a light one, being less affected by the resistance of the air, we may almost say that the heavier and longer a pendulum can be made the better ; at any rate, the only limit is one of convenience ; for instance, it would obviously be inconvenient to put a large pen dulum of 100 lb weight in the case of an astronomical or common house clock. It may perhaps be laid down as a rule, that no astronomical clock or regulator (as they are also called) will go as well as is now expected of such clocks with a pendulum of less than 28 lb weight, and no turret clock with less than 1 cwt. Long pendulums are generally made with heavier bobs than short ones ; and such a clock as that of the Houses of Par liament, with a two-seconds pendulum of 6 cwt., ought to go 44 times as well as a small turret clock with a one-second pendulum of 60 lb. Pendulums longer than 14 feet (2 seconds) are incon venient, liable to be disturbed by wind, and expensive to compen sate, and they are now quite disused, and most or all of the old ones removed, with their clocks, for better ones.

Pendulum Regulation.

The regulation of pendulums, or their exact adjustment to the proper length, is primarily effected by a nut on the end of the rod by which the bob can be screwed up or down. In the best clocks the rim of this nut is divided, with an index over it ; so the exact quantity of rise or fall, or the exact acceleration or retardation, may be known, the amount due to one turn ot tlic nut being previously ascertained. By the calculation used below for compensation of pendulums, it may be seen that if the J gtfl of the pendulum rod is I, and the breadth of one thread of the screw is called dl, then one turn of the nut will alte rate of the clock by 43200 y seconds a day ; which would be iust 80 seconds, if the pendulum rod is 45 inches long and the screw has 32 threads in the inch. To accelerate the clock the nut has always to be turned to the right, as it is called, and t But in astronomical and in large turret clocks, it i to avoid stopping, or in any way disturbing the pendulum ; and f the finer adjustments other methods of regu ation are adopted The best is that of fixing a collar, as shown in fig 2, capable o having very small weights laid upon it, half-way down th dulunf, this being the place where the addition of any smal 1 eig ht produces the greatest effect, and where, it may be added aiij moving of that weight up or down on the rod produces

effect If M is the weight of the pendulum and I its length (down to the centre of oscillation), and m a small weight added at the distance d below the centre of suspension or above the c.o. (since they are reciprocal), I the time of vibration, and - dt the acceleration due to adding m; then

-dt m_ id d*. ~T~ ~ 2M V " I 1 )

from which it is evident that if d? i, then - d T the daily acceleratioij:? 1080 m; or if m is the 10800th of the weight of M the pendulum it will accelerate the clock a second a day, or 10 grains will do that on a pendulum of 15 Ib. weight (7000 gr. being? 1 Ib.), or an ounce on a pendulum of 6 cwt. In like manner if d? - from either top or bottom, m must?, - to accelerate 3 7200 the clock a second a day. The higher up the collar is the less risk there is of disturbing the pendulum in putting on or taking oft the regulating weights. The weights should be made in a series, and marked 4, 1, 2, according to the number of seconds a day by which they will accelerate; and the pendulum adjusted at first to lose a little, perhaps a second a day, when there are no weights on the collar, so that it may always have some weight on, which can be diminished or increased from time to time with certainty, as the rate may vary.

Compensation of Pendulums.

Soon after pendulums began to be generally used in clocks, it was discovered that they contained within themselves a source of error independent of the action of the clock upon them, and that they lost time in the hot weather and gained in cold, in consequence of all the substances of which they could be made expanding as the temperature increases. If I is the length of a pendulum, and dl the small increase of it from increased heat, t time of the pendulum I, and t + d that of the pendulum l + dl; then't + dt VI dl + 2 J since ( ) may be neglected as very small; or dt?! and the daily loss of the clock will be 43200^ seconds The following is a table of the values of ^ for 1000 Fahr. of heat in different sub stances, and also the weight of a cubic inch of each:

ft White deal ..................................... 0024 036 Flint glass ........................................... 0048 116 Steel rod ......................................... 0064 28 Iron rod ............................................. 007 26 Brass ............................................... 010 30 Lead ................................................ -016 41 Zinc ............................................ -017 25 Mercury (iu bulk, not in length) ............. 100 49

Thus a common pendulum with an iron wire rod would lose 43200 x -00007? 3 seconds a day for 10 of heat; and if adjusted for the winter temperature it would lose about a minute a week in summer, unless something in the clock happened to produce a counteracting effect, as we shall see may be the case when we come to escapements. We want therefore some contrivance which will always keep that point of the pendulum on which, its time depends, viz., the centre of oscillation,, at the same distance from the point of suspension. A vast number of such contrivances have been made, but there are only three which can be said to be at all in common use; and the old gridiron pendulum, made of 9 alter nate bars of brass and steel is not one of them, having been super seded by one of zinc and iron, exactly on the same principle, but requiring much fewer bars on account of the greater expansion of zinc than brass. The centre of oscillation so nearly coincides in most clock pendulums with the centre of the bob that we may prac tically say that the object of compensation is to keep the bob always at the same height. For this purpose we must hang the bob from the top of a column of some rnetal which has so much more expan sion than the rod that its expansion upwards will neutralize that of the rod, and of the wires or tube by which the bob is hung, down wards. The complete calculation, taking into account the weight of all the rods and tubes is too long and complicated to be worth going through, especially as it must always be finally adjusted by trial either of that very pendulum or of one exactly similar. For prac tical purposes it is found sufficient to treat the expansion of zinc as being "016 to steel "0064, instead of "017 as it is really; and for large pendulums with very heavy tubes even the 016 is a little too much. Moreover the c.o. is higher above the e.g. of the bob in such large pendulums than in small ones with light rods and tubes.

But neglecting these minutiae for the first approximation, and supposing the bob either to be of iron, in which case it may be con sidered fixed anywhere to the iron tube which hangs from the top of the zinc tube, or a lead bob attached at its own centre, which obviates the slowness of the transmission of a change of temperature through it, the following calculation will hold. Letr be the length of thesteel rod and spring, z that of the zinc tube, b half the height of the bob; the length of the iron tube down the centre of the bob is % - b. If the iron tube is of steel for simplicity of calculation, we must evidently have -064(r + z-i)? I6z: z - g(r-J). It is practically found that for a seconds pendulum with a lead cylindrical bob 9 in. x 3 hung by its middle r has to be about 44 inches, and 2 nearly 27. At any rate it is safest to make it 27 at first, especially if the second tube is iron, which expands a little more than steel; and the tube can be shortened after trial but not lengthened. The rod of the standard sidereal pendulum at Green wich (down to the bottom of the bob, which is such as has been described and weighs 26 ft), is 43? and z is 26 inches, the descending wires being steel. A solar time pendulum is about % inch longer, as stated above. If the bob were fixed at its bottom to the steel tube the zinc would have to be 4 88 longer. Fig. 2 is a section of the great West minster pendulum. The iron rod which runs from top to bottom, ends in a screw, with a nut N, for adjusting the length of the pendulum after it was made by calculation as near the right length as possible. On this nut rests a collar M, which can slide up the rod a little, but is prevented from turning by a pin through the rod. On a groove or annular channel in the top of this collar stands a zinc tube 10 feet 6 inches long, and nearly half an inch thick, made of three tubes all drawn together, so as to become like one (for it should be observed that cast zinc cannot be depended on; it must be drawn). On the top of this tube or hollow column fits another collar with an annulai groove much like the bottom one M. The object of these grooves is to keep the unc column in its place, not touching the rod within it, as contact might produce friction, which would interfere with their relative motion under expansion and con traction. Round the collar C is screwed a large iron tube, also not touching the zinc, and ita lower end fits loosely on the collar M; and round its outside it has another collar D of its own fixed to it, on which the bob rests. The iron tube has a number of large holes in it down each side, to let the air get to the zinc tube; before that was done, it was found that the compensation lagged a day or two behind the changes of temperature, in consequence of the iron rod and tube being exposed, while the zinc tube was enclosed without touching the iron. The bottom of the bob is 14 feet 11 inches from the top of the spring A, and the bob itself is 18 inches high, with a domeshaped top, and twelve inches in diameter. As it is a 2-seconds pendulum, its centre of oscilla- _, . . tion is 13 feet from the top A, which is higher t m. t n than usual above the centre of gravity of the bob, t p i i on account of the great weight of the compensation tubes. The whole weighs very nearly 700 ft, and is probably the heaviest pendulum in the world.

Fig. 2.—Section of Great Westminster Pendulum.

The second kind of compensation pendulum in use is still more simple, but not so effective or certain in its action; and that is merely a wooden rod with a long lead bob resting on a nut at the bottom. According to the above table, it would appear that this bob ought to be 14 inches high in a 1-second pendulum; but the expansion of wood is so uncertain that this proportion is not found capable of being depended on, and a somewhat shorter bob is said to be generally more correct in point of compensation . All persons who have tried wooden pendulums severely have come to the same conclusion, that they are capricious in their action, and consequently unfit for the highest class of clocks.

The best of all the compensations was long thought to be the mercurial, which was invented by Graham, a London clockmaker, above a century ago, who also invented the well-known dead escapement for clocks, which will be hereafter explained, and the horizontal or cylinder escapement for watches. And the best form of the mercurial pendulum is that which was introduced by the late E. J. Dent, in which the mercury is enclosed in a cast iron jar or cylinder, into the top of which the steel rod is screwed, with its end plunged into the mercury itself. For by

this means the mercury, the rod, and the jar all acquire the new temperature at any change more simultaneously than when the mercury is in a glass jar hung by a stirrup (as it is called) at the bottom of the rod ; and moreover the pendulum is safe to carry about, and the jar can be made perfectly cylindrical by turning, and also air-tight, so as protect the mercury from oxidation ; and, if necessary, it can be heated in the jar so as to drive off any moisture, without the risk of breaking. The height of mercury required in a cast-iron jar, 2 inches in diameter, is about 6 8 inches; for it must be remembered, in calculating the rise of the mercury, that the jar itself expands laterally, and that expansion has to be deducted from that of the mercury in bulk.

The success of the Westminster clock pendulum, however, and of smaller zinc and steel pendulums at Greenwich and elsewhere, has established the conclusion that it is unnecessary to incur the expense of a heavy mercurial pendulum, which has become more serious from the great rise in the price of mercury and the admitted necessity for much heavier bobs than were once thought sufficient for astronomical clocks. The complete calculation for a compen sated pendulum in which the rods and tubes form any considerable proportion of the whole weight, as they must in a zinc pendulum, is too complicated to be worth undertaking generally, especially as it is always necessary to adjust them finally by trial, and for that purpose the tubes should be made at first a little longer than they ought to be by calculation, except where one is exactly copying pendulums previously tried.

Barometrical Error.

It has long been known that pendulums are affected by varia tions of density of the air as well as of temperature, though in a much less degree, in fact, so little as to be immaterial, except in the best clocks, where all the other errors are reduced to a minimum. An increase of density of the air is equivalent to a diminution of the specific gravity of the pendulum, and that is equivalent to diminution of the force of gravity while the inertia remains the same. And as the velocity of the pendulum varies directly as the force of gravity and inversely as the inertia, an increase of density must diminish the velocity or increase the time. The late Francis Baily, P. R.A.S., also found from some elaborate experiments (See Phil. Trans, of 1832) that swinging pendulums carry so much air with them as to affect their specific gravity much beyond that due to the mere difference of stationary weight, and that this also varies with their shape, a rod with a flat elliptical section dragging more air with it than a thicker round one (which is not what one would expect), though a lens-shaped bob was less affected than a spherical one of the same diameter, which of course is much heavier. The frictional effect of the air is necessarily greater with its increased density, and that diminishes the arc. In the ll.A.S. Memoirs of 1853 Mr Bloxam remarked also that the current produced in the descent of the pendulum goes along with it in ascending, and there fore does not retard the ascent as much as it did the descent, and therefore the two effects do not counteract each other as Baily assumed that they did. He also found the circular error always less than its theoretical value, and considered that this was due to the resistance of the air. The conclusions which were arrived at by several eminent clockmakers as to the effect of the pendulum spring on the circular error about 40 years ago were evidently erroneous, and the effect due to other causes.

It appears from further investigation of the subject in several papers in the R.A.S. Notices of 1872 and 1873, that the barometrical error also varies with the nature of the escapement, and (as Baily had before concluded from calculation) with the arc of the pendulum, so that it can hardly be determined for any particular clock a priori, except by inference from a similar one. The barometrical error of an ordinary astronomical clock with a dead escapement was said to be a loss of nearly a second a day for an inch rise of barometer, but with a gravity escapement and a very heavy pendulum not more than 3 second. Dr Robinson of Armagh (see R.A.S. Mem., vol. v.) suggested the addition of a pair of barometer tubes to the sides of the pendulum, with a bulb at the bottom, and such a diameter of tube as would allow a sufficient quantity of mercuiy to be transposed to the top by the expansion under heat, to balance the direct effect of the heat upon the pendulum. But it is not necessary to have two tubes. In a paper in the R.A.S. Notices of January 1873 Mr. Denison (now Sir E. Beckett) gave the calculations requisite for the barometrical compensation of pendulums of various lengths and weights, the principle of which is just the same as that above given for regulating a pendulum by adding small weights near the middle of its length. The formula is also given at p. 69 of the sixth edition of his Rudimentary Treatise on Clocks. A barometrical correction of a different kind has been applied to the standard clock at Green wich. An independent barometer is made to raise or lower a magnet so as to bring it into more or less action on the pendulum and so to accelerate or retard it. But we do not see why that should be better than the barometer tube attached to the pendulum. The necessity for this correction seems to be obviated altogether by giving the pendulum a sufficient arc of vibration. Baily calculated that if the arc (reckoned from 0) is about 2 45 the barometrical error will W self-corrected. And it is remarkable that the Westminster clock pendulum, to which that large arc was given for other reasons, appears to be free from any barometric error, after trying the results of the daily rate as automatically recorded at Greenwich for the whole of the year 1872. We shall see presently that all the escape ment errors of clocks are represented by fractions which have the square or the cube of the arc in the denominator, and therefore if the arc can be increased and kept constant without any objectionably increase of force and friction, this is an additional reason for pre ferring a large arc to a small one, though that is contrary to the usual practice in astronomical clocks.

Escapements.

The escapement is that part of the clock in which the rotary motion of the wheels is converted into the vibratory motion of the balance or pendulum, which by some contrivance or other is made to let one tooth of the quickest wheel in the train escape at each vibration; and hence that wheel is called the " scape 77heel. " Fig. 3 shows the form of the earliest clock escapement, if it is held sideways, so that the arms on which the two balls are set may vibrate on a horizontal plane. In that case the arms and weights form a balance, and the farther out the weights are set, the slower would be the vibrations. If we now turn it as it stands here, and consider the upper weight left out, it becomes the earliest form of the pendulum clock, with the crown- ivheel or vertical escapement. CA and CB are two flat pieces of steel, called pallets, projecting from the axis about at right angles to each other, one of them over the front of the wheel as it stands, and the other over the back. The tooth D is just escaping from the front pallet CA, and at the same time the tooth at the back of the wheel falls on the other pallet CB, a little above its edge. But the pendulum which is now moving to the right does not stop immediately, but swings a little further (otherwise the least failure in the force of the train would stop the clock, as the escape would not take place), and in so doing it is evident that the pallet B will drive the wheel back a little, and produce what is called the recoil; which is visible enough in any common clock with a seconds-hand, either with this escapement or the one which will be- next described.

Fig. 3.—Recoil Escapement.

Fig. 4.—Anchor Escapement.

It will be seen, on looking at figure 3, that the pallet B must turn through a considerable angle before the tooth can escape; in other words, the crown-wheel escapement requires a long vibration of the pendulum. This is objectionable on several accounts, first, because it requires a great force in the clock train, and a great pressure, and therefore friction, on the pallets ; and besides that, any variation in a large arc, as was explained be fore, produces a much greater variation of time due to the circular error than an equal variation of a small arc. The crown wheel escapement may in deed be made so as to allow a more moderate arc of the pendulum, though not so small as the 2 usually adopted in the best clocks, by putting the pallet arbor a good deal higher above the scape-wheel, and giving a small number of teeth to the wheel; and that also diminishes the length of the run of the teeth, and consequently the friction, on the pallets, though it makes the recoil very great and sudden; but, oddly enough, it never appears to have been resorted to until long after the escapement had be come superseded by the "anchor" escapement, which we shall now

describe, and which appears to have been invented by the celebrated Dr Hooke as early as the year 1656, very soon after the invention of pendulums.

