Popular Astronomy: A Series of Lectures Delivered at Ipswich/Lecture 2

by George Biddell Airy

LECTURE II.

Recapitulation of Lecture I.—Investigation of the form and dimensions of the earth.—Proof that the earth really revolves.—Apparent motion of the Sun among the stars, or real motion of the earth round the Sun.—Permanence of an axis of Rotation.

IN the last lecture, I endeavoured to point out to you the principal phenomena of the motions of the stars, as observed on any fine night. And I called your attention to the fact, that these motions are performed in such a way, as to give us the idea of rotation round an axis inclined to the horizon; that some of the stars move very little; that others describe larger circles; that others just touch the horizon and descend below it; that others descend on one side and rise on the other side. I mentioned the names of two or three stars admitting of easy observation, as I am desirous that you should observe a little for yourselves, because you will acquire more knowledge from personal observation than from my lectures. The first of these is the Polar Star, which everybody ought to know: the second is the constellation of the Great Bear, which most people know as Charles' Wain; the third is the bright star Capella; the fourth is the bright star of Lyra. I described their motions: and I then pointed out to you that the observations were rendered more accurate by means of the instrument named the Equatoreal, which makes a telescope turn on an axis parallel to the direction of the axis round which the stars appear to turn; and that we find, by fixing the telescope to the axis in such a position that it is directed to any one star, and then, by continuing to turn the instrument upon its axis, the telescope will follow the star from its rising to its setting. This I mentioned as establishing an important point, that the stars undoubtedly do appear to revolve round that axis. I then described the use of the clock-work for causing the Equatoreal instrument to revolve uniformly. And I pointed out to you, as a thing of importance, that when the clock-work is in action to whatever star we may direct the telescope, however far that star may be from the Pole, or however near it may be to the Pole, the telescope does continue to revolve after it, so that the star is always kept in sight, or in the field of view. Inasmuch, therefore, as all the stars appear to revolve uniformly round one axis, it follows that the stars keep their relative places or positions, that is to say, the heavens turn as it were all of a piece. Of course there is no explanation of that, except one of these two—either that the heavens are solid and go all of a piece; or that the heavens may be assumed to be fixed or immovable, and that we and the earth are turning instead of them.

I then particularly mentioned that, taking advantage of this circumstance, instruments are contrived for daily use in every Observatory in the world, as adapted to defining the places of celestial objects. In the first place I directed your attention to the transit instrument, as one of the most important instruments used in taking our observations. This is mounted like a cannon, turning upon two pivots, and possessing no other motion; these pivots resting on stone piers, if the instrument is of a large size, or upon metal piers, if the instrument is of a smaller size; the telescope so adjusted, and turning in this manner, moves only in the meridian. And here it is important to remark that in all standard observations in Astronomy, the instrument is not turned to stars in any part of the heavens, but we have to wait until the stars come upon the meridian. We must so manage as not to be too late, or we lose our observation. The transit instrument must be adjusted in reference to our notion of what we want to observe. The object of all this is to define the places of the stars, in relation one to another; the places of the planets, the sun, the comets, the moon, in relation to the stars, and so on: in fact the use of all observing instruments of this class is to define the place of one object in relation to some one or other fixed objects. I then endeavoured to explain that for exact definition of the place of an object, it is necessary to use a system of what, in mathematics, are called co-ordinates; and that, when the object is or appears to be upon a surface, two co-ordinates are necessary. By this term, I mean two measures of some kind or other; as distances from two fixed lines, or distances from two fixed points, or length of the line from one point and inclination of that line to the horizon. Thus, for determining the position of the stars in reference one to another, it is a matter of importance to choose the most convenient co-ordinates. Considering the stars as they are represented on the celestial globe, if we wish to define the place of any star, the most convenient co-ordinates we can use are these: in the first place, to see how far the globe must have turned from a certain position before the star passes under the brass meridian; and in the next place to see when that star passes under that meridian, how far it is from the Pole round which the globe turns.

I then pointed out that the transit instrument is one of the instruments particularly adapted to this purpose. The transit instrument does by its motion on the axis I described, trace on the sky a curve exactly similar to the brass meridian of the globe, provided these conditions be observed: first, the axis must be horizontal; secondly, the telescope must be square to its axis; and thirdly, when the telescope is turned to the north, it must in its sweep pass over the centre of rotation of the stars. All this I fully explained, but I give this recapitulation that it may be kept in recollection as we proceed with our lectures. By means then of this transit instrument, the condition of representing the brazen meridian by an imaginary track of the telescope through the heavens is fulfilled. I then mentioned that we make use of a clock in all observations; that the way of using it is, having noted the time when some star or object passes the meridian, to find by the clock the interval of time until other stars or planets pass the meridian.

I may now add one subject which I omitted, and it is to state what we mean by a Sidereal Day. We observe on this day a bright star, for instance Arcturus, passing the meridian. We note the time by our clock, in hours, minutes, and seconds, and the fraction of a second. To-morrow we again observe the passage of Arcturus across the meridian. The interval between these passages is a sidereal day. A sidereal day is not quite the same as a common day. But I do not insist on that at present, because it is connected with other things, one of which is the motion of the sun. It is important to understand that that is what we mean by a sidereal day. I cannot tell you now what sidereal time is, and for this plain reason: I have not yet got the starting-point which marks the beginning of the sidereal day. All that I can at present say is, that the interval from the time of the passage of one star one day, to the time of the passage of the same star next day, is understood to be twenty-four hours of sidereal time.

Having proceeded so far in relation to the times of the passing of the stars, and the quantity of rotation which the globe must perform from the meridianal passage of a fixed star which we know, to that of a planet or similar object whose position we want to determine, I mentioned the use of the Mural Circle, by which we determine the altitude of the object when it is passing the meridian. And here I must observe, that one of the most important adjustments of the Mural Circle depends on reflection from the surface of quicksilver. It is not my province now to allude to optics as a science; I merely allude to it to indicate a thing important to our present purpose: the law of reflection of light from a surface of quicksilver. The surface of the quicksilver takes a position parallel to the horizon, with a degree of suddenness and certainty to which we know nothing similar. Light is reflected from the surface of the quicksilver, just as it would be from a looking glass. Now, the thing which I wished to point out as the great practical fact is this: that supposing SG and S′O, in Figure 13, to represent the direction of the light coming from the star, and OG′F′ the direction of the light reflected from the quicksilver; then the inclination of S′O or SG to the horizon is the same as the inclination of OG′ to the horizon; and if S′O or SG approach nearly to a flat with the horizon, OG′ will approach nearly to a flat with the horizon; and if S′O or SG approach nearly to a perpendicular to the horizon, OG′ will approach nearly to a perpendicular to the horizon. These are the facts upon which the use of observations by reflection is founded. If we place this small trough in such a position that the telescope looks into it, and if we see a star, we know that the light which comes from that star is reflected in such a manner, that the position of that telescope must be as much inclined downwards, as the position of the direct ray of light from the star is inclined upwards. From these observations we infer the position of the telescope when it is horizontal I then pointed out to you that by the use of this, we ascertain the elevation of the Polar Star at its highest and its lowest positions, and that by taking the mean of these we have the height of the Pole; and therefore, getting the elevation of the Pole on one side of the Zenith, and getting the elevation of any other star or any object whatever, passing either on the same side of the Zenith or on the other side; by means of these we ascertain the angular distance of any object from the Pole.

