[36.] After this it is shewn, from the proportion of the equatorial diameter of the earth to its axis, how the same may be determined of any other planet, whose density in comparison of the density of the earth, and the time of its revolution about its axis, are known. And by the rule delivered for this, it is found, that the diameter of the equator in Jupiter should bear to its axis about the proportion of 10 to 9[276], and accordingly this planet appears of an oval form to the astronomers. The most considerable effects of this spheroidical figure our author takes likewise into consideration; one of which is that bodies are not equally heavy in all distances from the poles; but near the equator, where the distance from the center is greatest, they are lighter than towards the poles: and nearly in this proportion, that the actual power, by which they are drawn to the center, resulting from the difference between their absolute gravity and centrifugal force, is reciprocally as the distance from the center. That this may not appear to contradict what has before been said of the alteration of the power of gravity, in proportion to the change of the distance from the center, it is proper carefully to remark, that our author has demonstrated three things relating hereto: the first is, that decrease of the power of gravity as we recede from the center, which has been fully explained in the last chapter, upon supposition that the earth and planets are perfect spheres, from which their difference is by many degrees too little to require notice for the purposes there intended: the next is, that whether they be perfect spheres, or exactly such spheroids as have now been mentioned, the power of gravity, as we descend in the same line to the center, is at all distances as the distance from the center, the parts of the earth above the body by drawing the body towards them lessening its gravitation towards the center[277]; and both these assertions relate to gravity alone: the third is what we mentioned in this place, that the actual force on different parts of the surface, with which bodies are drawn to the center, is in the proportion here assigned[278].
[38.] The next effect of this figure of the earth is an obvious consequence of the former: that pendulums of the same length do not in different distances from the pole make their vibrations in the same time; but towards the poles, where the gravity is strongest, they move quicker than near the equator, where they are less impelled to the center; and accordingly pendulums, that measure the same time by their vibrations, must be shorter near the poles than at a greater distance. Both which deductions are found true in fact; of which our author has recounted particularly several experiments, in which it was found, that clocks exactly adjusted to the true measure of time at Paris, when transported nearer to the equator, became erroneous and moved too slow, but were reduced to their true motion by contracting their pendulums. Our author is particular in remarking, how much they lost of their motion, while the pendulums remained unaltered; and what length the observers are said to have shortened them, to bring them to time. And the experiments, which appear to be most carefully made, shew the earth to be raised in the middle between the poles, as much as our author found it by his computation[279].
39. These experiments on the pendulum our author has been very exact in examining, inquiring particularly how much the extension of the rod of the pendulum by the great heats in the torrid zone might make it necessary to shorten it. For by an experiment made by Picart, and another made by De la Hire, heat, though not very intense, was found to increase the length of rods of iron. The experiment of Picart was made with a rod one foot long, which in winter, at the time of frost, was found to increase in length by being heated at the fire. In the experiment of De la Hire a rod of six foot in length was found, when heated by the summer sun only, to grow to a greater length, than it had in the aforesaid cold season. From which observations a doubt has been raised, whether the rod of the pendulums in the aforementioned experiments was not extended by the heat of those warm climates to all that excess of length, the observers found themselves obliged to lessen them by. But the experiments now mentioned shew the contrary. For in the first of them the rod of a foot long was lengthened no more than 1/9 part of what the pendulum under the equator must be diminished; and therefore a rod of the length of the pendulum would not have been extended above ⅓ of that length. In the experiment of De la Hire, where the heat was less, the rod of six foot long was extended no more than 3/10 of what the pendulum must be shortened; so that a rod of the length of the pendulum would not have gained above 3/20 or 1/7 of that length. And the heat in this latter experiment, though less than in the former, was yet greater than the rod of a pendulum can ordinarily contract in the hottest country; for metals receive a great heat when exposed to the open sun, certainly much greater than that of a human body. But pendulums are not usually so exposed, and without doubt in these experiments were kept cool enough to appear so to the touch; which they would do in the hottest place, if lodged in the shade. Our author therefore thinks it enough to allow about 1/10 of the difference observed upon account of the greater warmth of the pendulum.
[40.] There is a third effect, which the water has on the earth by changing its figure, that is taken notice of by our author; for the explaining of which we shall first prove, that bodies descend perpendicularly to the surface of the earth in all places. The manner of collecting this from observation, is as follows. The surfaces of all fluids rest parallel to that part of the surface of the sea, which is in the same place with them, to the figure of which, as has been particularly shewn, the figure of the whole earth is formed. For if any hollow vessel, open at the bottom, be immersed into the sea; it is evident, that the surface of the sea within the vessel will retain the same figure it had, before the vessel inclosed it; since its communication with the external water is not cut off by the vessel. But all the parts of the water being at rest, it is as clear, that if the bottom of the vessel were closed, the figure of the water could receive no change thereby, even though the vessel were raised out of the sea; any more than from the insensible alteration of the power of gravity, consequent upon the augmentation of the distance from the center. But now it is clear, that bodies descend in lines perpendicular to the surfaces of quiescent fluids; for if the power of gravity did not act perpendicularly to the surface of fluids, bodies which swim on them could not rest, as they are seen to do; because, if the power of gravity drew such bodies in a direction oblique to the surface whereon they lay, they would certainly be put in motion, and be carried to the side of the vessel, in which the fluid was contained, that way the action of gravity inclined.