In fig. 4 a tooth of the scape-wheel is just escaping from the left pallet, arid another tooth at the same time falls upon the right hand pallet at some distance from its point. As the pendulum moves on in the same direction, the tooth slides farther up the pallet, thus pro ducing a recoil, as in the crown-wheel escapement. The acting faces of the pallets should be convex, and not Hat, as they are generally made, much less concave, as they have sometimes been made, with a view of checking the motion, of the pendulum, which is more likely to injure the rate of the clock than to improve it. But when they are flat, and of course still more when they are concave, the points of the teeth always wear a hole in the pallets at the extremity of their usual swing, and the motion is obviously easier and therefore better when the pallets are made convex ; in fact they then approach more nearly to the "dead" escapement, which will be described presently. We have already alluded to the effect of some escapements in not only counteracting the circular error, or the natural increase of the time of a pendulum as the arc increases, but overbalancing it by an error of the contrary kind. The recoil escapement does so ; for it is almost invariably found that whatever may be the shape of these pallets, the clock loses as the arc of the pendulum falls off, and vice versa. It is unfortunately impossible so to arrange the pallets that the circular error may be thus exactly neutralized, because the escapement error depends, in a manner reducible to no law, upon variations in friction of the pallets themselves and of the clock train, which produce different effects ; and the result is that it is impossible to obtain very accurate time keeping from any clock of this construction.

But before we pass on to the dead escapement, it may be proper to notice an escapement of the recoiling class, which was invented for the purpose of doing without oil, by the famous Harrison, who was at first a carpenter in Lincolnshire, but afterwards obtained the first Government reward for the improvement of chronometers. We shall not however stop to describe it, since it never came into general use, and it is said that nobody but Harrison himself could make it go at all. It was also objectionable on account of its being directly affected by all variations in the force of the clock. It had the peculiarity of being very nearly silent, though the recoil was very great. Those who are curious about such things will find it described in the seventh edition of this Encyclopaedia. The recorded performance of one of these clocks, which is given in some accounts of it, is evidently fabulous.

Dead Escapements.

The escapement which has now for a century and a half been con sidered the best practical clock escapement (though there have been constant attempts to invent one free from the defects which it must be admitted to pos sess) is the dead escapement, or, as the French call it with equal expressiveness, I echappement d repos, bu- cause instead of the recoil of the tooth upon the pallet, which took place in the pre vious escapements, it falls dead upon the pallet, and reposes there until the pen dulum returns and lets it off again. It is represented in fig. 5. It will be observed that the teeth of the scape- wheel have their points set the opposite way to those of the recoil escapement in fig. 4, the wheels themselves both turning the same way ; or (as our engraver has re presented it), vice versa. The tooth B is here also represented in the act of dropping on to the right hand pallet as the tooth A scapes from the left pallet. But instead of the pallet having a con tinuous face as in the recoil escapement, it is divided iiito~two, of which BE on the right pallet, and FA on the left, are called the im pulse faces, and BD, FG, the dead faces. The dead faces are portions of circles (not necessarily of the same circle), having the axis of the pallets C for their centre; and the consequence evidently is, that as the pendulum goes on, carrying the pallet still nearer to the wheel than the position in which a tooth falls on to the corner A or B of the impulse and the dead faces, the tooth still rests on the dead faces without any recoil, until the pendulum returns and lets the tooth slide down the impulse face, giving the impulse to the pendulum as it goes.

Fig. 5.—Dead Escapement.

The great merit of this escapement is that a moderate variation in the force of the clock train produces a very slight effect in the time of the pendulum. This may be shown in a general w~ay, without resorting to mathematics, thus : Since the tooth B drops on to the corner of the pallet (or ought to do so) immediately after the tooth A has escaped, and since the impulse will begin at B when the pendulum returns to the same point at which the impulse ceased on A, it follows that the impulse received by the pendulum before and after its vertical position, is very nearly the same. low that part of the impulse which takes place before zero, or while the pendulum is descending, tends to augment the natural force of gravity on the pendulum, or to make it move faster ; but in the de scending arc the impulse on the pallets acts against the gravity of the pendulum, and prevents it from being stopped so soon ; and so the two parts of the impulse tend to neutralize each other s disturbing effects on the times of the pendulum, though they both concur in. increasing the arc, or (what is the same thing) maintaining it against the loss from friction and resistance of the air. However, on the whole, the effect of the impulse is to retard the pendulum a little, because the tooth must fall, not exactly on the corner of the pallet, but (for safety) a little above it ; and the next impulse does not bt-gin until that same corner of the pallet has come as far as the point of the tooth ; in other words, the retarding part of the impulse, or that which takes place after zero, acts rather longer than the accel erating part before zero. Again, the friction on the dead part of the pallets tends to produce the same effect on the time ; the arc of course it tends to diminish. For in the descent of the pendulum the friction acts against gravity, but in the ascent with gravity, and so shortens the time ; and there is rather less action on the dead part of the pallets in the ascent than in the descent. For these reasons the time of vibration of a pendulum driven by a dead escapement is a little greater than of the same pendulum vibrating the same arc freely ; and when you come to the next difference, the variation of time of the same pendulum with the dead escapement, under a moderate variation in the force, is very small indeed, which is not the case in the recoil escapement, for there the impulse begins at each end of the arc, and there is much more of it duiing the descent of the pendulum than during the ascent from zero to the arc at which the escape takes place and the recoil begins on the opposite tooth ; and then the recoil itself acts on the pendulum in its ascent in the same direction as gravity, and so shortens the time. And hence it is that an increase of the arc of the pendulum with a recoil escapement is always accompanied with a decrease of the time. Something more than this general reasoning is re quisite in order to compare the real value of the dead escapement with others of equal or higher pretensions, or of the several contrivances that have been suggested for remedying its defects. But we must refer to the Rudimentary Treatise on Clocks for details of the mathematical calculations by which the numerical results are obtained, and the relative value of the different kinds of escape ments determined.

It camiot be determined a priori whether cleaning and oiling a dead escapement clock will accelerate or retard it, for reasons explained in those calculations ; but it may be said conclusively that the larger the arc is for any given weight x the fall per day, the better the clock will be ; and in order to diminish the friction and the necessity for using oil as far as possible, the best clocks are made with jewels (sapphires are the best for the purpose) let into the pallets.

The pallets are generally made to embrace about one-third of the circumference of the wheel, and it is not at all desirable that they should embrace more ; for the longer they are, the longer is the run of the teeth upon them, and the greater the friction. There is a good deal of difference in the practice of clockmakcrs as to the length of the impulse, or the amount of the angle 7 + if the im pulse begins at /8 before zero and at y after zero. Sometimes you see clocks in which the seconds hand moves very slowly and rests a very short time, showing that 7 + /3 is large in proportion to 2a ; and in others the contrary. The late Mr Dent was decidedly of opinion that a short impulse was the best, probably because there is less of the force of the impulse wasted in friction then. It is not to be forgotten that the scape-wheel tooth docs not overtake the face of the pallet immediately, on account of the menu-lit of inertia of the wheel. The wheels of astronomical clocks, and indeed of all English house-clocks, are generally made too heavy, especially the scape-wheel, which, by increasing the moment of inertia, requires a larger force, and consequently has more friction. We shall see presently, from another escapement, how much of the force is really wasted in friction in the dead escapement.

But before proceeding to other escapements, it is proper to notice a very useful form of the dead escapement, which is adopted in many of the best turret clocks, called the pin-wheel escapement. Fig. 6 will sufficiently explain its action and construction. Its advantages are that it does not require so much accuracy as the other; if a pin gets broken it is easily replaced, whereas in the oth^r the wheel is ruined if the point of a tooth is injured ; a wheel of given size will work with more pins than teeth, and therefore a

train of less velocity will do, and that sometimes amounts to a savin<? of one wheel in the train, and a good deal of friction; and the blow on both pallets being downwards, instead of one up and the other down, the action is more steady; all which things are of more consequence in the heavy and rough work of a turret clock than in an astronomical one. The details of the construction are given in the Rudimentary Treatise. It has been found expedient to make the dead faces not quite dead, but with a very slight recoil, which rather tends to check the variations of arc, and also the general disposition to lose time if the arc is increased; when so made the escapement is generally called "half-dead."

Fig. 6.—Pin-Wheel Escapement.

Passing by the various other modifications of the dead escapement which have been suggested and tried with little or no success, we proceed to describe one of an entirely different form, which was patented in 1851 by Mr C. Macdowall, though it appeared afterwards that one very similar had been tried before, but failed from the proportions being badly arranged. It is represented in fig. 7. The scape-wheel is only a small disc with a single pin in it, made of ruby, parallel and very near to the arbor. The disc turns half round at every beat of the pendulum, and the pin gives the impulse on the vertical faces of the pallets, and the dead friction takes place on the horizontal faces. Its advantages are that the greatest part of the impulse is given directly across the line of centres, and consequently with very little friction; and therefore also, the friction on the dead faces is less than usual, and scarcely any oil is required; moreover, it is very easy to make. But there must be two more wheels in the train, consuming a good deal of the force of the clock-weight by their friction, which rather more than makes up for the friction saved in the escapement. It was applied successfully to watches, but the expense of the additional wheels prevented their adoption. In order to make the angle of escape not more than 1º, the distance of the pin from the centre of the disc must not be more than 1/60th of the distance of centres of the disc and pallets.

With the view of getting rid of one of these extra wheels in the train, and that part of the impulse which is least effective and most oblique, Mr Denison shortly afterwards invented the three-legged dead escapement; which, though afterwards superseded by his three-legged gravity escapement, is still worth notice on account of the exceedingly small force which it requires, thereby giving a practical proof of the large proportion of the force which is wasted in friction in all the other impulse escapements.

Fig. 7. Macdowall's Escapement. }}

In fig. 8, the three long teeth of the scape-wheel are only used for locking on the dead pallets D and E, which are set on the front of the pallet plate; A and B are impulse pallets, being hard bits of steel or jewels set in the pallet plate, and they are acted upon by the three sharp-edged pins which are set in the scape-wheel and point backwards. As soon as the pendulum moves a little further to the left than is here shown, the long tooth will slip past the dead pallet or stop D, and the pin at B will run after and catch the corner of that impulse pallet and drive it until the wheel has turned through 60º, and then it will escape; and by that time the uppermost tooth will arrive at the stop E, and will slide along it as in the common dead escapement, but with a pressure as much less than that which gives the impulse as the points of the teeth are farther from the centre of the wheel than the impulse pins are. But the impulse is here given with so little friction, that even where the points of the teeth were made identical with the pins, the clock-weight required to keep the same pendulum with the same train (a common turret-clock movement), swinging to 2º, was only one-fifth of what had been required with the pin-wheel escapement; and the scape- wheel which kept the 6 cwt. pendulum of the Westminster clock going for half-a-year, until superseded by the gravity escapement, weighed only a sixth of an ounce. It appears also that it would be possible so to adjust the recoil of the half-dead pallets that the time would not be affected by any small variation of the force and the arc; since it was found that, when a certain amount of recoil was given the clock gamed instead of losing, under an increase of arc due to an increase of clock-weight. And if the force were kept constant by a train remontoire, such as will be described hereafter, there would in fact be nothing capable of altering the arc or the time. But on account of the small depth of intersection of the circles of the pins and the pallets, on which its action depends, this escapement requires very careful adjustment of the pallets, except where they are on a large scale; and considering the superior qualities of the corresponding gravity escapement, it is not likely to be used, except perhaps in clocks required to go a long time, in which economy of force is a matter of consequence. The pallets should be connected with the pendulum by a spring fork (which indeed is advisable in the common dead escapement with a heavy pendulum, especially the pin-wheel escapement), to prevent the risk of their driving backwards against the scape-wheel when it is not in motion, as it will not clear itself. The distance of the centres should be not less than 25 times the radius of the circle of the edges of the impulse pins.

Fig. 8.—Denison's Three-Legged Escapement.

Detached Escapements.

In all the escapements hitherto described the pallets are never out of moving contact with the scape-wheel, and there have been several contrivances for keeping them detached except during the impulse and at the moment of passing a click which is to release the wheel to give the impulse. This is an imitation of the chronometer escapement in watches which is sometimes called the "detached." There are only two of such contrivances which appear worth special notice. One was proposed by Sir G. Airy in vol. ii. of the Cambridge Transactions, but not executed (so far as we know) till a few years ago in the standard sidereal clock at Greenwich, which is reported to go extremely well. Suppose a dead escapement consisting of a single pallet only, say the right hand one of the pin-wheel escapement (fig. 6), for the Greenwich clock has a pin escapement, and that the wheel is locked generally by a spring detent hooking into any one of its teeth, and capable of being lifted or pushed aside by the pendulum, i.e., by a pin somewhere on the single pallet as it passes to the right, but also capable of being passed without being lifted as the pendulum goes to the left. We shall see afterwards how this is done, in the article Watches. Then as the pendulum goes .to the right, it first lifts the detent at about 1º before zero, and then a tooth or a pin drops on to the pallet and gives the impulse, exactly as in the dead pin-wheel escapement, and with exactly the same amount of friction, substituting only for the dead friction the resistance and friction of passing the detent one way and lifting it the other.

Fig. 9.—

A different escapement on the same principle but involving less friction was adopted by Sir E. Beckett in a clock described in the later editions of his book as having gone for above ten years very satisfactorily, except that, like all direct impulse escapements, including Sir G. Airy's, it must vary with the force of the clock train, due to different states of the oil. The scape-wheel (fig. 9) is five-legged, and has five sharp-edged pins which give the impulse to the hard steel pallet P whenever it passes to the right, provided the wheel is then free to move. It is stopped by the detent DEF, which turns on a pivot F, not in the pendulum crutch, as it looks in the drawing, but on the clock-frame. When the pendulum going to the right arrives at the position here drawn, the click CE on the crutch pushes the detent aside and so unlocks the wheel, which then gives the impulse, moving through 72º until another tooth arrives at the detent and is stopped, the click having then got far beyond it. When the pendulum returns the click lightly trips over the top of the detent. Here there is practically no friction in giving the impulse, as it is directly across the line of centres, as in the three-legged dead escapement, and the friction of passing

and unlocking is as little as possible, for the pressure on the locking teeth is less than half of that of the impulse pins.

In practice the pallet P is a separate bit of steel, screwed on, and therefore adjustable. The locking teeth are about 6 inches long from the centre, and the impulse pin-edges ¼ in. from the centre, which is 7 in. below the top of the pendulum and crutch, so that the impulse begins 1 before zero and ends 1 after, corresponding each to 36 turn of the scape-wheel. If r is the distance of the pins from the centre and p the length of the crutch down to the centre, rsin. 36must= p sin. 1, if you want an impulse of 1 on each side of; which makes p = 33 7r. BB are eccentric beat pins for adjusting the beat to whatever 1 position of the pendulum you please, i.e., you can make it less than 1 before or after zero as you please. In some respects it would be better to have no crutch, but it would be very difficult to make the adjustments. This escapement should evidently be at the bottom of the clock-frame instead of the top, as in the gravity escapements which will be described presently. The back part of the scapewheel is carried by a long cock or bridge within which the crutch also moves.

Remontoire or Gravity Escapements.

A remontoire escapement is one in which the pendulum does not receive its impulse from the scape-wheel, but from some small weight or spring which is lifted or wound up by the scape-wheel at every beat, and the pendulum has nothing to do with the scapewheel except unlocking it. When this impulse is received from a weight the escapement is also called a gravity escapement; and in asmuch as all the remontoire clock escapements that are worth notice have been gravity escapements, we may use that term for them at once. The importance of getting the impulse given to the pendulum in this way was recognized long before all the properties of the dead escapement, as above investigated, were known. For it was soon discovered that, however superior to the old recoil escapement, it was far from perfect, and that its success depended on reducing the friction of the train and the pallets as far as possible, which involves the necessity of high-numbered pinions and wheels, small pivots, jewelled pallets, and a generally expensive style of workmanship. Accordingly the invention of an escapement which will give a constant impulse to the pendulum, and be nearly free from friction, has been for a century the great problem of clockmaking. We can do no more than shortly notice a very few of the attempts which have been made to solve it. The most simple form of gravity escapement, and the one which will serve the best for investigating their mathematical properties (though it fails in some essential mechanical conditions), is that invented by Mudge. The tooth A of the scape-wheel in fig. 10 is resting against the stop or detant a at the end of the pallet OA, from the axis or arbor of which descends the half fork CP to touch the pendulum. From the other pallet CB descends the other half fork CO. The two arbors are set as near the point of suspension, or top of the pendulum spring, as possible. The pendulum,,,, A as here represented, must be moving to the right, and just leaving contact with the left pallet in. going to take up the right one; as soon as it has raised that 3t a little it will evidently unlock the wheel and let it turn, and then the tooth B will raise the left pallet until it is caught by the .top b on that pallet and then it will stay until the pendulum reurns and releases it by raising that pallet still higher! Each pallet!vW? tT" J h? IT lulum to a lo Point than that where it is taken up, and the difference between them is supplied by B lifting of each pallet by the clock, which does not act on the pendulum at all; so that the pendulum is independent of all varia tions of force and friction in the train.