Incidentally, I had occasion to point out to you some other things. One of these was the use of the wires in the telescope. And I constructed as it were a telescope, Figure 7, though it has no tube. The telescope I have here made consists of a lens, representing the object glass of a telescope, and a screen, representing the field of view. Formerly telescopes were made without any tubes at all, so that the tube of a telescope is totally unessential. The construction I have got there is a proper representation of a telescope, forming an image of the object on the screen, which screen is in the place in which you would see the object. Instead of looking at the screen from a distance, you may come close to it and view it with an eye-glass on the side opposite to to the object glass, and then the resemblance to the telescope is complete. You see upon it bars representing wires in the field of view. The object of these is to give definiteness and distinctness to the observations. Supposing I use the telescope by directing it to a star: if I see a star somewhere in the telescope, this is a very loose observation, because I have not sufficiently defined the place; but if I have wires in the telescope, and observe the star on any one of these wires, then I have observed it in a definite part of the field of view. The accuracy gained by that observation is very great indeed; it is the most important adjunct connected with the use of the telescope. Every surveyor knows the value of the wires in his theodolite telescope.

There was another thing I pointed out, which was that the rotation of the stars, when it is examined closely, is not so accurate as might be supposed at first, for this reason: that we always find that the stars near the horizon appear higher than they really are in fact—whether east, north, or west, they are always a little too high—I ascribed that to refraction. And I pointed out, as a law of refraction, by reference to a glass trough or prism of water, that if the light falls on a surface of glass, it is bent there in such a manner as to go more square to the surface. I had occasion in the last lecture to mention strongly my disapproval of the use of some words in a wrong sense. I shall now mention another word which is often used in a wrong sense: I allude to the word "perpendicular." Many people think that the word "perpendicular" means the position of a plumb-line. It means no such thing, The proper word for describing that position is " vertical." Perpendicular is a relative word, and it ought not to be used without reference to something else. Vertical is an absolute word. Thus, in speaking of the word perpendicular, with reference to that trough of water or prism in the experimental case before us, I mean a line perpendicular, not to the horizon, but to the surface of the trough. I explain that particularly, because in connection with these matters, from defective education and other causes, false meanings are often given to words. The law of refraction is this: that when that beam of light represented by AB, in Figures 4 and 5, enters the side of the prism, it is bent into a position approaching more nearly to the direction of the line perpendicular to the surface. The refraction of light produced by glass or water is well understood. We know by experiments too, that air produces refraction. We apply the same laws which relate to water or glass, to the computation of refraction by atmospheric air. We find that air will alter the course of the light in such a manner, that the beams of light enter our eye more vertically than they otherwise would do; that all objects will necessarily appear to be higher than they are in reality; and applying then a proper correction by the law of refraction, based upon experiments with water or glass, we find everything properly adjusted, and that the stars revolve round one axis most accurately in the manner we have represented. These, with some additions were the main points of the subject of yesterday's lecture; I will now proceed to the lecture of to-day.

I have stated my intention of explaining how we measure the distance of the sun, and the moon, and the stars from the earth by a yard measure. When I say that we really measure these distances by a yard measure, I do not wish to weary you by the word, and I do not wish to introduce anything inelegant; but I do wish to produce distinct and definite ideas in your minds to urge this, that we really do make use of a yard measure, or something equivalent to it, as our fundamental measure for these purposes. I will now proceed to explain the first step towards taking these measures.

The object we have in view is to measure a great distance upon the earth; a distance, for instance, extending the length of a kingdom. Figure 14 (see Frontispiece) represents nearly the whole of the British Islands. I wish to point out how the distance is measured from the Isle of Wight at A, to the Shetland Isles at B. In the first place I must tell you, that the distance has been measured with such accuracy that I think it likely that the distance is known with no greater error than perhaps the length of this room. Now, measures of this kind are effected by a system of triangulation. This is in some degree or other well known to every surveyor, but still I esteem it so important to the whole subject before me, that I shall point out to you the way in which it is done. Suppose then, that we have three places, EFG, Figure 15; the two nearest, E and F, on a plain

Fig. 15.

with even ground between them, and perhaps six or eight miles apart ; a third, G, at a considerable distance, perhaps inaccessible, at least in a straight line from E and F. I can measure the distance between E and F, because there is even ground between them. But how do we get the distance of G? In the first place we actually measure the distance between the two nearest, E and F. In the prosecution of surveys of this kind, it is a great object that we should choose ground favourable for taking the measure; it is necessary that the ground should be very level, and, if possible, firm. The line so measured is called the Base Line. Bases have been measured in the British survey on Hounslow Heath, Romney Marsh, Misterton Carr, Salisbury Plain, and other places; but the principal base measured in the United Kingdom for several years past, and on which the measure of almost every part of the kingdom depends, is one in Ireland, traced along the east side of Loch Foyle, near Londonderry. It was measured on the sand; and the smoothness and level of this soil served well for the purpose.

