Page:Encyclopædia Britannica, Ninth Edition, v. 6.djvu/26

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