Fig. 10.—Mudge's Gravity Escapement.

Again referring to the Rudimentary Treatise on Clocks for the mathematical investigation of the errors of this class of escapements, or to a paper by the late J. M Bloxam, in the R. A. S. M^unrs of Io3, we may say it is proved that though the time of a crravitv escapement pendulum differs from that of a free r.endulum more than from that of a dead escapement, yet the variations of that hflerence (which are the real variations of the dock) may be made much less than m any kind of dead escapement.

The difficulty which long prevented the success of gravity escapements was their liability to what is called (ripping. .Referring again to fig. 10, it will be seen at once that if the scape-wheel should happen to move too fast when it is released, the left pallet will not be raised gradually by the tooth B, but be thrown up with a jerk, perhaps so high that the tooth slips past the hook; and then not only will that tooth slip, but several more, and at last when the wheel is stopped it will be running fast, and the points of some of the teeth will probably be bent or broken by catching against the pallets. And even if the pallet is not raised high enough for the tooth to get past or completely trip, it may still be raised so high that the point of the tooth does not rest on the hook exactly where the slope of the pallet ends, but lower v and the friction between them is quite enough to keep the pallet there; and consequently the pendulum does not begin to lift it at the proper angle 7, but at some larger angle; and as the pallet always descends with the pendulum to the same point, the duration of the impulse is increased, and the pendulum made to swing farther. Sir E. Beckett called this approximate tripping, and though not so injurious to the clock as actual tripping, it is obviously fatal to its accurate performance, though it appears never to have been noticed before he pointed it out in 1851. Various contrivances have been resorted to for preventing tripping. But on account of the delicacy required in all of them, and other objections, none of them ever came into use until the invention of the three-legged and four-legged escapements to be mentioned presently. The only one which approached near enough to satisfying all the requisite conditions to be worth description is Mr Bloxam's, and we accordingly give a sketch of it in fig. 11, which is copied (with a little alteration for distinctness) from his own description of it, communicated in 1853 to the Astronomical. Society, some years after he had had it in action in a clock of his own. This drawing will enable any one conversant with these matters to understand its action. He made the pallet arbors cranked, to embrace the pendulum-spring, so that thencentres of motion might coincide with that of the pendulum as nearly as possible, perhaps an unnecessary refinement; at least the three-legged and four-legged gravity escapements answer very well with the pallet arbors set A on each side of the top of the spring. The size of the wheel determines the length of the pallets, as they must be at such an angle to each other that the radii of the wheel when in contact with each stop may be at right angles to the pallet arm; and therefore, for a wheel of this size, the depth of locking can only be very small. The pinion in Mr Bloxam's clock only raises the pallet through 40 at each beat; i.e., the angle which we called 7 is only 20; and probably, if it were increased to anything like -r-, the escapement would trip immediately. The two broad pins marked E, F. are the fork-pins. The clock which Mr Bloxam had went very well; but it had an extremely fine train, with pinions of 18; and nobody else appears to have been able to make one to answer. In short Bloxam's was not a practical solution of the gravity escapement problem, any more than those of Captain Kater, or Hardy, or various other inventors. A few clocks of Hardy's alone still exist.

Fig. 11.—Bloxam's Gravity Escapement.

The only gravity escapement or escapements that really have come into common use are the "four-legged" and the "double threelegged" escapements of Sir E. Beckett. They passed through various phases before settling into the present form, ot which it is unnecessary to say more now than that the first was the single three-legs described in the last edition of this Encyclopaedia, which was suggested by his three-legged dead escapement. A five-legged one was also tried; but though it had some slight advantages they are quite overbalanced by disadvantages, and it requires much more delicacy of construction than either the double three-legs or the four-legs which we shall now describe, remarking that the latter is the best for "regulators," and the formei in large clocks. Fig. 12 is a back view of the escapement part of an astronomical clock with the four-legged wheel; seen from the front the wheel would turn the other way. The long locking teeth are made about 2 inches loi.g from the centre, and the lifting pins, of which there are four pointing forwards and the other four intermediate pointing back wards, are at not more than one-30th of the distance between the

centres EC, of the wheel and pallets; or rather C is the top of the pendulum spring to which the pallets CS, CS converge, though their actual action are a little below C. It is not worth while to crank them as Mr Bloxam did, in order to make them coincide exactly with the top of the pendulum, as the friction of the beat pins on the pendulum at P is in significant, and even then would not be quite destroyed. The pallets are not in the same plane, but one is behind and the other in front of the wheel, with one stop pointing backwards and the other forwards to receive the teeth alternately, it does not matter which; in this figure the stop S is behind and the stop S forward. The pendulum is now going to the right, and just beginning to lift the right pallet and free the stop S; then the wheel will begin to turn and lift the other pallet by one of the pins which is now lowest, and which moves through 45 across the line of centres, and therefore lifts with very little friction. It goes on till the tooth now below S reaches S and is stopped there. Meanwhile the pallet CS goes on with the pendulum as far as it may go, to the end of the arc which we have through out called a, starting from 7; but it falls with the pendulum again, not only to 7 but to-7 on the other side of 0, so that the impulse is due to the weight of each pallet alternately falling through 2y; and the magnitude of the impulse also depends on the obliqueness of the pallet on the whole, i.e., on the distance of its centre of gravity from the vertical through C. The defect of the original three-legged escapement was that the pallets were too nearly vertical.

Fig. 12. Four-Legged Gravity Escapement.

Another most material element of these escapements with very few teeth is that they admit of a fly KK on the scape- wheel arbor to moderate its velocity, which both obviates all risk of tripping, wholly or partially, and also prevents the bang which goes all through the clock where there is no ny. The fly is set on with a friction spring like the common striking-part fly, and should be as long as there is room for, length being much more effective than width. For this purpose the second wheel arbor is shortened and set in a cock fixed on the front plate of the clock, which leaves room for a fly with vanes 2 inches long. The back pivot of the scape-wheel is carried by a long cock behind the back plate, so that the escapement is entirely behind it, close to the pendulum. The pallet arbors are short, as they come just behind the centre wheel, which is here also necessarily above the escapement, and the great wheel arbor on a level with it, and at the left hand (from the front) or the string would be in the way of the fly. No beat screws are required, as the pallets end in mere wires which are easily bent. It is found better to make the tails of the pallets long, rather than short as Mr Bloxam did. It is essential, too, that the angle CSE formed by the tooth and the pallet which is struck upwards should not the least fall short of a right angle, nor the other angle CS E be the least obtuse, or the escapement may very likely trip. Practically, therefore, it is safer to let CSE be just greater than 90 and CS E a little less, so that there may not be the least tendency in the blow on the stops to drive the pallets outwards. For the purpose of calculation, however, we must make them both 90 and then it follows that, calling the length of the teeth r, and the distance of centres d, and the length of the pallets from C down to the stops p, r must d sin. 22^ J and _p - d cos. 22 J D . Therefore if r is made 2 inches CE or d will bo 5 22, say 5j inches, and p ? 4 "82. The distance of the lifting pins from the centre will be

Gravity escapements require more weight than a direct impulse escapement with an equally fine train; and they try the accuracy of the wheelcutting more severely. If there is a weak place in the train of a common clock the scape-wheel only follows the pendulum more weakly; but in a gravity escapement it always has to raise the pallets, and ought to raise them quickly, and especially in clocks for astronomical purposes where you take its exact time from the sound of the beats, and so the lifting must not lag and sound uneven. Therefore although a fine train of high numbers is not requisite it must be perfectly well cut. And as the force of the weight does not reach the pendulum its increase is of no consequence, within reasonable limits. It is worth while to put large friction wheels under the arbor of the great wheel in all astronomical clocks, and it makes a material difference in the friction on account of the necessary thickness of the winding arbor. A variation of arc in dead escapement clocks is sometimes visible between the beginning and the end of the week according as the string is nearest to the thick or the thin end of the great arbor, when there are no friction wheels.

Fig. 13.—Double Three-legged Escapement.

The other form of the gravity escapement, which is now adopted for large clocks by all the best makers, having been first used in the great Westminster clock, is the double three-legged which is shown in fig. 13. The principle of it is the same as of the four-legs; but instead of the pallets being one behind and the other in front of the wheel, with two sets of lifting pins, there are two wheels ABC, abc, with the three lifting pins and the two pallets between them like a lantern pinion. One stop B points forward and the other A backward. The two wheels have their teeth set inter mediately or 60 apart, though that is not essential, and the angle of 120 3 may be divided between them in any other proportions, as 70 and 50, and in that way the pallets may be still more oblique than 30 from the vertical, which however is found enough to prevent tripping even if the fly gets loose, which is more likely to happen from carelessness in large clocks than in astronomical ones. The Westminster one was once found to have been left with the spring loose for several days, and it had not gained a second, and therefore had never tripped. The two wheels legged must be both squared on the arbor, or on a collar common to them both, and must not depend upon the three pins or they will shake loose. If the wheels are set with the teeth equidistant, their centre is evidently twice the length of the teeth below C, the theoretical centre of the pallets. The pins should not be farther from the centre than one-24th of the radius of the wheel; and they should be so placed that the one which is going to lift next may be vertically over the one which has just lifted, and is then holding up the other pallet. The third will then be level with the centre; i.e., they will stand on the radii which form the acting faces of the teeth of one of the wheels, and half way between those of the other. Of course the fly for those escapements in large clocks, with weights heavy enough to drive the hands in all weather, must be much larger than in small ones. For average church clocks with 1 sec. pendulum the legs of the scape-wheels are generally made 4 inches long and the fly from 6 to 7 inches long in each vane by lj orl^ wide. For 1^ sec. pendulums the scape-wheels are generally made 4^ radius. At Westminster they are 6 inches.

Sir E. Beckett has come to the conclusion that these escapements act better, especially in regulators, if the pallets do not fall quite on the lifting pins, but on a banking, or stops at any convenient place, so as to leave the wheel free at the moment of starting; just as the striking of a common house clock will sometimes fail to start unless the wheel with the pins has a little run before a pin begins to lift the hammer. The best way to manage the banking is to make the beat-pins long enough to reach a little way behind the pendulum, and let the banking be a thin plate of any metal screwed adjustably to the back of the case. This plate cannot well be shown in the drawings together with the pendulum, which, it may be added, should take up one pallet just when it leaves the other. It is no longer doubtful that these two escapements are far the best of all for large clocks, the three-legs for very large ones, while the four-legs does very well for smaller turret clocks. And they cost no more to make, though rather more is charged for them by some makers under the pretence that they do. It is absolutely impossible for any large clock exposed to the variations of weather and dust to keep as good time as an ordinary good house clock unless it has either a gravity escapement, or a train remontoire, which last is much more expensive, to intercept the variations of force before they reach the pendulum. And though a detached escapement clock while kept clean and the oil in good condition is as good as a gravity one and perhaps better, the gravity one is less affected by variations of the oil, and its rate is altogether more constant. They seem also to have a smaller barometric error.

Going Barrels.

A clock which is capable of going accurately must have some contrivance to keep it going while you are winding it up. In the old-fashioned house clocks, which were wound up by merely pulling one of the strings, and in which one such winding served for both the going and striking parts, this was done by what is called the endless chain of Huyghens, which consists of a string or chain with the ends joined together, and passing over two pulleys on the arbors of the great wheels, with deep grooves and spikes in them, to prevent the chain from slipping. In one of the two loops or festoons which hang from the upper pulleys is a loose pulley without spikes,

carrving the clock-weight, and in the other a small weight only heavy enough to keep the chain close to the upper pulleys. Now, suppose one of those pulleys to be on the arbor of the great wheel of the striking part, with a ratchet and click, and the other pulley fixed to the arbor of the great wheel of the going part; then (when ever the clock is not striking) you may pull up the weight by pulling down that part of the string which hangs from the other side of the striking part; and yet the weight will be acting on the going part all the time. And it would be just the same if you wound up the striking part and its pulley with a key, instead of pulling the string, and also the same, if there were no striking part at all, but the second pulley were put on a blank arbor, except that in that case, the weight would take twice as long to run down, supposing that the striking part generally requires the same weight x full as the going part.

This kind of going barrel, however, is evidently not suited to the delicacy of an astronomical clock; and Harrison's going ratchet is now universally adopted in such clocks, and also in chronometers and watches for keeping the action of the train on the escapement during the winding. Fig. 14 (in which the same letters are used as in the corresponding parts of fig. 1) shows its construction. The click of the barrel-ratchet R is set upon another larger ratchet-wheel, with its teeth pointing the opposite way, and its click rT is set in the clock-frame. That ratchet is connected with the great wheel by a spring ss pressing against the two pins s in the ratchet and s in the wheel. When you wind up the weight (which is equivalent to taking it off), the click IV prevents that ratchet from turning back or to the right; and as the spring ss is kept by the weight in a state of tension equivalent to the weight itself it will drive the wheel to the left for a short distance, when its end s is held fast, with the same force as if that end was pulled forward by the weight ; and as the great wheel has to move very little during the short time the clock is winding, the spring will keep the clock going long enough.

Fig. 14.—Harrison's Going-Ratchet.

In the commoner kind of turret clocks a more simple apparatus is used, which goes by the name of the bolt and shutter, because it consists of a weighted lever with a broad end, which shuts up the winding-hole until you lift it, and then a spring-bolt attached to the lever, or its arbor, runs into the teeth of one of the wheels, and the weight of the lever keeps the train going until the bolt has run itself out of gear. In the common construction of this apparatus there is nothing to ensure its being raised high enough to keep in gear the whole time of winding, if the man loiters over it. For this purpose Sir E. Beckett has the arbor of the bolt and shutter made to pump in and out of gear ; and, instead of the Fhutter covering the winding-hole, it ends in a circular arc advanced just far enough to prevent the key or winder from being put on, by obstructing a ring set on the end of the pipe. In order to get the winder on, you must raise the lever high enough for the arc to clear the ring. During the two or three minutes which the clock may take to wind, the arc will be descending again behind the ring, so that now you cannot get the winder off again without also pulling the maintaining power out of gear; so that even if it is constructed to keep in action ten minutes, if required, still it will never remain in action longer than the actual time of winding. The circular arc must be thick enough, or have a projecting flange added to it deep enough, to prevent the winder being put on by merely pushing back the maintaining power lever without lifting it.

In large clocks with a train remontoire, or even with a gravity escapement, it is hardly safe to use a spring going barrel, because is very likely to be exhausted too much to wind up the remon toire, or raise the gravity pallets, before the winding is finished, if t takes more than two or three minutes ; whereas, with the common escapements, the wheel has only to escape, as the pendulum will keep itself going for some time without any impulse.

Equation Clocks.

It would occupy too much space to describe the various contriv ances for making clocks show the variations of solar compared with mean time (called equation clocks), the days of the month, periods of the moon, and other phenomena. The old day of the month clocks required setting at the end of every month which has not 31 days, and have long been obsolete. Clocks are now made even to provide for leap year. But we doubt whether practically anybody ever takes his day of the month from a clock lace, especially as the figures are too small to be seen except quite near. Several persons have taken patents for methods of exhibiting the time by figures appear ing through a hole in the dial, on the principle of the "numbering machine." But they do not reflect that no such figures, on any practicable scale, are as conspicuous as a pair of hands ; and that nobody really reads the figures on a dial, but judges of the time in a moment from the position of the hands ; for which reason the minute hand should be straight and plain, while the hour hand has a "heart " near the end ; 12 large marks and 48 small ones make a more distinguishable dial than one with figures ; and the smaller the figures are the better, as they only tend to obscure the hands.