Now this base is measured by a very troublesome operation indeed. You may think it easy to measure a straight line, but, in fact, there is nothing so difficult. In the first place what are you to measure it by? Are you to use bars of metal? They expand by heat. It is to be measured by the yard. If so, what do you mean by a yard? By the measure of a yard we mean a certain distance, not something imaginary or variable, but a distance definite and certain. But we do not mean the length of any piece of metal, because it changes its state by the action of temperature: it becomes longer when hot, and shorter when cold. If I use a piece of metal, I say a yard means the length of this bar of iron or brass at a certain temperature. Now, many bases have been measured with, bars or chains of iron or brass, but in every part of the operation every possible care has been used to screen them from changes of temperature, by covering them with tents; putting perhaps half-a-dozen bars at a time in a row, with twenty yards of tent over them, so as to protect them effectually from the sun and wind. Having taken these precautions to guard them from the effects of changes of temperature, thermometers are placed by the side of the bars. Then by carefully observing the state of the thermometer, and knowing the expansion of the bars by heat, or their contraction by cold, we can ascertain what length these bars represent under the circumstances under which they are used. But there was another contrivance used specially in the Loch Foyle base. It was used for the first time there; it has been since used in India, and at the Cape of Good Hope. Figure 16 represents

Fig, 16.

a combination of two bars; one, ABC, of brass, and the other, DEF, of iron, connected at the middle BE, and having projecting tongues, ADG and CFH, which are connected with both bars at the two ends of the bars. Now, the use of the combination is this: brass expands by increase of warmth considerably more than iron, in the proportion of 5 to 3, as nearly as possible. If I arrange the bars in this manner, and choose points G and H in such positions that DG is three-fifths of AG, and FH is three-fifths of CH; then the distance between H and G is not disturbed by the expansion of the two bars. The iron bar expands, the brass bar expands more; and by that increased expansion of the brass bar, the two points G and H are brought inwards by exactly the proper quantity. In this manner a means of measuring has been attained, which, in the judgment of many persons who have used it, is better suited to the purpose than anything else that has been used or adopted. I have described in detail this apparatus to shew the extreme caution necessary in these matters.

A succession of combined bars like these are placed one after another, with a small interval between each and its successor; and then the question is, how is the interval between them to be measured? It will not do to make one bar touch the other, because expansions may be going on in one of the series of bars, and it would jostle the others throughout the whole extent. In the measure of which I spoke, this small distance was measured by means of microscopes; and these microscopes were so mounted (on the same principle as the bars) that the measure which they gave was not affected by temperature. In some of the surveys on the Continent, glass wedges have been dropped between the successive bars; in some others, there have been sliding tongues used; indeed an infinity of contrivances have been used to overcome the difficulty. The effect of all this has been, that a distance of 8 or 10 miles has been measured to within a very small fraction of an inch. This is the first application of the yard measure, by which the distances of the sun, the moon, and the stars are to be measured. In figure 17,^[1] EF represents the base on Misterton Carr, connected with, the triangulation, by which the distance from A (Shanklin Down, in the Isle of Wight) to D, (a place called Clifton, in Yorkshire,) was measured.

The next thing to be done, having measured the length of the line EF, Figure 15, is to measure the distance of the signal G. It is, perhaps, on a mountain, perhaps with sea between it and EF. The object is to get the signal as far off as it can be seen. These signals have been observed at the distance of 110 miles. Signals in Ireland, on the Wicklow Mountains, and on Slieve Donard, have been observed from Ben Lomond, in Scotland; from Precelly and Snowdon, in Wales; and from Scaw Fell, in Cumberland. Having, then, measured EF, I wish to ascertain the distance of G. For that purpose I take away the signal at E, and plant a theodolite in its place. The theodolite is adjusted on the point E with the utmost care. Now, by means of this theodolite, making use of it in the usual manner, first of all I observe the signal F at the end of the base, and then turning it until I observe the signal G on the distant hill, I obtain the angle of an imaginary triangle GEF, if you may so call it The triangle is, in fact, formed by the rays of light which come from the signal at one station, to the eye, or instrument, at the other; when I turn the telescope of the theodolite at E towards F, it is in the direction of one side, EF, of the triangle; and when I turn it so as to view the distant signal G, it is in the position of the other side of the triangle; and therefore the angle, by which the theodolite turns, is the measure of that angle FEG of the triangle. I then plant the theodolite at F; I direct it in like manner to the end of the base E, and then the light it receives is in the direction of the side of the triangle FE ; I turn it then to the same distant signal G. Therefore, by these observations, I have really and truly got, by the theodolite, the measure of the two angles of the triangle at E and F. Now, that is sufficient. Every person who has a knowledge of trigonometry, knows that if we have got the measures of the side EF, and of these two angles, we are able, either to construct the triangle on paper, or to determine, by calculation, the whole of its parts. Or, without pretending to understand or to have heard of such a word as trigonometry, any person can see, that by observing how much I turn the telescope at E, for instance, I can make the same turn of a line on paper; that I can make the two directions of the line incline to each other by that angle. Knowing how much this telescope has been turned from one object to the other, I can make the same angle on paper here; I can do the same for the other end of the base, and then, prolonging these lines until they meet, I get the distance of the distant signal. This is sufficient. But, to make assurance doubly sure, it is usual to place a third theodolite at G, and then to observe the signals at E and F. And the reason is this: we know by geometry that if we take the measures of the three angles at A, at B, and at C, in degrees, minutes, and seconds, and add them together, the sum will be 180 degrees; so that the observation of the angle at G, is a verification of the measures of the two angles at E and F.

Now, then, we have made the first step in triangulation. Having measured the base line EF, by means of a yard measure, as represented by some of our standard rods, and having measured the angles, we have, by the process I have described, got the length of these other sides of the triangle. Then, in like manner, having thus got the length of the side FG, we can use it as a base measure to determine the distance of the signal on another distant point; and thus we go on, step by step, until we get from one end of the kingdom to the other. I have represented, in Figure 17, the triangulation connecting Shanklin Down with Clifton Beacon. This is a part of the great Meridional Arc of England. Some persons, I have no doubt, are present now who have seen a place in the Isle of Wight, called Shanklin. Northeast of the village is a high swelling Down; a point on this Down is the southern extremity of this triangulation. The names of the stations which follow are marked in the diagram. Signals were placed upon the successive stations; at each of these theodolites were placed; from each of these the signals were observed upon the other stations; and so we step on from one point to another, till we arrive at Clifton, a village in the south of Yorkshire; and (by continuing the triangulation) at Balta, in the Shetland Islands. The outlines of the counties through which the survey was made are roughly drawn on the diagram, in order to give a notion of the size of the triangles. The line, for instance, which connects Brill with Stow goes over the widest part of Oxfordshire, from a signal external to it on the eastern side, to another signal external to it on the opposite or western side. In this way we step over a country at few steps; and when the angles of all the triangles are accurately measured, the results may be laid down on paper. I have spoken of beginning from the south end of the triangulation; but in the process of making the computation, we must (in this instance) begin from the north end, because it happens that the base EF is there.

The next thing is to get the direction of one of these lines. This is got by a transit instrument, or something equivalent to it, adjusted in the same manner which I described yesterday, by the Polar Star. The transit instrument suppose at K, Figure 17, is adjusted to the north, so that the telescope passes through the Pole: the telescope is turned down to the horizon, and a mark L is fixed by means of it in the true north direction of the horizon. Then the theodolite is used to measure the angle LKM between this mark and some other signal: and knowing the northern direction in that way, we are enabled to lay down the whole of the triangulation on paper, and to see how many yards the point D is north of the point A. That is the first result of the meridional triangulation through a country; it is a point which it is most important for us to understand by way of beginning.