41. Hence it follows, that as we stand, our bodies are perpendicular to the surface of the earth. Therefore in going from north to south our bodies do not keep in a parallel direction. Now in all distances from the pole the same length gone on the earth will not make the same change in the position of our bodies, but the nearer we are to the poles, we must go greater length to cause the same variation herein. Let M I L K (in fig. 117) represent the figure of the earth, M, L the poles, I, K two opposite points in the middle between these poles. Let T V and P O be two arches, T V being most remote from the pole L; draw T W, V X, P Q, O R, each perpendicular to the surface of the earth, and let T W, V X meet in Y, and P Q, O R in S. Here it is evident, that in passing from V to T the position of a man’s body would be changed by the angle under T Y V, for at V he would stand in the line Y V continued upward, and at T in the line Y T; but in passing from O to P the position of his body would be changed by the angle under O S P. Now I say, if these two angles are equal the arch O P is longer than T V: for the figure M I L K being oblong, and I K longer than M L, the figure will be more incurvated toward I than toward L; so that the lines T W and V X will meet in Y before they are drawn out to so great a length as the lines P Q and O R must be continued to, before they will meet in S. Since therefore Y T and Y V are shorter than P S and S V, T V must be less than O P. If these angles under T Y V and O S P are each 1/90 part of the angle made by a perpendicular line, they are said each to contain one degree. And the unequal length of these arches O P and V T gives occasion to the assertion, that in passing from north to south the degrees on the earth’s surface are not of an equal length, but those near the pole longer than those toward the equator. For the length of the arch on the earth lying between the two perpendiculars, which make an angle of a degree with each other, is called the length of a degree on the earth’s surface.
42. This figure of the earth has some effect on eclipses. It has been observed above, that sometimes the nodes of the moon’s orbit lie in a straight line drawn from the sun to the earth; in which case the moon will cross the plane of the earth’s motion at the new and full. But whenever the moon passes near the plane at the full, some part of the earth will intercept the sun’s light, and the moon shining only with light borrow’d from the sun, when that light is prevented from falling on any part of the moon, so much of her body will be darkened. Also when the moon at the new is near the plane of the earth’s motion, the inhabitants on some part of the earth will see the moon come under the sun, and the sun thereby be covered from them either wholly or in part. Now the figure, which we have shewn to belong to the earth, will occasion the shadow of the earth on the moon not to be perfectly round, but cause the diameter from east to west to be somewhat longer than the diameter from north to south. In eclipse of the sun this figure of the earth will make some little difference in the place, where the sun shall appear wholly or in any given part covered. Let A B C D (in fig. 118.) represent the earth, A C the axis whereon it turns daily, E the center. Let F A G C represent a perfect globe inscribed within the earth. Let H I be a line drawn through the centers of the sun and moon, crossing the surface of the earth in K, and the surface of the globe inscribed in L. Draw E L, which will be perpendicular to the surface of the globe in L: and draw likewise K M, so that it shall be perpendicular to the surface of the earth in K. Now whereas the eclipse would appear central at L, if the earth were the globe A G C F, and does really appear so at K; I say, the latitude of the place K on the real earth is different from the latitude of the place L on the globe F A G C. What is called the latitude of any place is determined by the angle which the line perpendicular to the surface of the earth at that place makes with the axis; the difference between this angle, and that made by a perpendicular line or square being called the latitude of each place. But it might here be proved, that the angle which K M makes with M C is less, than the angle made between L E and E C: consequently the latitude of the place K is greater, than the latitude, which the place L would have.
43. The next effect, which follows from this figure of the earth, is that gradual change in the distance of the fixed stars from the equinoctial points, which astronomers observe. But before this can be explained, it is necessary to say something more particular, than has yet been done, concerning the manner of the earth’s motion round the sun.
44. It has already been said, that the earth turns round each day on its own axis, while its whole body is carried round the sun once in a year. How these two motions are joined together may be conceived in some degree by the motion of a bowl on the ground, where the bowl in rouling on continually turns upon its axis, and at the same time the whole body thereof is carried straight on. But to be more express let A (in fig. 119) represent the sun B C D E four different situations of the earth in its orbit moving about the sun. In all these let F G represent the axis, about which the earth daily turns. The points F, G are called the poles of the earth; and this axis is supposed to keep always parallel to it self in every situation of the earth; at least that it would do so, were it not for a minute deviation, the cause whereof will be explained in what follows. When the earth is in B, the half H I K will be illuminated by the sun, and the other half H L K will be in darkness. Now if on the globe any point be taken in the middle between the poles, this point shall describe by the motion of the globe the circle M N, half of which is in the enlightened part of the globe, and half in the dark part. But the earth is supposed to move round its axis with an equable motion; therefore on this point of the globe the sun will be seen just half the day, and be invisible the other half. And the same will happen to every point of this circle, in all situations of the earth during its whole revolution round the sun. This circle M N is called the equator, of which we have before made mention.
45. Now suppose any other point taken on the surface of the globe toward the pole F, which in the diurnal revolution of the globe shall describe the circle O P. Here it appears that more than half this circle is enlightned by the sun, and consequently that in any particular point of this circle the sun will be longer seen than lie hid, that is the day will be longer than the night. Again if we consider the same circle O P on the globe situated in D the opposite part of the orbit from B, we shall see, that here in any place of this circle the night will be as much longer than the day.