Striking Clocks.

There are two kinds of striking work used in clocks. The older of them, which is still used in most foreign clocks, and in turret clocks in England also, will not allow the striking of any hour to be either omitted or repeated, without making the next hour strike wrong; whereas, in that which is used in all English house clocks, the number of blows to be struck depends merely on the position of a wheel attached to the going part ; and therefore the strik ing of any hour may be omitted or repeated without deranging the following ones. In turret clocks there is no occasion for the repeating movement; and for the purpose of describing the other, which is called the locking-plate movement, we may as well refer to fig. 22, which is the front view of a large clock, striking both hours and quarters on this plan. In the hour part (on the left), you observe a bent lever BAH, called the " lifting-piece," of which the end H has just been left off by the snail on the hour-wheel 40 of the going part; and at the other end there are two stops on the back side of the lever, one behind, and rather below the other ; and against the upper one a pin in the end of a short lever 9 B, which is fixed to the arbor of the fly, is now resting, and thereby the train is stopped from running, and the clock from striking any more. The stops are shown on the quarter lifting-piece in the figure (27) of the Westminster clock. We omit the description of the action of the wheels, because it is evident enough. At D may be seen a piece projecting from the lever AB, and dropping into a notch in the wheel 78. That wheel is the locking-wheel or locking-plate ; and it has in reality notches such as D all round it, at distances 2, 3, up to 12, from any given point in the circumference, which may be considered as marked off into 78 spaces, that being the number of blows struck in 12 hours. These notches are shown in the locking-plate of the quarter part in fig. 22, but not in the hour part, foi want of size to show them distinctly.

When the arm AB of the lifting-piece is raised by the

snail depressing the other end H, a few minutes before the hour, the fly -pin slips past the first of the stops at B, but is stopped by the second and lower one, until the lever is dropped again exactly at the hour. Thus the pin can pass, and would go once round, allowing the train to go on a little; but before it has got once round, AB has been lifted again high enough to carry both stops out of the way of the fly-pin, by means of the cylinder with two slices taken off it, which is set on the arbor of the wheel 90, and on which, the end of the lifting-piece rests, with a small roller to diminish the friction. If the clock has only to strike one, the lifting-piece will then drop again, and the fly-pin will be caught by the first stop, having made (according to the numbers of the teeth given in fig. 22) 5 turns. But if it has to strike more, the locking- wheel comes into action. That wheel turns with the train, being either driven by pinion 20 on the arbor of the great wheel, or by a gathering pallet on the arbor of the second wheel, like G in fig. 15 ; and when once the lifting- piece is lifted out of a notch in the locking-plate, it cannot fall again until another notch has come under the bit D ;

nd as the distance of the notches is proportioned to the hours, the locking-plate thus determines the number of blows struck. It may occur to the reader, that the cylinder 10 and roller are not really wanted, and that the locking-plate would do as well without; and sometimes clocks are so made, but it is not safe, for the motion of the locking-plate is so slow, that unless everything is very carefully adjusted and no shake left, the corner of the notch may not have got fairly under the bit D before the fly has got once round, and then the lifting-piece will drop before the clock can strike at all; or it may hold on too long and strike 13, as St Paul's clock did once at midnight, when it was heard at Windsor by a sentinel.

Small French clocks, which generally have the striking part made in this way, very commonly strike the half hours also, by having a wide slit, like that for one o'clock, in the locking-plate at every hour. But such clocks are unfit for any place except a room, as they strike one three times between 12 and 2, and accordingly turret clocks, or even large house clocks, are never made so. Sir E. Beckett has lately introduced the plan of making turret clocks strike one at all the half hours except 12.V and 1

In all cases the locking-plate must be considered as divided into as many parts as the number of blows to bo struck in 12 hours, i.e., 78, 90, or 88, according as half hours are or are not struck; and it must have the same number of teeth, driven by a pinion on the striking wheel arbor of as many teeth as the striking cams, or in the same ratio.

Fig. 15 is a front view of a common English house clock with the face taken off, showing the repeating or rack striking movement. Here, as in fig. 1, M is the hourwheel, on the pipe of which the minute-hand is set, N the reversed hour- wheel, and n its pinion, driving the 12-hour wheel H, on whose socket is fixed what is called the snail Y, which belongs to the striking work exclusively. The hammer is raised by the eight pins in the rim of the second wheel in the striking train, in the manner which is obvious.

The hammer does not quite touch the bell, as it would jar in striking if it did, and prevent the full sound; and if you observe the form of the hammer-shank at the arbor where the spring S acts upon it, you will see that the spring both drives the hammer against the bell when the tail T is raised, and also checks it just before it reaches the bell, and so the blow on the bell is given by the hammer having acquired momentum enough to go a little farther than its place of rest. Sometimes two springs are used, one for impelling the hammer, and the other for checking it. A piece of vulcanized India-rubber, tied round the pillar just where the hammer-shank nearly touches it, forms as good a check spring as anything. But nothing will check the chattering of a heavy hammer, except making it lean forward so as to act, partially at least, by its weight. The pinion of the striking-wheel generally has eight leaves, the same number as the pius; and as a clock strikes 78 blows in 12 hours, the great wheel will turn in that time if ifc has 78 teeth instead of 96, which the great wheel of the going part has for a centre pinion of eight. The striking-wheel, drives the wheel above it once round for each blow, and that wheel drives a fourth (in which you observe a single pin P). six, or any other integral number of turns, for one turn of its own, and that drives a fan-fly to moderate the velocity of the train by the resistance of the air, an expedient at least as old as De Vick's clock in 1370.

Fig. 15.—Front view of Common English House Clock.

The wheel N is so adjusted that, within a few minutes of the hour, the pin in it raises the lifting-piece LONF so far that that piece lifts the click C out of the teeth of the rack BKRV, which immediately falls back (helped by a spring near the bottom) as far as its tail V can go >j reason of the snail Y, against which it falls; and it is so arranged that the number of teeth which pass the click is proportionate to the depth of the snail; and as there is one step in the snail for each hour, and it goes round with the hour-hand, the rack always drops just as many teeth as the number of the hour to be struck. This drop makes the noise of "giving warning." But the clock is not yet ready to strike till the lifting piece has fallen again; for, as soon as the rack was let off the tail of the thing called the gathering pallet G, on the prolonged arbor of the third wheel, was enabled to pass the pin K of the rack om which it was pressing before, and the striking train began to move; but before the fourth wheel had got half round, its pin P was caught by the end of the lifting-piece, which is bent back and goes through a hole in the plate, and when raised stands in the way of the pin P, so that the train cannot go on till the lifting-piece drops, which it does exactly at the hour, by the pin N then slipping past it. Then the train is free; the striking wheel begins to lift the hammer, and the gathering pallet gathers up the rack, a tooth for each blow, until it has returned to the place at which the pallet is stopped by the pin Iv coming

under it. In this figure the lifting-piece is prolonged to F, where there is a string hung to it, as this is the proper place for such a string when it is wanted for the purpose of learning the hour in the dark, and not (as it is generally put) on the click C ; for if it is put there and you hold the string a little too long, the clock will strike too many; and if the string accidentally sticks in the case, it will go on striking till it is run down; neither of which things

can happen when the string is put on the lifting-piece.

The snail is sometimes set on a separate stud with the apparatus called a star-ivheel and jumper ; but as this only increases the cost without any advantage that we can see, we omit any further reference to it. On the left side of the frame we have placed a lever x, with the letters st below it, and si above. If it is pushed up to si, the other end will come against a pin in the rack, and prevent it from falling, and will thus make the clock silent; and this is much more simple than the old-fashioned " strike and silent " apparatus, which we shall therefore not describe, especially as it is seldom used now.

If the clock is required to strike quarters, a third " part" or train of wheels is added on the right hand of the going part ; and its general construction is the same as the hour- striking part ; only there are two more bells, and two hammers so placed that one is raised a little after the other. If there are more quarter-bells than two, the hammers are generally raised by a chime-barrel, which is merely a cylinder set on the arbor of the striking- wheel (in that case generally the third in the train), with short pins stuck into it in the proper places to raise the hammers in the order required for the tune of the chimes. The quarters are usually made to let off the hour, and this con nection may be made in two ways. If the chimes are different in tune for each quarter, and not merely the same tune repeated two, three, and four times, the repetition movement must not be used for them, as it would throw the tunes into confusion, but the old locking-plate move ment, as in turret clocks ; and therefore, if we conceive the hour lifting-piece connected with the quarter locking- plate, as it is with the wheel N, iu fig. 15, it is evident that the pin will discharge the hour striking part as the fourth quarter finishes.

But where the repetition movement is required for the quarters, the matter is not quite so simple. The principle of it may shortly be described thus. The quarters them selves have a rack and snail, &c., just like the hours, ex cept that the snail is fixed on one of the hour-wheels M or N, instead of on the twelve-hour wheel, and has only four steps in it. Now suppose the quarter-rack to be so placed that when it falls for the fourth quarter (its greatest drop), it falls against the hour lifting-piece some where between and N, so as to raise it and the click C. Then the pin Q will be caught by the click Q?, and so tho lifting-piece will remain up until all the teeth of the quar ter-rack are gathered up ; and as that is done, it may be made to disengage the click Q?, and so complete the let ting off the hour striking part. This click Q? has no existence except where there are quarters.

These quarter clocks are sometimes made so as only to strike the quarters at the time when a string is pulled as by a person in bed, just like repeating watches, which are rarely made now, on account of the difficulty of keep ing in order such a complicated machine in such a small space. In this case, the act of pulling the string to make the clock strike winds up the quarter-barrel, which is that of a spring clock (not yet described), as far as it is allowed to be wound up by the position of a snail on the hour wheel against which a lever is pulled, just as the tail of the common striking-rack falls against the snail on the twelve-hour wheel; and it is easy to see that the number of blows struck by the two quarter hammers may thus be made to depend upon the extent to which the spring that drives the train is wound up; and it may even be made to indicate half-quarters ; for instance, if the snail has eight steps in it, the seventh of them may be just deep enough to let the two hammers strike three times, and the first of them once more, which would indicate 7^ minutes to the hour. It is generally so arranged that the hour is struck first, and the quarters afterwards.

Alarums.

In connection with these bedroom clocks we ought to mention alarums. Perhaps the best illustration of the mode of striking an alarum is to refer to either of the recoil escapements (figs. 3 and 4). If you suppose a short hammer instead of a long pendulum attached to the axis of the pallets, and the wheel to be driven with sufficient force, it will evidently swing the hammer rapidly back wards and forwards ; and the position and length of the hammerhead may be so adjusted as to strike a bell inside, first on one side and then on the other. Then as to the mode of letting off the alarum at the time required ; if it was always to be let off at the same time, you would only have to set a pin in the twelve-hour wheel at the proper place to raise the lifting-piece which lets oft* the alarum at that time. But as you want it to be capable of alteration, this discharging pin must beset in another wheel (without teeth), which rides with a friction-spring on the socket of tho twelve-hour wheel, with a small movable dial attached to it, having figures so arranged with reference to the pin that whatever figure is made to come to a small pointer set as a tail to the hour hand, the alarum shall be let oft at that hour. The letting off does not require the same apparatus as a common striking part, because an alarum has not to strike a definite number of blows, but to go on till it is run down ; and therefore the lifting-piece is nothing but a lever with a stop or hook upon it, which, when it is dropped, takes hold of one of the alarum wheels, and lets them go while it is raised high enough to disen gage it. You must of course not wind up an alarum till within twelve hours of the time when it is wanted to go off.

The watchman s or tell-tale clock may be seen in one of the lobbies of the House of Commons, and in prisons, and some other places where they want to make sure of a watchman being on the spot and awake all the night ; it is a clock with a set of spikes, generally 48 or 96, sticking out all round the dial, and a handle somewhere in the case, by pulling which you can press in that one of the spikes which is opposite to it, or to some lever connected with it, for a few minutes ; and it will be observed, that this wheel of spikes is carried round with the hour-hand, which in these clocks is generally a twenty-four hour one. It is evident that every spiks which is seen still sticking out in the morning indicates that at the particular time to which that spike belongs the watchman was not there to push it in or at any rate, that he did not ; and hence its name. At some other part of their circuit, the inner ends of the pins are carried over a roller or an inclined plane which pushes them out again ready for business the next night.

Spring Clocks.

Hitherto we have supposed all clocks to be kept going

by a weight. But, as is well known, many of them are driven by a spring coiled up in a barrel. In this respect

they differ nothing from watches, and therefore for consideration of the construction of parts belonging to the spring reference is made to the article Watches. It may,

however, be mentioned here that the earliest form in which a spring seems to have been used was not that of a spiral rib bon of steel rolled up, but a straight stiff spring held fast to the clock frame at one end, and a string from the other end going round the barrel, which was wound up ; but such a spring would have a very small range. Spring clocks are generally resorted to for the purpose of saving length ; for as clocks are generally made in England, it is impossible to make a weight-clock capable of going a week, without either a case nearly 4 feet high, or else the weights so heavy as to produce a great pressure and friction on the arbor of the great wheel. But this arises from nothing but the heavi ness of the wheels and the badness of the pinions used in most English clocks, as is amply proved by the fact that the American and Austrian clocks go a week with smaller weights and much less fall for them than the English ones, and the American ones with no assistance from fine work manship for the purpose of diminishing friction, as they are remarkable for their want of what is called "finish" in the machinery, on which so much time and money is wasted in English clock-work.

All the ornamental French clocks, and all the short " dials," as those clocks are called which look no larger than the dial, or very little, and many of the American clocks, are made with springs. Indeed we might omit the word "French" after "ornamental;" for the manufacture of ornamental clocks has practically ceased in England, anil we are losing more of all branches of the horological trade yearly, as w r e are unable, i.e., our workmen do not choose, to compete with the cheaper labour of the Continent, or with the much more systematic manufacture of clocks and watches by machinery in America than exists here, though labour there is much dearer. It is true that most of the American clocks are very bad, indeed no better than the old-fashioned Dutch clocks (really German) made most ingeniously of wood and wire, besides the wheels. But some better American ones are also made now, and they will no doubt improve as their machine made watches have done. Though this has been going on now for 30 years and more, no steps appear to have been taken to establish anything of the kind in this country, except that watch " movements," which means only the wheels set in the frame, are to a certain extent made by machinery in Lancashire and Coventry for the trade, who finish them in London and elsewhere. That is the real meaning of the advertisements of "machine-made watches" here.

The French clocks have also been greatly improved within the same time, and are now, at least some of them, quite different both in construction and execution from the old-fashioned French drawing-room clock which generally goes worse than the cheapest "Dutchman," and is nearly always striking wrong, because they have the locking-plate striking work, which if once let to strike wrong, either by altering the hands or letting it run down, cannot be set right again except by striking the hours all round, which few people know how to do, even if they can get their fingers in behind the clock to do it, .The Americans have a slight wire hanging down a little below the dial which you can push up and so make the clock strike. All locking- plate clocks ought to have a similar provision.

There is not much use in having clocks to go more than a little over eight days (to allow the possible forgetting of a day), as a week is the easiest period to remember. The French spring-clocks generally go a fortnight, but most people wind them up weekly. Occasionally English clocks are made to go a month by adding another wheel ; and even a year by adding two. But in the latter case it is better to have two barrels and great wheels acting on opposite sides of a very strong pinion between them, as it both reduces the strain on the teeth and the friction of the pivot of that pinion. Such clocks sometimes have a 5 feet or l sec. pendulum, as the case must be a tall one. The great thing is to make the scape-wheel light, and even then you can never get more than a small arc of vibration, which is undesirable for the reason given above, and such a long train is peculiarly sensitive to friction.

In the American clocks the pinions are all of the kind called lantern pinions, which have their leaves made only of bits of wire set round the axis in two collars ; and, oddly enough, they are the oldest form of pinion, as well as the best, acting with the least friction, and requiring the Last accuracy in the wheels, but now universally disused in all English and French house clocks. The American clocks prove that they are not too expensive to be used with advantage when properly made ; although, so long as there are no manufactories of clocks here as there are in America, it may be cheaper to make pinions in the slovenly way of cutting off all the ribs of a piece of pinion wire, so as to reduce it to a pinion a quarter of an inch wide, and an arbor 2 or 3 inches long. On the whole, the common English house clocks, so far from having improved with the general progress of machinery, are worse than they were fifty years ago, and at the same time are of such a price that they are being fast driven out of the market by the American plain clocks and by the French and German ornamental ones.