Now let us see how this is to be used. What do we want to ascertain? We want to ascertain something about the size and form of the earth. I remember a man in my youth who used to say he should like to go to the edge of the earth and look over. I don't think that many people, who have ever considered carefully the state of things around them are impressed with notions of that kind; but my friend was, in his inquiries, an ingenious man, a sort of philosopher in his way. Still, if he had looked about him, he would have seen that the earth did not present such a condition as would enable him to go to the edge of it and look over. I dare say that there are many persons here who have come by sea from London to Ipswich, and have observed Walton Tower rising out of the edge of the waters. Many persons, too, who have gone across the Irish Channel, have seen the mountains on one side disappear, as if they dipped into the sea, and they have also seen the mountains arise out of the sea on the other side, perfect in shape, coming out by degrees, just as if seen rising over the brow of a hill. The inference is, that the water is curved, to produce these phenomena. These are to be seen in the course of ordinary expeditions; but those who voyage further, those who have gone to the Cape of Good Hope, know that, as they go on, every night they lose sight of our stars by degrees, and other stars come up on the other side. In a southern latitude they lose the northern stars, and they get more of the southern stars. All this leads us to the conclusion that the earth is something curved. Again, people have sailed round the earth. This was done for the first time by Magellan and his successors in command: and for the second time by Sir Francis Drake. From the time of Sir Francis Drake, this has been done every year; ships are indeed almost daily prosecuting such voyages. It is a common thing for ships to sail in an easterly direction to Australia, and to return by continuing their eastward course, and not by coming back the same way they set out. The earth, therefore, roughly speaking, is something round, and there are limits to its extent.

Now, the question is, what is its extent? Having got a measure of considerable length by such a process as I have described, how can we use that to determine what is the size of the earth? In order to explain this, suppose Figure 18 to represent a slice of the earth, curved as a slice of the earth would be.

Fig. 18.

Now, you will understand from the description which I have given, that in the first place, by measuring a base by means of a yard measure; in the next, by measuring successive triangles originating with that base; and therefore, in fact, computing the length of every side of these triangles by means of a yard measure; you will understand we have really ascertained, by means of the yard measure, the distance from the Isle of Wight A, to the little Island of Balta B, in the Shetland Isles. Now, we want to measure the corresponding curvature of the earth, that is, to find how much the line drawn from A to B on the surface of the earth is bent. For that purpose we use an instrument called the Zenith Sector, Figure 19—a telescope swinging upon pivots AB, and having attached to it an arc CDE graduated into degrees and minutes. There is a plumb-line CF connected with the upper end of the telescope, or with one of the pivots; it is a very fine silver wire, supporting a weight F, which weight is hanging in water, to keep it steady. It gives us the direction of the vertical there, or the direction of the perpendicular to the horizon, (see page 15.)
Fig. 19.

Now, assuming that we are observing a star very nearly overhead—it is plain if the telescope be directed to the star, then by observing the point of this divided arc CDE, which is crossed by the plumb-line, I have got a measure in degrees, minutes, and seconds, of how far the star is from the vertical. And the peculiar advantages of using this instrument instead of the Mural Circle, are these: first, it is easier to carry about from one situation to another; and next, the observations made by it are confined to that part of the heavens where the refraction is scarcely sensible. Refraction is a thing which, (from the uncertainty attending the calculation of it,) baulks us perpetually, and which it is very desirable to get rid of as much as possible.

Now then, the way in which this instrument is used, in order to ascertain the form of the earth, is as follows: we take our Zenith Sector to Shanklin Down and to the Shetland Islands. Now, consider for a moment. What do I mean by the earth and water being curved? The direction of the vertical is perpendicular to the surface of water; and therefore, if the water be curved, it is connected essentially with the circumstance that the direction of the vertical is varied, or that the direction in which the plumb-line hangs is not the same at different places. Therefore, if the earth, Figure 18, be curved, as we suppose, and as previous rough considerations have given us reason to think, the plumb-line at A would hang in the direction CGF, and that at B in the direction c g f. The place of the star, however, which I observe, is unaltered. The telescope is to be pointed in the same direction, whether we use it at Shanklin or Balta: or the line CD is parallel to c d. Suppose, therefore, I have gone through the observations in the way I have described, by observing what part of the limb of the Zenith Sector is crossed by the plumb-line; I get different parts of the limb in the observations at these two points. When I am observing the star at Balta, the plumb-line crosses at g; when I am observing it at Shanklin Down, the plumb-line crosses at G. Thus we obtain the difference of the direction of the vertical at the two places.

Fig. 20. Now, then, I have arrived at something which I can use for taking the dimensions of the earth. In the way that I have described I have the inclination between the line, which is perpendicular to the surface at A, Figure 20, and the line which is perpendicular to the surface at B. If I continue these two lines downwards until they meet at a great distance below, as at H, I shall get a centre from which I may make a sweep to describe the curvature of this part; or, in other words, a centre, about which I may describe a circle passing through A and B, and such, that its arc AB, shall be exactly as much bent as the line AB on the earth's surface. If the earth be spherical or round, it is plain that these lines come to the earth's centre, and the distance AH, which I have found is the semi-diameter of the earth.

If you take numbers, you will see how we assume this to be effected. Suppose the measure of AB is 830 miles. Suppose I find that the directions of the two vertical lines AH and BH, in the two places A and B, make an angle of 12 degrees. You will remember what a degree means. It is not a measure of length; it is a measure of inclination of these two lines. I have to pass over a distance of 830 miles, in order to get from one place to another, where the direction of the vertical changes 12 degrees. From that I infer that the curvature of the earth is such, that I have to pass over 69 miles to find the distance of two places whose verticals are inclined one degree. Having got that, it is easy to find what is the semi-diameter of the circle which you must sweep, in order that that distance of 69 miles may give one degree of inclination of the two lines, drawn from the centre to the ends of the 69-mile arc. Making the calculation, you find the semi-diameter is about 4000 miles. And this is the way in which the measure of the earth was ascertained in the first instance. The first accurate measure was made in Holland, by a man named Snell; the next by a celebrated man, Picard, in France.

Shortly after this, Sir Isaac Newton's theory of gravitation was broached. He predicted, as a result of theory, that the earth would be ascertained not to be round, not spherical, but spheroidal, or flattened, turnip-shaped. It was a matter of importance to verify this. The first expedition for this purpose was made by the French Government, under the Kings of France; and all honour be to the French for the part they took in this matter! Many of you are aware that Guizot, the late Prime Minister of France, before he was appointed Minister of the Crown, was Professor in one of the French Colleges. He gave lectures on the History of Civilization, and he maintained that France had been the great pioneer in science; that civilization generally had originated in France. I believe that in matters of science it is as stated by Guizot. When the question of the figure of the earth came to be debated, two celebrated expeditions were made under the auspices of the French government; the first great scientific expeditions ever made in the history of the world. The party composing one expedition was sent to Lapland, to make a triangulation in the way I have described, and to make corresponding observations with the Zenith Sector, beginning at Tornea, at the head of the Gulf of Bothnia, and carrying the survey northward for about fifty miles. Another party was sent to Peru to make a similar measurement, but about two hundred miles in length. And no two expeditions ever rendered themselves more justly celebrated than these. Now, observe the results.
Fig. 21.In Figure 21, AB represents the Lapland measure, a b the Peruvian measure. It was found, that in Lapland they had to go 69¾ miles, or something like that, in order that the directions of the verticals should change one degree. It was found in Peru that they had to go only 69 miles, in order that the direction should change one degree. From this, it follows that the verticals AH and BH in Lapland meet at a point H, whose distance from A or B is about 4000 miles; and that the verticals a h and b h in Peru meet at a point h, whose distance from a or b, is about 3950 miles.

What is to be inferred from this? We have said that the estimation of the semi-diameter of the earth, supposing it to be a sphere, would depend on the distance you have to go, in order that the direction of the vertical might be altered by one degree. We have to go further in the northern measure than in the equatorial measure. It would seem at first sight, as a consequence, that the earth was not turnip-shaped, but egg-shaped; and this was maintained by many respectable people at the time. On consideration, it appeared that this was not a correct inference. And the reasons were these: when we assume that the earth is spheroidal, not spherical, then, inasmuch as we mean by the direction of the vertical "the direction of a line perpendicular to the surface of the water," the direction of the vertical will not go to the earth's centre at all. It is necessary to consider something different, and that is, that the measures which we have obtained, give us information of the curvature of different points of the earth. They tell us that at AB the curvature is little, but that at a b the curvature is very sharp. Altogether, when properly considered, they lead us to the inference that the form of the earth is something like the oval in Figure 21; that it is flatter at the Poles, and sharper in its curvature at the Equator. The rule which theory gave was, that the earth would be spheroidal; that is, that its form would be that which is produced by the curve called the ellipse,^[2] Figure 2la, revolving round its shorter axis BB′. Adopting then the supposition that the earth is spheroidal, it was a

Fig. 21a.

matter of calculation to determine from the geometrical properties of the ellipse, what would be the proportion of the two axes, AA′, BB′, of the earth, which would make the proportions of the curvatures at AB and a b, similar to those determined from the observations. It was inferred that they were in a proportion something like 299 to 300.

Since that time, extensive measures have been taken on other parts of the earth. At the Cape of Good Hope, a measure was made by Lacaille, a Frenchman, in the first instance. At the present time, I am happy to say, that this measure has been repeated and much extended, under the direction of the British Government, by Mr. Maclear, the Astronomer at the Observatory of the Cape of Good Hope. In England, the arc from the Isle of Wight to the Shetland Islands, to which I have several times alluded, has been measured. In India, an arc, extending from Cape Comorin to the neighbourhood of the Himalaya Mountains, has been measured under the direction of the East India Company. In Russia, the measurement of an arc is going on at the present time, extending from the mouth of the Danube to the North Cape. It will form one of the best means of determining accurately the dimensions of the earth. There is also one measure which is worth mentioning, on account of the extraordinary times in which it was effected. It was the great measure extending from Dunkirk, in France, to Barcelona, in Spain, and which was afterwards continued to Formentera, a small island, near Minorca. It is worth mentioning, because it was done in the hottest times of the French Revolution. We are accustomed to consider that time as one purely of anarchy and bloodshed; but the energetic Government of France, though labouring under the greatest difficulties, could find the opportunity of sending out an expedition for these scientific purposes; and thus did actually, during the hottest times of the revolution, complete a work to which nothing equal has been attempted by England.

Now, from all these measures put together, we are able to infer a proportion of the axes of the earth, and we are able to try whether all these different measures agree well with the supposition that the earth is a spheroid. There is a quantity of mathematical calculations concerned in it; the problem is this: suppose the earth to be a spheroid, with axes in any proportion that we choose to try; then to calculate mathematically the length of the measure corresponding to the observed inclination to the vertical in different parts of the earth, and to find how nearly these calculated measures agree with the measured arcs; to ascertain whether they agree so nearly that there is no discordance beyond what can be fairly explained by the circumstances of the observations. They come to this: the proportion of the two axes of the earth is as 299 to 300: the shorter axis of 41,707,600 feet would pass through the Pole, and the longer one of 41,847,400 feet would pass through the Equator: and the measures computed on this supposition for different parts of the earth, do agree well with the measures actually made.

There is another method used for the same purpose, founded on the observations of arcs of longitude, which has not, however, been used so extensively as the other. Suppose we place a transit instrument at Greenwich, and observe the time when a star passes the meridian; suppose we place a transit instrument on the coast of Ireland, and observe the time when the same star passes the meridian there. It will be found that they do not pass at the same time. Why? Because the earth is curved. Let figure 22 be

Fig. 22.

understood to represent the earth, with its Pole P turned towards the eye, K and L, two stations, and S a star that is viewed; and consider what will be the positions of the transit instrument at K and L. If I place a transit instrument at K (which may represent Greenwich), the plane in which the instrument will move is the plane of PK, (see page 25,) and the instrument will catch the stars where they pass through that plane. If I erect a transit instrument at L, (which may represent a station on the west of Ireland,) its plane of movement will be PL, inclined to the plane PK. They both pass through the axis of the earth. The two planes will be inclined; and the stars will not appear to pass these two planes, or through the two transit instruments, at the same time. The interval of time will depend entirely on the inclination of the meridian at these two places. If, then, we erect a transit instrument in one place, and another transit instrument at another place, and compare the times at which the same star passes the two transit instruments, we have the means of seeing how much the planes of the meridian are inclined. Its makes no difference whether we suppose the earth to turn round so as to bring the plane of PL to pass through S, or suppose the star to turn round the earth, so as to make S pass through the plane of PL; the result is just the same. Now there are various ways^[3] in which the comparison of the times may be effected. One of them is by the use of an instantaneous signal of light. If I fire gunpowder on a high mountain, and if my assistants observe, from the two places where the instruments are placed, the time when the flash of gunpowder is seen, I can compare the clock at the two places. One person observes the clock-time at the one place when the flash occurs, and another observes the clock-time at the other place when the flash occurs; and therefore, as soon as a letter can be sent by post from one place to another, I know how much one clock is faster or slower than the other. Another method is, by conveying watches, or small chronometers from one place to another. For instance, an expedition was arranged by myself some years since, to observe the difference of time between Greenwich and Valentia, on the south-west coast of Ireland. I had thirty chronometers carried backwards and forwards more than twenty times from Greenwich to Valentia, to compare the clocks. The chronometers were conveyed by railway carriages, by steam boats, by mail coaches, and by Irish cars, between Greenwich and the west of Ireland. By means of these I was enabled to compare the clocks at the two places; and by transit observations made with the assistance of these clocks, and with proper calculations, the times of the transits of the stars were compared, and therefore, I got the inclination of the planes of the meridian. By a survey-triangulation, extending in the east and west direction from Greenwich to Valentia, the distance was known in yards; and, knowing the distance, and knowing the inclination of the planes, the whole circumference of the parallel