Clocks have been contrived to wind themselves up by the alternate expansion and contraction of mercury and other fluids, under variations of temperature. Wind-mill decks might be made still more easily, the wind winding up a weight occasionally. Water-clocks have also been made, not on the clepsydra principle, where the flow of the water determined the time very inaccurately ; but the water is merely the weight, flowing from a tap into a hollow hori zontal axis, and thence by branches into buckets, which empty themselves as they pass the lowest point of the circle in which they move, or flowing directly into buckets, so emptying themselves. But the slopping of the water, and the rusting of any parts made of iron, and the cost of the water itself always running, destroy all chance of such things coming into use.

Electrical Clocks.

It should be understood that under this term two, or wo may say three, very different things are comprehended. The first is a mere clock movement, i.e., the works of a clock without either weight or pendulum, which is kept going by electrical connection with some other clock of any kind (these ought to be called electrical dials, not clocks) ; the second is a clock with a weight, but with the escape ment worked by electrical connection with another clock instead of by a pendulum ; and the third alone are truly electrical clocks, the motive power being electricity instead of gravity; for although they have a pendulum, which of course swings by the action of gravity, yet the requisite impulse for maintaining its vibrations against friction and resistance of the air is supplied by a galvanic battery, instead of by the winding up of a weight.

If you take the weight off a common recoil escapement

clock, and work the pallets backward and forwards by hand, you will drive the hands round, only the wrong way ; consequently, if the escapement is reversed, and the pallets are driven by magnets alternatively made and unmade, by the well-known method of sending an electrical current through a wire coil set round a bar of soft iron, the contact being made at every beat of the pendulum of a standard clock, the clock without the weight will evidently keep exact time with the standard clock ; and the only question

is as to the best mode of making the contact, which is not so easy a matter as it appears to be, and though various plans apparently succeeded for a time, and were mechanically perfect, not one has succeeded permanently; i.e., the contact sometimes fails to produce the current of sufficient strength to lift the weight or spring on which the driving of the subordinate clock depends. It is therefore unnecessary to repeat the description of the various contrivances for this purpose by Wheatstone and others.

The first person who succeeded in making one clock regulate or govern others by electricity, Mr R. L. Jones, accordingly abandoned the idea of electrical driving of one clock by another; and instead of making the electrical connection with a standard clock (whether itself an electrical one or not) drive the others, he makes it simply let the pallets or the pendulum of the subordinate clock, driven by a weight or spring, be influenced by attraction at every beat of the standard clock; and, by way of helping it, the pallets are made what we called half-dead in describing the dead escapement, except that they have no impulse faces, but the dead faces have just so much slope that they would overcome their own friction, and escape of themselves under the pressure of the clock train, except while they are held by the magnet, which is formed at every beat of the standard clock, or at every half-minute contact, if it is intended to work the dials by half-minute jumps. This plan has been extensively used for regulating distant clocks from Greenwich Observatory.

Fig. 16.—Bain's Pendulum.

The first electrical clocks, in the proper sense of the term, were invented by Mr Bain in 1840, who availed himself of the discovery of Oersted that a coil of insulated wire in the form of a hollow cylinder is attracted in one direction or the other by a permanent magnet within the coil, not touching it, when the ends of the coil are connected with the poles of a battery; and if the connection is reversed, or the poles changed, so that the current at one time goes one way through the coil from the - or copper plate to the + or zinc plate, and at other times the other way, the direction of the attraction is reversed. Mr Bain made the bob of his pendulum of such a coil enclosed in a brass case so that it looked like a hollow brass cylinder lying horizontal and moving in the direction of its own axis, and in that axis stood the ends of two permanent magnets with the north poles pointed at each other and nearly touching, as in the right hand part of fig. 16. The pendulum pushed a small sliding bar backwards and forwards so as to reverse the current through the coil as the pendulum passed the middle of the arc, and so caused each magnet in turn to attract the bob. But this also failed practically, and especially in time-keeping, as might have been expected, from the friction and varying resistance of the bar to the motion of the pendulum, and in the attractions.

Fig. 17.—Ritchie s Pendulum.

Mr Ritchie of Edinburgh, however, has combined the principle of Bain's and Jones's clocks in a manner which is testified to be completely successful in enabling one standard clock to control and keep going any number of subordinate ones, which do not require winding up as Jones's do, but are driven entirely by their pendulums. This differs from Wheatstone's plan in this, that his subordinate clocks had no pendulum swinging naturally and only wanting its vibrations helping a little, but the pallets had to be made to vibrate solely by the electrical force. The figures are taken from Mr Ritchie's paper read before the Royal Scottish Society of Arts in 1873. The controlled pendulum P is that just now described as Bain's (seen in fig. 17 the other way, across the plane of vibration); the rod and spring are double, and the wire cd is connected with one spring and rod (say the front one) and the wire d′e with the other; so that the current has to pass down one spring and one rod and through the coil in the bob and up the other spring. The other pendulum O of the normal or standard clock is a common one. except that it touches two slight contact springs a, b alternately, and so closes the circuit on one side and leaves it broken on the other. When that pendulum touches a the B battery does nothing, and the - current from the battery A passes by a to c and d and down the d spring and rod and up through d to e and back again to + of A. But when the standard pendulum O touches b the A battery does nothing, and the current from - to + of the B battery goes the other way, through the controlled pendulum and its coil. The two fixed magnets SN, NS consequently attract the coil and bob each way alternately. And even if the current is occasionally weak, the natural swing of the pendulum will keep it going for a short time with force enough to drive its clock through a reversed escapement; and further, if that pendulum is naturally a little too fast or too slow the attraction from the standard pendulums will retard or accelerate it. In practice, however, it is found better not to make the contact by springs, which, however light, disturb the pendulum a little, but by a wheel in the train making and breaking contact at every beat; and if the clock has a gravity escapement there is no danger of this friction affecting the pendulum at all.

Fig. 18.—Ritchie's Elliptical Escapement.

In order to get the machinery into a smaller compass than a 39 inches pendulum requires, Mr Ritchie uses a short and slow pendulum with two bobs, one above and the other below the suspension, as shown in fig. 17. Such a pendulum, like a common scale-beam, be made to vibrate as slow as you like by bringing the suspension nearer to the centre of gravity of the whole mass. But they are quite unfit for independent clock pendulums, having very little regulating power, or what we may call force of vibration. He applies magnets to both the bobs, so as to double the electrical force. Fig. 17 is the section across the plane of vibration.

Fig. 18 shows the kind of reversed escapement, or "propelment," used with these short and slow pendulums. The pendulum here is returning from the extreme right, and has just deposited the right hand pallet BCD with its end D pressing on a tooth of the scape-wheel, but unable to turn it because another tooth is held by the stop G on the left pallet. As soon as the pendulum lifts that pallet the weight of the other pallet turns the wheel,until a tooth falls against the stop C. When the pendulum returns from the left the left pallet presses on a tooth at E but cannot turn the wheel because it is yet held by C, until that is released. In order to prevent the hands being driven back by wind where they are exposed to it, a click is added to the teeth. The wind cannot drive the hands forward by reason of the stops C, G.

Church and Turret Clocks.

Seeing that a clock at least the going part of it is a machine in which the only work to be done is the over coming of its own friction and the resistance of the air, it is evident, that when the friction and resistance are much increased, it may become necessary to resort to expedients for neutralizing their effects which are not required in a smaller machine with less friction. In a turret clock the friction is enormously increased by the great weight of all the parts; and the resistance of the wind, and sometimes snow, to the motion of the hands, further aggravates the difficulty of maintaining a constant force on the pendulum; and besides that, there is the exposure of the clock to the dirt and dust which are always found in towers, and of the oil to a temperature which nearly or quite freezes it all through the usual cold of winter. This last circumstance alone will generally make the arc of the pendulum at least half a degree more in summer than in winter; and in as much as the time is materially affected by the force which arrives at the pendulum, as well as the friction on the pallets when it does arrive there, it is evidently impossible for any turret clock of the ordinary construction, especially with large dials, to keep any constant rate through the various changes of temperature, weather, and dirt, to which it is exposed.

Within the last twenty years all the best clockmakers have accordingly adopted the four-legged or three-legged gravity escapement for turret clocks above the smallest size; though inferior ones still persist in using the dead escapement, which is incapable of maintaining a constant rate under a variable state of friction, as has been shown before. When the Astronomer Royal in 1844 laid down the condition for the Westminster clock that it was not to vary more than a second a day, the London Company of Clockmakers pronounced it impossible, and the late Mr Vulliamy, who had been for many years the best maker of large clocks, refused to tender for it at those terms. The introduction of the gravity escapement enabled the largest and coarsest looking clocks with cast-iron wheels and pinions to go for long periods with a variation much nearer a second a week than a second a day. And the consequence was that the price for large clocks was reduced to about one-third of what it used to be for an article inferior in performance though more showy in appearance.

Fig. 19.—Clock at Meanwood Church, Leeds.

Another great alteration, made by the French clockmakers before ours, was in the shape and construction of the frame. The old form of turret clock-frame was that of a large iron cage, of which some of the vertical bars take off, and are fitted with brass bushes for the pivots of the wheels to run in; and the wheels of each train, i.e., the striking, the going, and the quarter trains, have their pivots all in the vertical bar belonging to that part. Occasionally they advanced so far as to make the bushes movable, i.e., fixed with screws instead of rivetted in, so that one wheel may be taken out without the others. This cage generally stood upon a wooden stool on the floor of the clock room. The French clockmakers long ago saw the objections to this kind of arrangement, and adopted the plan of a horizontal frame or bed, cast all in one piece, and with such smaller frames or cocks set upon it as might be required for such of the wheels as could not be conveniently got on the same level. The accompanying sketch (fig. 19) of the clock of Meanwood church, near Leeds, one of the first on that plan, will sufficiently explain it. All the wheels of the going part, except the great wheel, are set in a separate frame called the movement frame, which is complete in itself, and light enough to take off and carry away entire, so that any cleaning or repairs required in the most delicate part of the work can be done in the clock factory, and the great wheel, barrel, and rope need never be disturbed at all. Even this movement frame is now dispensed with; but we will reserve the description of the still more simple kind of frame in which all the wheels lie on or under the great horizontal bed, until we have described train remontoires.

Train Remontoires.

Although the importance of these is lessened by the invention of an effective gravity escapement, they are still occasionally used, and are an essential part of the theory of clockmaking. It was long ago perceived that all the variations of force, except friction of the pallets, might be cut off by making the force of the scape-wheel depend on a small weight or spring wound up at short intervals by the great clock weight and the train of wheels.

This also has the advantage of giving a sudden and visible motion to the minute hand at those intervals, say of half a minute, when the remontoire work is let off, so that time may be taken from the minute hand of a large public clock as exactly as from the seconds hand of an astronomical clock; and besides that, greater accuracy may be obtained in the letting off of the striking part. We believe the first maker of a large clock with a train remontoire was Mr Thomas Reid of Edinburgh, who wrote the article on clocks in the first edition of this Encyclopædia, which was afterwards expanded into a well-known book, in which his remontoiro was described. The scape-wheel was driven by a small weight hung by a Huyghens's endless chain, of which one of the pulleys was fixed to the arbor, and the other rode upon the arbor, with the pinion attached to it, and the pinion was driven and the weight wound up by the wheel below (which we will call the third wheel), as follows. Assuming the scape- wheel to turn in a minute, its arbor has a notch cut half through it on opposite sides in two places near to each other; on the arbor of the wheel, which turns in ten minutes, suppose, there is another wheel with 2 spikes sticking out of its rim, but alternately in two different planes, so that one set of spikes can only pass through one of the notches in the scape-wheel arbor, and the other set only through the otter. Whenever then the scape-wheel completes a half turn, one spike

is let go, and the third wheel is able to move, and with it the whole clock-train and the hands, until the next spike of the other set is stopped by the scape-wheel arbor; at the same time the pinion on that arbor is turned half round, winding up the remontoire weight, but without taking its pressure off the scape-wheel. Reid says that, so long as this apparatus was kept in good order, the clock went better than it did after it was removed in consequence of its getting out of order from the constant banging of the spikes against the arbor.

Fig. 20.—Gravity Train Remontoire.

The Royal Exchange clock was at first made in on the same principle, except that, instead of the endless chain, an internal wheel was used, with the spikes set on it externally, which is one of the modes by which an occasional secondary motion may be given to a wheel without disturbing its primary and regular motion. A drawing of the original Exchange clock remontoire is given in the Rudimentary Treatise on Clocks; but for the reasons which will appear presently, it need not be repeated here, especially as the following is a more simple arrangement of a gravity train remontoire, much more frequently used in principle. Let E in fig. 20 be the scape-wheel turning in a minute, and e its pinion, which is driven by the wheel D having a pinion d driven by the wheel C, which we may suppose to turn in an hour. The arbors of the scape-wheel and hour-wheel are distinct, their pivots meeting in a bush fixed somewhere between the wheels. The pivots of the wheel D are set in the frame AP, which rides on the arbors of the hour-wheel and scape-wheel, or on another short arbor between them. The hour-wheel also drives another wheel G, which again drives the pinion f on the arbor which carries the two arms f A, f B; and on the same arbor is set a fly with a ratchet, like a common striking fly, and the numbers of the teeth are so arranged that the fly will turn once for each turn of the scapewheel. The ends of the remontoire arms f A, f B are capable of alternately passing the notches cut half through the arbor of the scape-wheel, as those notches successively come into the proper position at the end of every half minute; as soon as that happens the hour-wheel raises the movable wheel D and its frame through a small angle; but nevertheless, that wheel keeps pressing oil the scape-wheel as if it were not moving, the point of contact of the wheel C and the pinion d being the fulcrum or centre of motion of the lever A d P. It will be observed that the remontoire arms f A, f B have springs set on them to diminish the blow on the scape-wheel arbor, as it is desirable not to have the fly so large as to make the motion of the train, and consequently of the hands, too slow to be distinct. For the same reason it is not desirable to drive the fly by an endless screw, as was done in most of the French clocks on tins principle in the 1851 Exhibition. There is also an enormous loss of force by friction in driving an endless screw, and consequently considerable risk of the clock stopping either from cold or from wasting of the oil.

Another kind of remontoire is on the principle of one bevelled wheel lying between two others at right angles to it. The first of the bevelled wheels is driven by the train, and the third is fixed to the arbor of the scape-wheel; and the intermediate bevelled wheel, of any size, rides on its arbor at right angles to the other two arbors which are in the same line The scape-wheel will evidently turn with the same average velocity as the first bevelled wheel, though the intermediate one may move up and down at intervals. The transverse arbor which carries it is let off and lifted a little at half-minute intervals, as in the remontoire just now described; and it gradually works down as the scape-wheel turns under its pressure, until it is freed again and lifted by the clock train.

In all these gravity remontoires, however, it must have been observed that we only get rid of the friction of the heavy parts of the tram and the dial-work, and that the scape-wheel is still subject to the friction of the remontoire wheels, which, though much less than the other, is still something considerable. And accordingly, attempts have frequently been made to drive the scape-wheel by a spiral spring, like the mainspring of a watch. One of these, was described in the 7th edition of this Encyclopaedia; and Sir G. Atry, a few years ago, invented another on the same principle, of which two or three specimens were made. But it was found, and indeed it ought to have been foreseen, that these contrivances were all defective in the mode of attaching the spring, by making another wheel or pinion ride on the arbor of the scape-wheel, which produced a very mischievous friction, and so only increased the expense of the clock without any corresponding advantage; and the consequence was that spring remontoires, and remontoires in general, had come to be regarded as a mere delusion. It has however now been fully proved that they are not so; for, by a very simple alteration of the previous plans, a spiral spring remontoire may be made to act with absolutely no friction, except that of the scape-wheel pivots, and the letting-off springs A, B, in the last drawing. The Meanwood clock (fig. 17) was the first of this kind; but it will be necessary to give a separate view of the remontoire work.

Fig. 21.