of latitude passing through Greenwich was easily computed. Then we have to examine whether this circumference corresponds to the circumference calculated on the supposition that the earth is a spheroid, with a shorter axis of 41,707,600 feet, and a larger axis of 41,847,400 feet, and it is found to correspond well.

By means, then, of meridional measures by triangulation, and the Zenith Sector, and by means of east and west measures by triangulation, and observations with the transit instruments and comparisons of clocks, we have got sufficient information upon the form of the earth. Now, observe the very important conclusion to which that leads. In the observations given in the former lecture, we found that the whole of the heavens appeared to revolve, and we say, either the heavens revolve in the direction from the east, through south, to west; or the earth revolves in the direction from west, through south, to east. Which of these is the more likely? Astronomers agree without exception, that it is the earth which revolves. And I will tell you why. I dare say every person whom I see here has been brought up in the belief that the earth does turn round. But, I ask, if they had not been brought up in that belief, whether they would believe it now from what I am telling them? I do not think they would. Amongst all the subjects of natural philosophy presented to the human mind, there is none that staggers it so effectually as the assertion that the earth moves. We must not be uncharitable, then, towards people in the middle ages who did not believe it. To think that the solid earth moves, that the solid ground is going round at the rate of one thousand miles an hour, do you believe it? I will endeavour to give you grounds for the belief.

In the first place, I must say that even the astronomers of antiquity had got a rough notion of the distances of some of the celestial bodies. But one will do for our present purpose. The moon is a long way off. There are phenomena observed frequently, in the interpretation of which there can be no mistake, namely eclipses of the moon. We see that the moon, in her motion through the stars, dips into something which obscures her. There cannot be a doubt that it is the shadow of the earth. The moon goes into this shadow on one side, and comes out of it on the other side. The time which the moon occupies in passing through this shadow is, roughly speaking, four hours. The moon, then, is at such a distance that in passing through the shadow of an object as big as the earth, she is occupied only four hours. The moon, therefore, in her course describes the breadth of the earth in four hours; in one day she describes six times the breadth; and as thirty days is a rough measure for the time of her revolution, she describes in one revolution 180 times the breadth of the earth, and therefore the whole circumference of the moon's orbit is something about 180 times the breadth of the earth, and the diameter of the moon's orbit is about 60 times the breadth of the earth. Therefore the moon is distant from us by about 30 times the earth's breadth.

But there are other facts founded on observation. The sun is further off than the moon. There are phenomena called eclipses of the sun. We know that these correspond to times when the moon apparently approaches the sun; they are undoubtedly caused by the moon passing in front of the sun. Again, the stars are further off than the moon; because the moon passes in front of the stars, producing what is called occultation. But they are not only further off than the moon, but they are a good deal further off than the moon; and the reason for knowing it is this; suppose one object is close behind another, then the more distant object will either be hidden by the nearer, in whatever part of the earth we may observe it, or will not be hidden at all. But suppose the more distant object to be a long way off, then, when it was hidden from one part of the earth, it would be visible to another part of the earth. Now, that is the case with regard to the eclipses of the sun and occupations of the stars. If we examine into the appearances of an occultation, as seen at different parts of the earth, in some parts a star is hidden by the moon, in others it is not hidden at all. If we examine into the circumstances of a solar eclipse, as seen at different parts of the earth, in some parts the moon is seen on the north side of the sun: in other places the moon covers the sun; and in other places the moon is seen on the south side of the sun. It follows that the sun is, a good deal further off than the moon. Thus it appears that the system of heavenly bodies which surrounds the earth is of considerable size. The moon is far off; the sun and stars are much further off than the moon. The moon, therefore, is not a small body, and the sun (which in spite of its great distance appears so large) must be a very large body. The stars are either connected in one system, or are so very far off that their relative movements are insensible.

Now, is it more likely that this large frame of things is turning one way, or that this small earth is turning the other way? Anybody must see at once, from the magnitude of things, that it is most probable the earth is turning round. And, as regards the stars, the mere circumstance of their seeming to move all in a piece is a strong proof that they do not move sensibly, but that the earth moves. If you apply the same reasoning to any ordinary sublunary considerations, you will be struck at once with the conclusion. If I am sailing in a ship on the open sea and see vessels moving about me in all directions, and if any person in the ship asserts that our own ship is at rest and that all the others are moving, there is nothing particularly unreasonable in it. But if I am entering into the Ipswich river, and I see not only ships moving, but every church and warehouse, and the solid banks which connect them, moving past me, and if a friend at my elbow should say, "you are not moving, but all these solid things, churches and houses, and fixed objects and banks, are in motion," I should consider him to be a madman. The argument is precisely the same as applied to the heavens. If we had nothing but the sun and moon turning about in various ways, even then, and remarking their great size and their great distance, and the great speed with which they must be supposed to turn, (for the moon must be supposed to move at the rate of 60,000 miles an hour, and the sun very much quicker,) their daily revolution round the earth would be very unlikely. But when we have things of such an immovable character as the system of the stars, (like that of the banks of a river, or the solid erections which are there visible, as compared with our small sailing ships,) then the reason of man tells him at once that these things must be things of a fixed character—and that if these things be things of a fixed character, it is we who are turning and the earth which goes round. This is reasoning which ought to be received, and I cannot see why it was not received by those who were able to reason on the matter in more distant times.

But when the telescope was invented, fresh objects presented themselves for contemplation, and new arguments were furnished. We then obtained a sight of the planets, particularly of Jupiter. We saw that he is a spherical, or rather spheroidal planet, like the earth, but probably much bigger. We can see spots upon Jupiter, and by these we can ascertain, that he revolves in a much shorter time than the earth, or in about ten hours. Now, the knowledge of these things in later days has become a very strong argument indeed. Jupiter is a large planet that turns on his axis, and why do not we turn? We are very much alike in our general character.

But, finally, we come to another observation, founded on our determinations of the figure of the earth. We have found, from measures, that the earth is flattened at the Poles, or turnip-shaped. This leads, then, to the question—is that connected with the rotation of the earth? Most certainly it is. If we take anything circular which admits of a change of form; if, for instance, we mount a hoop, as in

FIG. 23.

Fig. 23, in such a manner that we can make it revolve rapidly, and whirl it round; then as soon as the motion of rotation takes place, the hoop becomes flattened.

From all these considerations then, put together in proper order, we infer, as a matter of positive certainty (however hard it may be at first for our minds to receive it), we infer as a matter of certainty that it is the earth which revolves.^[4]

I shall now proceed with the next subject—the apparent motion of the sun amongst the stars. I make a point of entering upon this subject at the present time, that I may address to you some rough observations for your guidance in the enquiries which this subject involves. I shall explain to you the evidence which is within your own reach, and which proves that the sun apparently moves through the stars. I have not yet specially alluded to the sun in speaking of revolution; my remarks on that point referred only to the stars. I am now, however, going to speak of the sun a little, though it is necessary to have the stars to begin with, as fixed points in the heavens.

Everybody knows the leading difference between summer and winter; we know that the days are longer in the summer than in the winter. If you consider for a moment something else which you know and have remarked, you will see this, that the position of the sun is different in summer from what it is in winter. In summer, the sun at noon-day is high in the heavens; in the winter at noon-day he is low. In summer, the sun is a long time above the horizon, and a short time below: in winter he is a short time above the horizon, and a long time below. In summer, the sun rises north of the east point, and sets north of the west point; in winter he rises south of the east point, and sets south of the west point. These observations are all explained by saying that in summer the sun is nearer to the North Pole, and in winter nearer to the South Pole. And this you can verify without the smallest trouble, from your own observations.

Now, I will offer a few words in regard to the stars visible at different times of the year. I will suppose that at eleven o'clock at night you look out to see what stars are on the meridian. On the first of January if you look out at eleven o'clock at night, you will see the grand constellation Orion on the meridian; Aldebaran and Pleiades are west of the meridian. The bright star Sirius has not yet come to the meridian. I now suppose that you look out, in the same way, on the first of February, taking the same hour. On the first of February, at eleven o'clock at night, you see that Aldebaran and the Pleiades are setting in the west; that Orion has got a good way to the west; and that Sirius has passed the meridian a little way. There are three conspicuous stars near the meridian, well known by everybody who is accustomed to look at the constellations; namely, the pair of twins, Castor and Pollux, and Procyon, or the Little Dog. On the first of March, at eleven o'clock at night, you again look out; Castor, Pollux, Sirius, and the Dog Star, have then gone away to the west; Orion is now setting; and we then have the stars of the constellation Leo, which is a bright constellation, approaching the meridian. On the first of April, at eleven o'clock at night, you again look out, and you see what is the state of things. The constellation Leo then has almost passed the meridian, except the bright star B (Beta) Leonis. On the first of May, at eleven o'clock at night, you again look out. You then observe that Leo and the whole set of stars are travelling away to the west; and then we have the bright star Spica, in the constellation Virgo, on the meridian: and we have the great red star Arcturus approaching the meridian. In the following month, on the first of June, at the same hour of the night, we again look out. We find that Spica has gone away to the west; that Arcturus has passed the meridian; and that other less conspicuous stars are on the meridian. In the same manner, if we go through the other months of the year; if, at eleven o'clock at night, on the first day of every month, we watch the appearances of the stars on the meridian, and compare them with those of the preceding month, we find that, from one month to another, they all travel on in the same direction towards the west.

Now, what is the inference? Is there any peculiarity in the motions of the stars? No, it is the motion of the sun. Our hour of eleven at night is referred by habit to the motion of the sun; and thus, when we speak of eleven o'clock at night, we mean that the sun is in a certain position; and, therefore, that the stars have moved in a direction from east to west, with respect to the sun.

But this may be interpreted another way. Regarding the stars as fixed objects, we get this: the sun travels round in the direction from west to east among the stars. Besides this, we have found that he travels in such a manner, that he goes nearer the North Pole in summer, and further from it in winter. These are the general facts deduced from our observations. But, supposing we do not trust to them; supposing we make use of the Transit Instrument, and the Mural Circle. By the former we observe how long the sun is passing the meridian after a star; we find it is later and later every day; that every time the sun comes to the meridian, he has travelled (with respect to the stars) towards the left or towards the east, in such a manner, that, in the apparent diurnal motion, or passage, he is later and later, with respect to the stars, every day. Suppose that with the Mural Circle we observe the altitude of the sun every day when he passes the meridian; we find that he is nearer to the North Pole in summer than in winter. Thus, the sun travels to the left, and at the same time changes his distance from the North Pole.

Now, putting these things together, if we were to dot on the globe a succession of observed places of the sun, we should find they would follow each other in a curve, like that marked on Figure 24, (see Frontispiece,) which represents two views of a celestial globe, on opposite sides. This curve is called the ecliptic. It is convenient now to refer our description of this curve to the equator, which is the great circle on the globe equally distant from both Poles. Now, we find that the sun's path or ecliptic, crosses the equator at two points. One of these is called the First Point of Aries, and this is the sun's apparent place at the beginning of spring; from this point the sun appears to approach nearer and nearer to the North Pole until midsummer. He then appears to recede from the North Pole, and crosses the equator in the first point of Libra, at the beginning of autumn, and approaches the South Pole till mid- winter; after which, he turns towards the first point of Aries.

Now, upon examining that curve or ecliptic, we find that it is one of those circles which are called "great circles"; they divide the glohe into equal halves. I have stated this as a thing which would be one of rough evidence; that if, by means of the observations I have mentioned, (namely, how long the sun is in passing the meridian after a star, and what is its angle of elevation when it passes the meridian,) if by means of these we mark on a globe the successive places of the sun, we shall find all the successive points in a curve, such as I have described. When I say that it goes on the globe in such a curve, you must understand that there are ways of computing these things; that having got the interval of time between the sun and a star in passing the meridian, and the angular elevation of the sun when it does pass the meridian, it is possible, by computation, to find whether it is going on in such a curve as I have described; but that these computations, though they amount to the same thing as dotting the sun's places down on the globe, are a great deal more accurate. It is thus found that the ecliptic, or apparent path of the sun through the stars, is accurately a great circle, or one which divides the globe into equal halves.