In the next figure (21), A, B, D, E, e, f are the same things as in fig. 20. But e, the scape-wheel pinion, is no longer fixed to the arbor, nor does it ride on the arbor, as had been the case in all the previous spring remontoires, thereby producing probably more friction than was saved in other respects; but it rides on a stud k, which is set in the clock-frame. On the face of the pinion is a plate, of which the only use is to carry a pin h (and consequently its shape is immaterial), and in front of the plate is set a bush b, with a hole through it, of which half is occupied by the end of the stud k to which the bush is fixed by a small pin, and the other half is the pivot-hole for the scape-wheel arbor. On the arbor is set the remontoire spring s (a moderate-sized musical-box spring is generally used) of which the outer end is bent into a loop to take hold of the pin h. In fact, there are two pins at h, one a little behind the other, to keep the coils of the spring from touching each other. Now, it is evident that the spring may be wound up half or a quarter of a turn at the proper intervals without taking the force off the scape-wheel, and also without affecting it by any friction whatever. When the scape-wheel turns in a minute, the letting-off would be done as before described, by a couple of notches in the scape-wheel arbor, through which the spikes A, B, as in fig. 20, would pass alternately. But in clocks with only three wheels in the train it is best to make the scape-wheel turn in two minutes, and consequently you would want four notches and four remontoire arms, and the fly would only make a quarter of a turn. And therefore Sir E. Beckett, who invented this remontoire, made the following provision for diminishing the friction of the letting-off work. The fly pinion f has only half the number of teeth of the scape-wheel pinion, being a lantern pinion of 7 or 8, while the other is a leaved pinion of 14 or 16, and therefore the same wheel D will properly drive both, as will be seen hereafter. The scape-wheel arbor ends in a cylinder about ⅜ inch in diameter, with two notches at right angles cut in its face, one of them narrow and deep, and the other broad and shallow, so that a long and thin pin B can pass only through one, and a broad and short pin A through the other. Consequently, at each quarter of a turn of the scape-wheel, the remontoire fly, on which the pins A, B are set on springs, as in fig. 20, can turn half round. It is set on its arbor f by a square ratchet and click, which enables you to adjust the spring to the requisite tension to obtain the proper vibration of the pendulum. A better construction, afterwards introduced, is to make the fly separate from the letting-off arms, whereby the blow on the cylinder is diminished, the fly being allowed to go on as in the gravity escapement. The performance of this is so much more satisfactory than that of the gravity remontoires, that Mr Dent altered that of the Royal Exchange to a spring one in 1854, which had the effect of reducing the clock-weight by one-third, besides improving the rate of going. It should be observed, however, that even a spring remontoire requires a larger weight than the same clock without one; but as none of that additional force reaches the pendulum, that is of no

consequence. The variation of force of the remontoire spring from temperature, as it only affects the pendulum through the medium of the dead escapement, is far too small to produce any appreciable effect; and it is found that clocks of this kind, with a compensated pendulum 8 feet long, and of about 2 cwt., will not vary above a second a month, if the pallets are kept clean and well oiled. No turret clock without either a train remontoire or a gravity escapement will approach that decree of accuracy. The King's Cross clock, which was the first of this kind, went with a variation of about a second in three weeks in the 1851 Exhibition, and has sometimes gone for two months without any discoverable error, though it wants the jewelled pallets which the Exchange clock has. But these clocks require more care than gravity escapement ones, and are certain to be spoilt as soon as they get into ignorant or careless hands; and consequently the gravity ones have superseded them.

The introduction of this remontoire led to another very important alteration in the construction of large clocks. Hitherto it had always been considered necessary, with a view to diminish the friction as far as possible, to make the wheels of brass or gun-metal, with the teeth cut in an engine. The French clockmakers had begun to use cast-iron striking parts, and cast-iron wheels had been occasionally used in the going part of inferior clocks for the sake of cheapness; but they had never been used in any clock making pretensions to accuracy before the one just mentioned. In consequence of the success of that, it was determined by the astronomer royal and Mr Denison, who were jointly consulted by the Board of Works about the great Westminster clock in 1852, to alter the original requisition for gun-metal wheels there to cast-iron. Some persons expressed their apprehension of iron wheels rusting; but nothing can be more unfounded, for the non-acting surfaces are always painted, and the acting surfaces oiled. A remarkable proof of the folly of the clockmakers denunciations of the cast-iron wheels was afforded at the Royal Exchange the next year. In consequence of the bad ventilation of the clock-room, together with the effects of the London atmosphere, some thin parts of the brass work had become so much corroded that they had to be renewed, and some of it was replaced with iron; for all the polished iron and brass work had become as rough as if it had never been polished at all; the only parts of the clock which had not suffered from the damp and the bad air were the painted iron work. The room was also ventilated, with a draught through it, and all the iron work, except acting surfaces, painted. Even in the most favourable positions brass or gun-metal loses its surface long before cast-iron wants repainting.

There is, however, a curious point to be attended to in using cast-iron wheels. They must drive cast-iron pinions, for they will wear out steel. The smaller wheels of the going part may be of brass driving steel pinions; but the whole of the striking wheels and pinions may be of iron. A great deal of nonsense is talked about gun-metal, as if it was necessarily superior to brass. The best gun-metal may be, and is, for wheels which are too thick to hammer; but there is great variety in the quality of gun-metal; it is often unsound, and has hard and soft places; and on the whole, it has no advantage over good brass, when not too thick to be hammered. In clocks made under the pressure of competing tenders, if the brass is likely not to be hammered, the gun metal is quite as likely to be the cheapest and the worst possible, like everything else which is always specified to be "best," as the clockmakers know very well that it is a hundred to one if anybody sees their work that can tell the difference between the best and the worst.

Turret Clocks with Gravity Escapement.

Fig. 22 is a front view of a large quarter clock of Sir E. Beckett's design, with all the wheels on the great horizontal bed, a gravity escapement, and a compensated pendulum. They are made in two sizes, one with the great striking wheels 18 inches wide, and the other 14. The striking is done by cams cast on the great wheels, about 1⅛ inch broad in the large-sized clocks, which are strong enough for an hour bell of thirty cwt., and corresponding quarters. Wire ropes are used, not only because they last longer, if kept greased, but because a sufficient number of coils will go on a barrel of less than half the length that would be required for hemp ropes of the same strength, without overlapping, which it is as well to avoid, if possible, though it is not so injurious to wire ropes as it is to hemp ones. By this means also the striking cams can be put on the great wheel, instead of the second wheel, which saves more in friction than could be imagined by any one who had not tried both. In clocks of the common construction two-thirds of the power is often wasted in friction and in the bad arrangement of the hammer work, and the clock is wearing itself out in doing nothing.

Fig. 22.—Front view of Turret Quarter Clock.

Fig. 22.—Front view of Turret Quarter Clock.

The same number of cams are given here to the quarter as to hour-striking wheel, rather for the purpose of suggesting the expediency of omitting the 4th quarter, as has been done in many clocks made from this design. It is of no use to strike ding-dong quarters at the hour, and it nearly doubles the work to be done; and if it is omitted it allows the bells to be larger, and therefore louder, because the 1st quarter bell ought to be an octave above the hour bell, if they are struck at the hour; whereas, if they are not heard together the quarters may be on the 4th and 7th of a peal of eight bells. Moreover, the repetition of the four ding-dongs can give no musical pleasure to any one.

The case is different with the Cambridge and Westminster quarter chimes on 4 bells, and the chime at the hour is the most complete and pleasing of all. It is singular that those beautiful chimes (which are partly attributed to Handel) had been heard by thousands of men scattered all over England for 70 years before any one thought of copying them, but since they were introduced by Sir E. Beckett in the great Westminster clock, on a much larger scale and with a slight difference in the intervals, they have been copied very extensively and are already almost as numerous in new clocks as the old-fashioned ding-dong quarters. Properly, as at Cambridge and Westminster, the hour bell should be an octave below the third (or largest but one) quarter bell; but as the interval between the quarters and hour is always considerable, it is practically found that the ear is not offended by a less interval. At Worcester cathedral the great 4½ ton hour bell is only 1½ notes below the 50 cwt. tenor bell of the peal, which is made the fourth quarter bell; and at some other places the quarters are the 2d, 3d, 4th, and 7th of a peal of 8, and the hour bell the 8th. Thereby you get more powerful and

altogether better sounding quarters. The quarter bells are the 1st, 2d, 3d, and 6th of a peal of 6 independent of the hour bell ; and the following is their arrangement:—

01 /3126 2(1 ( 3213 1326 3d 6213 1236 1st hour. ..10

The interval between each successive chime of four should be two or at most two and a half times that between the successive blows. At Cambridge it is three times, decidedly too slow; at Westminster twice, which is rather too fast ; at Worcester cathedral and most of the later large clocks 2J times, which sounds the best.

At Cambridge the chimes are set on a barrel which turns twice in the hour, as this table indicates, and which is driven by the great wheel with a great waste of power ; the clock is wound up every day. An eight-day clock would require a very heavy weight, and a very much greater strain on the wheels, and they arc alto gether inexpedient for these quarters on any large scale of bells.

Indeed there is some reason for doubting whether the modern introduction of eight-day clocks is an improvement, where they have to strike at all on large bells. Such clocks hardly ever bring the full sound out of the bells ; because, in order to do so, the weights would have to be so heavy, and the clock so large, as to increase the price considerably. A good bell, even of the ordinary thickness, which is less than in the Westminster bells, requires a hammer of not less than ^th of its weight, rising 8 or 9 inches from the bell, to bring out the full sound ; and therefore, allowing for the loss by friction, a bell of 30 cwt, which is not an uncommon tenor for a large peal, would require a clock weight of 15 cwt., with a clear fall of 40 feet ; and either the Cambridge quarters on a peal of ten, or the Doncaster ones on the 2d, 3d, 4th, and 7th bells of a peal of eight, will require above a ton, according to the usual scale of bells in a ring ing peal (which is thinner than the Westminster clock bells). Very few clocks are adapted for such weights as these ; and without abundance of strength and great size in all the parts, it would be unsafe to use them. But if the striking parts are made to wind up every day, of course }th of these weights will do ; and you may have a more powerful clock in effect, and a safer one to manage, in half the com pass, and for much less cost. Churches with such bells as these have always a sexton or some other person belonging to them, and in attendance every day, who can wind up the clock just as well as a clockmaker s man, The going part always requires a much lighter weight, and may as well go a week, and be in the charge of a clock- maker, where it is possible.

There should be some provision for holding the hammers off the bells while ringing, and at the same time a friction-spring or weight should be brought to bear on the fly arbor, to compensate for the removal of the weight of the hammers ; otherwise there is a risk of the train running too fast and being broken when it is stopped.

No particular number of cams is required in the striking wheel ; any number from 10 to 20 will do ; but when four quarters on two bells are used, the quarter-striking wheel should have half as many cams again as the hour-wheel ; for, if not, the rope will go a second time over half of the ban-el, as there are 120 blows on each quarter bell in the 12 hours to 78 of the hours, while with the three quarters there are only 72. If the two quarter levers are on the same arbor, there must be two sets of cams, one on each side of the wheel ; but one set will do, and the same wheel as the hour- wheel, if they are placed as in fig. 23. The hour-striking lever, it will be seen, is differently shaped, so as to diminish the pressure on its arbor by making it only the difference, instead of the sum, of the pressures.at the two points of action. This can be done with the two quarter levers, as shown in the Rudimentary Treatise; but the arrangement involves a good deal of extra work, and as the quarter hammers are always lighter than the hour one, it is hardly worth while to resort to it. The shape of the cams is a matter requiring some attention, but it will be more properly considered when we come to the teeth of wheels. The 4th quarter bell in the Cambridge and Westminster quarters should have two hammers and sets of cams longer than the others, acting alternately, on account of the quick repetition of the blows.

The fly ratchets should not be made of cast-iron, as they some times are by clockmakers who will not use cast-iron wheels on any account, because the teeth get broken off by the click. This break ing may perhaps be avoided by making the teeth rectangular, like a number of inverted V s set round a circle, and the click only reach ing so far that the face of the tooth which it touches is at right angles to the click ; but, as before observed, cast-iron and steel do not work well together.

The hammer of a large clock ought to be left " on the lift," when the clock has done striking, if the first blow is to be struck exactly at the hour, as there are always a good many seconds lost in the train getting into action and raising the hammer. Moreover, when it stops on the lift, the pressure on the stops, and on all the pinions above the great wheel, is only that due to the excess of the power of the clock over the weight of the hammer, and not the full force of the weight, and it is therefore easier for the going part to discharge, and less likely to break the stops.

In fig. 22 the wheel marked 60 in each of the striking parts is a winding wheel on the front end of the barrel, and the winding pinion is numbered 10 ; a larger pinion will do where the hammer does not exceed 40 ft ; and in small clocks no auxiliary winding wheel is needed. But in that case the locking-plate must be driven by a gathering pallet, or pinion with two teeth, on the arbor of the second wheel, with a spring click to keep it steady. In all cases the hammer shanks and tails should not be less than two feet long, if possible ; for the shorter they are, the more is lost by the change of inclination for any given rise from the bell. In some clocks with fixed (not swinging) bells, the hammer-head is set on a double shank embracing the bell, with the pivots, not above it in the French way, which makes the hammer strike at a wrong angle, but on each side of the bell, a little below the top. On this plan less of the rise is lost than in the common mode of fixing. The Westminster clock hammers are all fixed in this way.

The first thing to remark in the going part of fig. 22 is that the hour-wheel which carries the snails for letting off the quarters and striking, is not part of the train leading up to the scape-wheel, but independent, so that the train from the great wheel to the scape- v/heel, is one of three wheels only. If it were a dead escapement, instead of a gravity escapement clock, the wheel numbered 96 would be the scape-wheel ; and as it turns in 90 seconds, it would require 36 teeth or pins for a 1J sec. pendulum which most of these gravity -escapement clocks have ; it is about 6 feet long to the bottom of the bob, which, if sunk just below the floor, brings the clock-frame to a very convenient height. The hour-wheel rides loose on its arbor, or rather the arbor can turn within it, carrying the snails and the regulating hand and the bevelled wheel which drives all the dials, and it is fixed to the hour-wheel by means oi clamping screws on the edge of a round plate on the arbor just behind it, which turn by hand. In a gravity escapement clock this adjusting work is not really necessary ; because you can set the clock by merely lifting the pallets oli the scape-wheel, and letting the train run till the hands point right. The regulating hand, you observe, in fig. 22 turns the wrong way; because, where the dial is opposite to the back of the clock, no bevelled wheels are wanted, and the arbor leads straight off to the dial. It used to be the fashion to put clocks in the middle of the room, so that the leading- off rod might go straight up to the horizontal bevelled wheel in the middle, which drove all the dials. But the clock can be set much more firmly on stone corbels, or on cast-iron brackets built into the wall; and it is not at all necessary for the leading-off rod to be vertical. Provided it is only in a vertical plane parallel to the wall, or the teeth of the bevelled wheels adapted to the inclination, the rod may stand as obliquely as you please ; and when it does, it ought on no account to be made, as it generally is, with universal joints, but the pivots shouldgo into oblique pivot-holes at the top and bottom. The joints increase the friction considerably, and are of no use whatever, except where the rod is too long to keep itself straight. Where the rod does happen to be in the middle of the room, and there are three or four dials, the two horizontal bevelled wheels at each end of it must be a little larger than all the others both the one in the clock and those of the dial-work ; for otherwise the three or four wheels in the middle will meet each other and stick fast.

When the pendulum is very long and heavy, it should be sus pended from the -wall, unless the clock-frame has some strong support near the middle ; but a six-feet pendulum, of not more than two cwt., may be suspended from the clock-frame, provided it is as strong as it ought to be for the general construction of the clock, and supported on corbels or iron beams. It has generally been the practice to hang the pendulum behind the clock-frame ; but inasmuch as the rope of the going part may always be thinner than that of the striking part, and that part requires less depth in other respects, a different and more compact plan is adopted in the clocks we are describing. The back pivots of the going wheels run in bushes in an intermediate bar, three or four inches from the back of the frame, joining the two cross bars, of which the ends are dotted in the drawing. The pendulum cock is set on the back frame, and the pendulum hangs within it. And in the gravity escapement clocks there is yet another thin bar about half way between the back frame and the bar on which the bushes of the wheels are set the only use of which is to carry the bush of the scape-wheel, which is set behind the fly; the wheel, the fly, and the pallets, or gravity- arms, stand between these two intermediate bars ; and the pallet- arbors are set in a brass cock screwed to the top of the pendulum- cock. The beat-pins should be of brass, not steel, and no oil put to them, or they are sure to stick. The escapement in fig. 22 is not drawn rightly for the present form of them, which is given hi fig. 13.