The first point of Aries, as I have said, is one of the places where the ecliptic crosses the equator; it is the point which the sun passes at the beginning of spring; it is not marked by any star, or fixed object of any kind. Though it is an imaginary point, yet, from having a series of places of the sun, defined by the difference of times at which the sun and a bright star passes the meridian, we can tell as exactly where that intersection is, as if it were marked by a conspicuous point in the heavens.

Now, the statement that the sun appears to move in a great circle on the globe amounts to this: that the sun appears to move in a plane which passes through the earth. For all globes represent the stars as they would appear if the observer were at the centre of the globe; and a great circle is one whose plane passes through the centre of the globe. If we found that the sun was describing one of the smaller circles on the globe, then we should say the sun was not moving in a plane round the earth. But, as it appears to describe a great circle, then we can assert that the sun appears to be moving in a plane round the earth. Now we come to the question. Cannot we explain this differently in another way? Is it certain that the sun is moving in a plane round the earth, or is it certain that the earth is moving in a plane round the sun? Either supposition will do. At the present moment we have no evidence to guide us; we have nothing to tell us whether the sun is moving round the earth in a plane, or whether the earth is moving round the sun in a plane. But we shall shortly have evidence on the point.

In the meantime I will mention this: that there is no inconsistency in supposing that the earth does move round the sun. As regards the position of the earth's axis there are two suppositions: either that the earth remains with the place of its centre unmoved and with its axis in a certain position, and that the sun goes round at a certain inclination to that axis, thereby causing the change of seasons; or else, if the sun is fixed and the earth goes round the sun, the position of the earth's centre is changed with regard to the sun, but the position of the axis must remain the same relatively with itself. This is a point of great importance. You will remark that all these conclusions are derived from observations of the stars; that observations of the Polar Star are used to determine the Pole round which the heavens appear to revolve; or on the more rational supposition, to determine the point of the heavens towards which the axis of the rotation of the earth is supposed to be directed; summer or winter the Polar Star is the Polar Star still, and guides our observations; summer or winter the axis of the earth is directed towards that same part of the heavens where the Polar Star is seen. Therefore if the earth does revolve round the sun, we must suppose it to revolve in such a manner, not that its North Pole is always inclined towards the sun, but that it is sometimes inclined away from the sun; in point of fact, the motion will be imitated by the motion of the earth in the simple orrery,^[5] represented in Figure 25.

Fig. 25.

Everybody who knows the character of the seasons at the different parts of the earth, will know that this representation is entirely in conformity with their respective changes. Therefore, we must make the following supposition: that if the earth does turn round the sun, its axis of rotation remains parallel to itself, having no reference whatever to the sun, whilst the earth is going round the sun; or, to express it in other words—that the earth has the power of preserving its axis of rotation in the same position all the time.

Now, it is remarkable, as a mechanical fact, that nothing is so permanent in nature as the axis of rotation of anything which is rapidly whirled. We have examples of this in every-day practice. The first is the motion of a boy's hoop. You will think perhaps that this illustration is of a rather superficial character, but it is of great importance. What keeps the hoop from falling? It is its rotation. I cannot now enter upon an explanation of this, which is one of the most complicated subjects in mechanics. Another thing pertinent to the question before us, is the motion of a quoit. Everybody who ever threw a quoit knows, that to make it preserve its position as it goes through the air, it is necessary to give it a whirling motion. It will be seen, that while whirling it preserves its plane in the same position, whatever that position may be, and however it may be inclined to the direction in which the quoit travels. Now, this has greater analogy with the motion of the earth than anything else. Another admirable illustration is the motion of a spinning top I hope I shall not be thought derogating from the dignity of science by giving such an illustration. The greatest mathematician of the last century, the celebrated Euler, has written a whole "book on the motion of a top, and his Latin Treatise "De motu Turbinis" is one of the most remarkable books on mechanics, I ever read in my life. The motion of a top, I repeat, is a matter of the greatest importance; it is applicable to the elucidation of some of the greatest phenomena of nature. In all these instances there is this wonderful tendency in rotation to preserve the axis of rotation unaltered.

Now, from all these circumstances, we see sufficient reason to explain how, whilst the earth is going round the sun, its axis of rotation should remain parallel to itself without being disturbed, that is to say, that the position of the axis has no respect whatever to the sun. Whatever the position of the axis of rotation be, the earth will travel through space keeping that axis of rotation in the same position with regard to the distant stars. Having reached this very important point in the science, I will stop for the present.

1. See lithographic plate fronting title page.
2. The nature of this curve is more fully explained in the next Lecture.
3. Since the delivery of these Lectures, the comparison of clock-times, by means of the Electric Telegraph, has been applied to the determination of the difference of longitudes, first in America, and subsequently in Europe. The mode of procedure is as follows: suppose it is desired to ascertain the difference of longitudes of Paris and Greenwich. At the moment when a star crosses the meridian of Paris the clock-time is observed; and simultaneously the observer, by means of the Electric Telegraph, transmits a signal to Greenwich; the time at which the signal arrives at the latter place is noted by an observer there. If electricity travelled instantaneously from the one place to the other, the difference in hours, minutes, and seconds, between the times at which the signal was despatched and received, would be exactly the difference between Paris and Greenwich time; but, the velocity of the electric fluid being finite, the quantity in question is less than the difference between Paris and Greenwich time, by the time occupied in the transmission of the signal: less, because Greenwich time is behind Paris time. Again, when the star reaches the meridian of Greenwich, a signal is in like manner sent to Paris by the observer: the difference in hours, minutes, and seconds, between the times of its being sent and received is now greater than the difference between Paris and Greenwich time by the time occupied in the transmission of the signal: greater, because Paris time is before Greenwich time. The mean between the two quantities thus determined by observation, is the difference between Paris and Greenwich times.
4. Since these Lectures were delivered, M. Foucault has devised some experiments which demonstrate that the Earth does rotate. An account of these will be found in the Appendix.
5. In Figure 25, A represents a block to be screwed to the table; B, a grooved pulley fixed firmly to A, and having no motion whatever; C, a stand supporting a lamp D, which represents the sun; E, an arm which turns round the axis of B, running upon a small roller F; G, a grooved pulley of the same size as B, which turns in E and carries the axis of the earth H at the inclination 23½ degrees to the vertical. A band is passed round B and G. Then, when the earth is turned round the sun, its axis moves always parallel to itself.