The same gen.eral arrangement will serve for a dead escapement

clock with or without a train remoutoire ; only the pendulum will not stand so high, and the front end of the pallet arbor must he set in a cock like those of the striking flies, oil the front bar of the frame. And for a dead escapement, if there are large dials and no rernontoire, the pendulum should be longer and heavier than that which is quite sufficient for a gravity escapement. The rod of a wooden pendulum should be as thin as it can conveniently be made, and varnished, to prevent its absorbing moisture.

Dials and Hands.

The old established form of dial for turret clocks is a sheet of copper made convex, to preserve its shape ; and this is just the worst form which could have been contrived for it. For, in the first place, the minute-hand, being necessarily outside of the hour-hand, is thrown still farther off the minutes to which it has to point, by the convexity of the dial ; and consequently, when it is in any posi tion except nearly vertical, it is impossible to see accurately where it is pointing ; and if it is bent enough to avoid this effect of parallax, it looks very ill. Secondly, a convex dial at a consider able height from the ground looks even more convex than it really is, because the lines of sight from the middle and the top of the dial make a smaller angle with the eye than the lines from the middle and the bottom, in proportion to the degree of convexity. The obvious remedy for these defects, is simply to make the dial concave instead of convex. As convex dials look more curved than they are, concave ones look less curved than they are, and in fact might easily be taken for flat ones, though the curvature is exactly the same as usual. Old convex dials are easily altered to concave, and the improvement is very striking where it has been done. There is no reason why the same form should not be adopted in stone, cement, slate, or cast-iron, of which materials dials are some times and properly enough made, with the middle part countersunk for the hour hand, so that the minute-hand may go close to the figures and avoid parallax. When dials are large, copper, or even iron or slate, is quite a useless expense, if the stonework is moder ately smooth, as most kinds of stone take and retain paint very well, and the gilding will stand upon it better than it often does on copper or iron.

The figures are generally made much too large. People have a pattern dial painted ; and if the figures are not as long as one-third of the radius, and therefore occupying, with the minutes, about two- thirds of the whole area of the dial, they fancy they are not large enough to be read at a distance ; whereas the fact is, the more the dial is occupied by the figures, the less distinct they are, and the more difficult it is to distinguish the position of the hands, which is what people really want to see, and not to read the figures, which may very well be replaced by twelve large spots. The figures, after all, do not mean what they say, as you read " twenty minutes to" something, when the minute-hand points to vm. The rule which has been adopted, after various experiments, as the best for the proportions of the dial, is this. Divide the radius into three, and leave the inner two-thirds clear and flat, and of some colour forming a strong contrast to the colour of the hands, black or dark blue if they are gilt, and white if they are black. The figures, if there are any, should occupy the next two-thirds of the remaining third, and the minutes be set in the remainder, near the edge, and with every fifth minute more strongly marked than the rest ; and there should not be a rim round the dial of the same colour or gilding as the figiires. The worst kind of dial of all are the things called skeleton-dials, which either have no middle except the stone work, forming no contrast to the hands, or else taking special trouble to perplex the spectator by filling up the middle with radiating bars. Where a dial cannot be put without interfering with the architecture, it is much better to have none, as is the case in many cathedrals and large churches, leaving the information to be given by the striking of the hours and quarters. This also will save something, perhaps a good deal, in the size and cost of the clock, and if it is one without a train remoutoire or gravity escape- Uient, will enable it to go better. The size of public dials is often rery inadequate to their height and the distance at which they are intended to be seen. They ought to be at least 1 foot in diameter for every 10 feet of height above the ground, and more whenever the dial will be seen far off; and this rule ought to be enforced on archi tects, as they are often not aware of it ; and indeed they seldom make proper provisions for the clock or the weights in building a tower, or, in short, know anything about the matter.

The art of illuminating dials cannot be said to be in a satisfactory state. Where there happens to be, as there seldom is, a projecting roof at some little distance below the dial, it may be illuminated by reflection, like that at the Horse Guards about the only merit which that superstition sly venerated and bad clock has ; and the same thing may be done in some places by movable lamp reflectors, like those put before shop windows at night, to be turned back against the wall during the day. It has also been proposed to sink the dial within the wall, and illuminate it by jets of gas pointing inwards from, a kind of projecting rim, like what is called in church windows a "hood-moiddiiig," carried all round. But it is a great objection to sunk dials, even of less depth than would be required here, that they do not receive light enough by day, and do not get their faces washed by the rain. The common mode of illumina tion is by making thelials either entirely, or all except the figures and minutes and a ring to carry them, of glass, either ground or lined in the inside with linen (paint loses its colour from the gas). The gas is kept always alight, but the clock is made to turn it nearly off and full on at the proper times by a 24-hour wheel, with pins set in it by hand as the length of the day variew. Self-acting apparatus has been applied, but it is somewhat complicated, and an unnecessary expense. But these dials always look very ill by day ; and it seems often to be forgotten that dials are wanted much more by day than by night ; and also, that the annual expense of lighting 3 or 4 dials far exceeds the interest of the entire cost of any ordinary clock. Sometimes it exceeds the whole cost of the clock annually. The use of white opaque glass with black figures is ver) superior to the common method. It is used in the great Westminster clock dials. It is somewhat of an objection to illuminating large dials from the inside, that it makes it impossible to counterpoise the hands outside, except with very short, and there fore very heavy, counterpoises. And if hands are only counterpoised inside, there is no counterpoise at all to the force of the wind, which is then constantly tending to kosen them on the arbor, and that tendency is aggravated by the hand itself pressing on the arbor one way as it ascends, and the other way as it descends ; and if a large hand once gets in the smallest degree loose, it becomes rapidly worse by the constant shaking. It is mentioned in Reid s book that the minute-hand of St Paul s cathedral, which is above 8 feet long, used to fall over above a minute as it passed from the left to the right side of xii, before it was counterpoised outside. In the conditions to be followed in the Westminster clock it was expressly required that "the hands be counterpoised externally, for wind as well as weight. " The long hand should be straight and plain, to distinguish it as much as possible from the hour hand, which should end in a "heart" or swell. Many clockmakers and architects, on the con trary, seem to aim at making the hands as like each other as they can ; and it is not uncommon to see even the counterpoises gilt, probably with the same object of producing apparent symmetry and the same result of producing real confusion.

The old fashion of having chimes or tunes played by machinery on church bells at certain hours of the day has greatly revived in the last few years, and it has extended to town halls, as also that of having very large clock bells, which had almost become extinct until the making of the Westminster clock. The old kind of chime machinery consisted merely of a large wooden ban-el about 2 feet in diameter with pins stuck in it like those of a musical box, which pulled down levers that lifted hammers on the bells. Generally there were several tunes " pricked " on the barrel, which had an endway motion acting automatically, so as to make a shift after each tune, and with a special adjustment by hand to make it play a psalm tune on Sundays. But though these tunes were very pleasing and popular in the places where such chimes existed they were generally feeble and irregular, because the pins and levers were not strong enough to lift hammers of sufficient weight for the large bells, and there were no means of regulating the time of dropping off the levers. Probably the last large chime work of this kind was that put up by Dent to play on 16 bells at the Royal Exchange in 1845, with the improvement of a cast-iron barrel and stronger pins than in the old wooden barrels.

A much improved chime machine has been introduced since, at first by an inventor named Imhoff, who sold Ms patent, or the right to use it, to Messrs Gillett and Bland of LYoydon, and also to Messrs Lund and Blockley of Pall Mall, who have both added further improvements of their own. The principle of it is this : instead of the hammers being lifted by the pins which let them off, they are lifted whenever they are down by an independent set of cam wheels of ample strength ; and all that the pins on the barrel have to do is to trip them up by a set of comparatively light levers or detents. Consequently the pins are as small as those of a barrel organ, and many more tunes can be set on the same barrel than in the old plan, and besides that, any number of barrels can be kept, and put in from time to time as you please ; so that you may have as many tunes as the peal of bells will admit. There are various provisions for regulating and adjusting the time, and the machinery is altogether of a very perfect kind for its purpose, but it must bo seen to be understood.

It is always necessary in chimes to have at least two hammers to each bell to enable a note to be repeated quickly. Some ambitious musicians determined to try " chords" or double notes struck at them, ine largest peaia ana cmmus wt "* -< cester cathedral, and the town halls of Bradford and Rochdale, and a still larger one is now making for Manchester, all by Gillett ano Bland. The clock at Worcester, which as yet ranks next to West- minster, was made by Mr Joyce of Whitchurch ; the others are by Gillett and Bland. At Boston church they have chimea m

tion of some of the foreign ones on above 40 small bells, which were added for that purpose to the eight of the peal; but they are not successful, and it is stated in Sir E. Beckett's book on clocks and bells, that he warned them that the large and small bells would not harmonize, though either might be used separately. Other persons have attempted chimes on hemispherical bells, like those of house clocks; but they also are a failure for external bells to be heard at a distance. This however belongs rather to the subject of bells; and we must refer to that book for all practical information about them.

Teeth of Wheels.

Before explaining the construction of the largest clock in the world it is necessary to consider the shape of wheel teeth suitable for different purposes, and also of the cams requisite to raise heavy hammers, which had been too much neglected by clockmakers previously. At the same time we are not going to write a treatise on all the branches of the important subject of wheel-cutting; but, assuming a knowledge of the general principles of it, to apply them to the points chiefly involved in clock-making. The most comprehensive mathematical view of it is perhaps to be found in a paper by the astronomer royal in the Cambridge Transactions many years ago, which is further expanded in Professor Willis's Principles of Mechanism. Respecting the latter book, however, we should advise the reader to be content with the mathematical rules there given, which are very simple, without attending much to those of the odontograph, which seem to give not less but more trouble than the mathematical, and are only approximate after all, and also do not explain themselves, or convey any knowledge of the principle to those who use them.

For all wheels that are to work together, the first thing to do is to fix the geometrical, or primitive, or pitch circles of the two wheels, i.e., the two circles which, if they rolled perfectly together, would give the velocity-ratio you want. Draw a straight line joining the two centres; then the action which takes place between any two teeth as they are approaching that line is said to be before the line of centres; and the action while they are separating is said to be after the line of centres. Now, with a view to reduce the friction, it is essential to have as little action before the line of centres as you can; for if you make any rude sketch, on a large scale, of a pair of wheels acting together, and serrate the edges of the teeth (which is an exaggeration of the roughness which produces friction), you will see that the further the contact begins before the line of centres, the more the serration will interfere with the motion, and that at a certain distance no force whatever could drive the wheels, but would only jam the teeth faster; and you will see also that this can not happen after the line of centres. But with pinions of the numbers generally used in clocks you cannot always get rid of action before the line of centres; for it may be proved (but the proof is too long to give here), that if a pinion has less than 11 leaves, no wheel of any number of teeth can drive it without some action before the line of centres. And generally it may be stated that the greater the number of teeth the less friction there will be, as indeed is evident enough from considering that if the teeth were infinite in number, and infinitesimal in size, there would be no friction at all, but simple rolling of one pitch circle on the other. And since in clock-work the wheels always drive the pinions, except the hour pinion in the dial work, and the winding pinions in large clocks, it has long been recognized as important to have high numbered pinions, except where there is a train remontoire, or a gravity escapement, to obviate that necessity.

And with regard to this matter, the art of clock-making has in one sense retrograded; for the pinions which are now almost universally used in English and French clocks are of a worse form than those of several centuries ago, to which we have several times alluded under the name of lantern pinions, so called from their resembling a lantern with upright ribs. A sketch of one, with a cross section on a large scale, is given at fig. 24. Now it is a property of these pinions, that when they are driven, the action begins just when the centre of the pin is on the line of centres, however few the pins may be; and thus the action of a lantern pinion of 6 is about equal to that of a leaved pinion of 10; and indeed, for some reason or other, it appears in practice to be even better, possibly from the teeth of the wheel not requiring to be cut so accurately, and from the pinion never getting clogged with dirt. Certainly the running of the American clocks, which all have these pinions, is remarkably smooth, and they require a much smaller going weight than English clocks; and the same may be said of the common "Dutch," i.e., German clocks. It should be understood, however, that as the action upon these pinions is all after the line of centres when they are driven, it will be all before the line of centres if they drive, and therefore they are not suitable for that purpose. In some of the French clocks in the 1851 Exhibition they were wrongly used, not only for the train, but for winding pinions; and some of them also had the pins not fixed in the lantern, but rolling,—a very useless refinement, and considerably diminishing the strength of the pinion. For it is one of the advantages of lantern pinions with fixed pins, that they are very strong, and there is no risk of their being broken in hardening, as there is with common pinions.

The fundamental rule for the tracing of teeth, though very simple, is not so well known as it ought to be, and therefore we will give it, premising that so much of a tooth as lies within the pitch circle of the wheel is called its root or flank, and the part beyond the pitch circle is called the point, or the curve, or the addendum; and moreover, that before the line of centres the action is always between the flanks of the driver and the points of the driven wheel or runner (as it may be called, more appropriately than the usual term follower); and after the line of centres, the action is always between the points of the driver and the flanks of the runner. Consequently, if there is no action before the line of centres, no points are required for the teeth of the runner.

Fig. 23.

In fig. 23, let AQX be the pitch circle of the runner, and ARY that of the driver; and let GAP be any curve whatever of smaller curvature than AQX (of course a circle is always the kind of curve used); and QP the curve which is traced out by any point P in the gene rating circle GAP, as it rolls in the pitch circle AQX; and again let HP be the curve traced by the point P, as the generating circle GAP is rolled on the pitch circle ARY; then RP will be the form of the point of a tooth on the driver ARY, which will drive with uniform and proper motion the flank QP of the runner; though hot without some friction, because that can only be done with involute teeth, which are traced in a different way, and are subject to other conditions, rendering them practically useless for machinery, as may be seen in Professor Willis's book. If the motion is reversed, so that the runner becomes the driver, then the flank QP is of the proper form to drive the point RP, if any action has to take place before the line of centres.

And again, any generating curve, not even necessarily the same as before, may be used to trace the flanks of the driver and the points of the runner, by being rolled within the circle ARY, and on the circle AQX.

Now then, to apply this rule to particular cases. Suppose the generating circle is the same as the pitch circle of the driven pinion itself, it evidently can not roll at all; and the tooth of the pinion is represented by the mere point P on the circumference of the pitch circle; and the tooth to drive it will be simply an epicycloid traced by rolling the pitch circle of the pinion on that of the wheel. And we know that in that case there is no action before the line of centres, and no necessity for any flanks on the teeth of the driver. But in asmuch as the pins of a lantern pinion must have some thickness, and cannot be mere lines, a further process is necessary to get the exact form of the teeth; thus if RP, fig. 24, is the tooth that would drive a pinion with pins of no sensible thickness, the tooth to drive a pin of the thickness 2Pp must have the width Pp or Rr gauged off it all round. This, in fact, brings it very nearly to a smaller tooth traced with the same generating circle; and therefore in practice this mode of construction is not much adhered to, and the teeth are made of the same shape, only thinner, as if the pins of the pinion had no thickness. Of course they should be thin enough to allow a little shake, or "back-lash," but in clock-work the backs of the teeth never come in contact at all.

Fig. 24.—Lantern Pinion.

Next suppose the generating circle to be half the size of the pitch circle of the pinion. The curve, or hypocycloid, traced by rolling this within the pinion, is no other than the diameter of the pinion; and consequently the flanks of the pinion teeth will be merely radii of it, and such teeth or leaves are called radial teeth; and they are far the most common; indeed, no others are ever made (except lanterns) for clock-work. The corresponding epicyeloidal points of

the teeth cf the driver arc more curved, or a less pointed arc, than those required for a lantern pinion of the same size and number. The teeth in fig. 25 are made of a different form on the opposite sides of the line of centres CA, in order to show the difference between driving and driven or running teeth, where the number of the pinion happens to be as much as 12, so that no points are required to its teeth when driven, since with that number all the action may be after the line of centres. The great Westminster clock affords a very good illustration of this. In F - - both the striking parts the great wheel of the train and the great winding-wheel on the other end of the barrel are about the same size ; but in the train the wheel drives, and in winding the pinion drives. And there fore in the train the pinion-teeth have their points cut off, and wheel-teeth have their points on, as on the right side of fig. 25, and in the winding-wheels the converse ; and thus in both cases the action is made to take place in the way in which there is the least friction. Willis gives the following table, " derived organi cally" (i.e., by actual trial with large models), of the least numbers which will work together without any action before the line of centres, provided there are no points to the teeth of the runner, assuming them to be radial teeth, as usual:—

Fig. 25.

Driver 54302420171514131211109 876 Runner 11 12 13 14 15 16 17 18 19 21 23 27 35 32 176

In practice it is hardly safe to leave the driven teeth without points, unless the numbers slightly exceed these ; because, if there is any irregularity in them, the square edges of those teeth would not work smoothly with the teeth of the driver. Sometimes it happens that the same wheel has to drive two pinions of different numbers. It is evident that, if both are lanterns, or both pinions with radial teeth, they cannot properly be driven by the same wheel, because they would require teeth of a different shape. It is true that on account of the greater indifference of lantern pinions to the accuracy of the teeth which are to drive them, the same wheel will drive two pinions of that kind, differing in the numbers in the ratio of even 2 to 1, with hardly any sensible shake ; but that would not be so with radial pinions, and of course it is not correct. Accordingly, in clocks with the spring remontoire, as in fig. 21, where the scape-wheel or remontoire pinion is double the size of the fly pinion, the larger one is made with radial teeth and the smaller a lantern, which makes the same wheel teeth exactly right for both. In clocks of the same construction as fig. 22, and in the West minster clock, there is a case of a different kind, which cannot be so accommodated ; for there the great wheel has to drive both the second wheel s pinion of 10 or 12, and the hour-wheel of 40 or 48; the teeth of the great wheel were therefore made to suit the lantern pinion, and those of the hour- wheel (i.e., their flanks) then depend on those of the great wheel, and they were accordingly traced by rolling a generating circle of the size of the lantern pinion on the inside of the pitch circle of the hour-wheel ; the result is a tooth thicker at the bottom than usual. These are by no means unnecessary refinements ; for if the teeth of a set of wheels are not properly shaped so as to work smoothly and regularly into each other, it increases their tendency to wear out in proportion to their inaccuracy, besides increasing the inequalities of force in the train. Sometimes turret clocks are worn out in a few years from the defects in their teeth, especially Avhen they are made of brass or soft gun-metal.

In the construction of clocks which have to raise heavy hammers it is important to obtain the best form for the cams, as pins are quite unfit for the purpose. The conditions which are most impor tant are that the action should begin at the greatest advantage, and therefore at the end of the lever, that when it ceases the face of the lever should be a tangent to the cam at both their points, and that in no part of the motion should the end of the lever scrape on the cam. In the common construction of clocks the first con dition is deviated from as far as possible, by the striking pins beginning to act at some distance from the end of the lever; and con sequently, at the time when the most force is required to lift the ham mer there is the least given, and a great deal is wasted afterwards.

The construction of curve for the cams, which is the most perfect mathematically, is that which is described in mathematical books under the name of the tractrix. But there are such practical difficulties in describing it that it is of no use. It should be observed that, in a well-known book with an appropriate name ( Camus on the Teeth of Wheels), a rule for drawing cams has been inserted by some translator, which is quite wrong. It may be proved that epicycloidal cams described as follows are so nearly of the proper mathematical form that they may be used without any sensible error. Let r be the radius of the circle or barrel on which the cams are to be set theoretically, i.e., allowing nothing tor the clearance which must be cut out afterwards, for fear the fever should scrape the back of the cams in falling ; in other words r is the radius of the pitch circle of the cams Call the length of the lever I. Then the epicycloidal cams may be traced by rolling on the pitch circle a smaller one whose diameter is Vr a + P - r Thus, if I is 4 inches and r 8 inches (which is about the proper size tor an 18-inch striking wheel with 20 cams), the radius of the tracing circle from the cams will be 0-9 inch. The advantage of cams of this kind is that they waste as little force as possible in the lift, and keep the lever acting upon them as a tangent at its point the whole way ; and the cams themselves may be of any length according 1 to the angle through which you want the lever to move ,

Most people however prefer dealing with circles, when they can instead of epicycloids ; and drawing by compasses is safer than calculating in most hands. We therefore give another rule, suggested by Mr E. J. Lawrence, a member of the horological jury in the 1851 ^Exhibition, which is easier to work, and satisfies the principal conditions stated just now, though it wastes rather more in lift than the epicycloidal curve ; and the cams must not have their points cut off, as epicycloidal ones may, to make the lever drop off sooner ; because a short cam has to be drawn with a different radius from a long one, to work a lever of any given length. But, on the other hand, the same curve for the cams will suit a lever of any length, whereas with epicycloidal cams you must take care to put the centre or axis of the lever at the exact distance from the centre of the wheel for which the curve was calculated an easy enough thing to do, of cours e, but for the usual disposition of workmen to deviate from your plans, apparently for the mere pleasure of doing wrong. It is astonishing how, by continually making one machine after another, with a little deviation each time, the thing gradually assumes a form in which you can hardly recognise your original design at all. The prevention of this kind of blundering is one of the many advantages of making machines by machinery, for which no machine offers more facilities than clocks, and yet there is none to which it is less applied.

Fig. 26.

In fig. 26 let CA be a radius of the wheel, L in the same straight line the centre of the, lever, and AB the space of one cam on the pitch circle of the cams, A being a little below the line of centres; AP is the arc of the lever. Draw a tangent to the two circles at A, and a tangent to the cam circle at B ; then T, their point of in tersection, will be the centre of the circle which is the face of the cam BP ; and TB also ?TA, which is a convenient test of the tangents being rightly drawn. The action begins at the point of the lever, and advances a little way up, but recedes again to the point, and ends with the lever as a tangent to the cam at P. The backs of the cams must be cut out rather deeper than the circle AP, but retaining the point P, to allow enough for clearance of the lever, which should fall against some fixed stop or banking on the clock-frame, before the next cam reaches it. The point of the lever must not be left quite sharp, for if it is, it will in time cut off the points of the cast-iron cams.

Oil for Clocks.

We will add a few words on the subject of oil for clocks. Olive- oil is most commonly used, sometimes purified in various ways, and sometimes not purified at all. We believe, however, that purified animal oil is better than any of the vegetable oils, as some of them are too thin, while others soon get thick and viscid. For turret clocks and common house clocks, good sperm oil is fine enough, and is probably the best. For finer work the oil requires some purifi cation. Even common neat s foot oil may be made fine and clear by the following method. Mix it with about the same quantity of water, and shake it in a large bottle, not full, until it becomes like a white soup ; then let it stand till fine oil appears at the top, which maybe skimmed ofT; it will take several months before it has all separated into water at the bottom, dirt in the middle, and fine oil at the top. And it should be done in cold weather, because heat makes some oil come out as fine, which in cold would remain among the dirty oil in the middle, and in cold weather that fine oil of hot weather will become muddy. There are various vegetable oils sold at tool-shops as oil for watches, including some for which a prize medal was awarded in the Exhibition, but not by any of the mechanical juries ; we have no information as to the test which was

applied to it, and nouc but actual use for a considerable time would be of mucLi value.

The Westminster Clock.

It is unnecessary to repeat the account of the long dispute between the Government, the architect of the House of Parliament, the astronomer royal, Sir E. Beckett, and some of the London clock- makers, which ended in the employment of the late E. J. Dent and his successor F. Dent from the designs and under the superintend ence of Sir E. Beckett, as the inscription on it records The fullest account of these was given in the 4th and 5th editions of the Treatise on Clocks, and we shall now only describe its construction. Fi". 27 is a front elevation or section lengthwise of the clock, The frame is 16 feet long and 5? wide, and it rests on two iron plates lying on the top of the walls of the shaft near the middle of the tower, down which the weights descend. That wall reaches up to the bell chamber, and those iron plates are built right through it, and so is the great cock which carries the pendulum. The clock- room is 28 feet x 19, the remaining 9 of the square being occupied by the staircase and an air-shaft for ventilating the whole building. The going part of the clock, however, not requiring such a long barrel as the striking parts, which have steel wire ropes 55 inch thick, is shorter than they are, and is carried by an intermediate bar or frame bolted to the cross bars of the principal frame. The back of them is about 2^ feet from the wall, to leave room for a man behind, and the pendulum cock is so made as to let his head come within it in order to look square at the escapement. The escape ment is the double three legs (fig. 13), and the length of the teeth or legs is 6 inches. The drawing represents the wheels (except the Welled wheels leading off to the dials) as mere circles to prevent confusion. The numbers of teeth and the time of revolution of the principal ones are inserted and require no further notice. Their size can be taken from the scale ; the great wheels of the striking parts are 2

The maintaining power for keeping the clock going while winding is peculiar and probably unique. None of those already described could have kept in gear long enough, maintaining sufficient force all the time, as that part takes 10 minutes to wind, even if the man does not loiter over it. This is managed without a single extra wheel beyond the ordinary winding pinion of large clocks. The winding wheel on the end of the barrel is close to the great wheel, and you see the pinion with the winding arbor in the oblique piece of the front frame of the clock. Consequently that arbor is about 6 feet long, and a little movement of its back end makes no material obliquity in the two bushes ; i.e., it may go a little out of parallel with all the other arbors in the clock without any impediment to its action. Its back pivot is carried, not in a fixed bush, but in the lower end of a bar a little longer thanthe great wheel s radius, hang ing from the back of the great arbor ; and that bar has a spring click upon it which takes into ratchet teeth cast on the back of the great wheel. When the great wheel is turning, and you are not winding, the ratchets pass the click as usual, but as soon as you begin to wind the back end of the winding arbor would rise but for the click catching those teeth, and so the great wheel itself become the fulcrum for winding for the time. After the winding has gone a few minutes a long tooth projecting from the back of the arbor catches against a stop, because that end of the hanging bar and pinion have all risen a little with the motion of the great wheel. Then the man is obliged to turn the handle back a little, which lets down the pinion, &c., and the click takes up some lower teeth ; and so if he chooses to loiter an hour over the winding he can do no harm. The winding pinion "pumps" into gear and out again as usual. The going part will go Si days, to provide for the possible forgetting of a day in winding. The weight is about 160 K ; but only one-14th of the whole force of that weight is requisite to drive the pendulum, as was found by trial ; the rest goes in overcoming the friction of all the machinery, including a ton and a half of hands and counterpoises, and in providing force enough to drive them through all weathers, except heavy snows, which occasionally accumu late thick enough on several minute hands at once, on the left side of the dials, to stop the clock, those hands being 11 feet long. For the dials are 22 feet in diameter, or contain 400 square feet each, and there are very few rooms where such a dial could be painted on the floor. They are made of iron framing rilled in with opal glass. Each minute is 14 inches wide. The only larger dial in the world is in Mechlin church, which is 40 feet wide ; but it has no minute hand, which makes an enormous difference in the force required in the clock. They are completely walled off from the clock-room by a passage all round, and there are a multitude of gas lights behind them, which are lighted by hand, though provision was originally made in the clock for doing it automatically. The hour hands go so slow that their weight is immaterial, and were left as they were made of gun metal under the- architect s direction but it was impossible to have minute hands of that construction and weight without injury to the clock, and so they were removed by Sir E. Beckett, and others made of copper tubes, with a section com posed of two circular arcs put together, and are consequently very stiff, while weighing only 28 lt>. The great weight is in the wheels, tubes, and counterpoises. The minute hands are partly counterpoised i-.utside, making their total length 14 feet, to relieve the strain upon their arbors. They all run on friction wheels imbedded in the larger tubes 5k inches wide, which carry the hour hands, which themselves run on fixed friction wheels.

Fig. 27.—Section of Westminster Clock.

Fig. 27.—Section of Westminster Clock.

There is nothing peculiar in the quarter striking part except its size, and perhaps in the barrel turning in an hour and a half, i.e., iu three repetitions of the five chimes already described. The cams are of wrought iron with hard steel faces. Each bell has two hammers, which enables the cams to be longer and the pressure on them less. The hour-striking wheel has ten cams 24 in. wide cast on it ; but those cams have solid steel faces screwed on them. All this work was made for a hammer of 7 cwt., lifted 13 inches from the bell, i.e., about 9 inches of vertical lift. The hammer was reduced to K cwt. after the partial cracking of the bell. The rod from the lever to the hammer is made of the same wire rope as the weight ropes, and the result is that there is no noise in the room while the clock is strik ing. The lever is 5 feet 4 inches long, and strikes against the buffer spring shown in the drawing, to prevent concussion on the clock-frame, of which you cannot feel the least. The quarter ham mer levers have smaller springs for the same purpose, and the stops of the striking part are also set on springs instead of rigid as usual. The ilies, for which there was not room in the drawing, are near the top of the room and are each 2 feet 4 inches square. They make a considerable wind in the room when revolv ing. The only noise made in striking is their running on over their ratchets when the striking stops. Each striking weight is a ton and a half or was before the great hammer was reduced. They take 5 hours to wind up, and it has to be done twice a week, which was thought better than making the parts larger and the teeth more numerous and the weights twice as much, to go a week, and of course the winding must have taken twice as long, as it was adapted to what a man can do continuously for some hours. Con- sequently it was necessary to contrive something to stop the man.

winding just before each time of striking. And that is done by a lever being tipped over by the snail at that time, which at once stops the winding. When the striking is done the man can put the lever up again and go on. The loose winding wheels are not pumped in and out of gear as usual, being too heavy, but one end of the arbor is pushed into gear by an eccentric bush turned by the oblique handle or lever which you see near the upper corner of each striking part, and they can be turned in a moment. They are held in their place for gear by a spring catch to prevent any risk of slip ping out. Moreover the ropes themselves stop the winding when the weights came to the top, pretty much as they do in a spring clock or a watch, though not exactly.

The mode of letting off the hour striking is peculiar, with a view to the first blow of the hour being exactly at the GOth second of the GOth minute. It was found that this could not be depended on to a single beat of the pendulum, and probably it never can in any clock, by a mere snail turning in an hour, unless it was of a very inconvenient size. Therefore the common snail only lets it off par tially, and the. striking stop still rests against a lever which is not dropped but tipped up with a slight blow by another weighted lever resting on a snail on the ] 5-miiiute wheel, which moves more exactly with the escapement than the common snail lower in the train. The hammer is left on the lift, ready to fall, and it always does fall within half a second after the last beat of the pendulum at the hour. This is shown in fig. 28, where BE is the spring stop noticed above, and P the ordinary first stop on the long lifting lever PQ (which goes on far beyond the reach of this figure to the hour snail). The second or warning stop is CD, and BAS is the extra lever with its heavy end at S on the 15-minute snail. When that falls the end B tips up CD with certainty by the blow, and then the striking is free. The first, second, and third quarters begin at the proper times ; but the fourth quarter chimes begin about 20 seconds before the hour.

The clock reports its own rate to Greenwich Observatory by gal vanic action twice a day, i.e., an electric circuit is made and broken by the pressing together of certain springs at two given hours. And in this way the rate of the clock is ascertained and recorded, and the general results published by the astronomer royal in his annual report. This has been for some years so remarkably uniform, that the error has only reached 3 seconds on 3 per cent, of the days in the year, and is generally under two. He has also reported that "the rate of the clock is certain to much less than a second a week " subject to abnormal disturbances by thunder storms which sometimes amount to seven or eight seconds, and other casualties, which are easily distinguishable from the spontaneous variations. The original stipulation in 1845 was that the rate should not vary more than a second a day not a week ; and this was pronounced impossible by Mr Vulliamy and the London Company of Clock- makers, and it is true that up to that time no such rate had ever been attained by any large clock. In 1851 it was by the" above- mentioned clock, now at King s Cross Station, by means of the train remontoirc, which was then intended to be used at Westminster, but was superseded by the gravity escapement.

Fig. 28.

Fig. 28.

The great hour tfell, of the note E, weighs 134 tons and is 9 feet diameter and 9 inches thick. The quarter bells weigh respectively 78, 33, 26, and 21 cwt. ; with diameters 6 feet, 4J, 4, and 3 feet 9 inches, and notes B, E, F sh. and G sh. The hammers are on double levers embracing the bells, and turning on pivots pro jecting from the iron collars which carry the mushroom shaped tops of the bells. The bells, including 750 for recasting the first great bell, cost nearly 6000, and the clock 4080. The bell frame, which is of wrought iron plates, and the dials and hands, all provided by the architect, cost 11,934 a curious case of the accessories costing more than the principals.

(e. b.)