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be acquired only by falling an hour at the height 

 of the moon. And it can be easily proved by 

 calculation that the falling action of the moon is, 

 in an hour, exactly that of a stone in a second. 

 It being thus shewn that the moon is deflected by 

 gravity, it was then concluded that the planets are 

 deflected to the sun by the same cause ; or that 

 gravity is the great central force throughout the 

 solar system. 



After thus identifying the mechanical causes of 

 the planetary motions, Newton deduced all the 

 laws of Kepler from the combination of the two 

 great forces of Gravitation and Straight Impulse. 

 In this way he found that these laws are not 

 strictly true, as given by Kepler, and that therefore 

 the prediction of the places from them could not 

 be perfectly accurate. Not only was the sun's 

 centre not the true focus of the ellipse, that being 

 the common centre of gravity of the sun and the 

 planet, but he shewed that not one of the paths 

 is an exact ellipse. If there were only one planet 

 to the sun, that planet would describe a perfect 

 ellipse ; but if a second planet is introduced, this 

 planet is not only attracted by the sun (and the 

 sun attracted by it), but there is an attraction 

 between it and the first planet which disturbs the 

 motion of both. 



In like manner, if the moon and the earth were 

 alone in the universe, the moon would go round 

 the common centre of gravity of the two in a 

 perfect ellipse ; but as both move round the sun, 

 and he acts upon both, very great deviations take 

 place from the elliptic orbit ; in fact, the applica- 

 tion of Kepler's two first laws to the moon could 

 never predict her place with anything like accu- 

 racy. 



Perturbations. But the same discoveries that 

 shew the defects of Kepler's laws, give the means 

 of correcting those defects, or of calculating the 

 disturbing influences, so as to predict what the 

 real motions will be under those disturbances. 

 The special disturbances are known as perturba- 

 tions or inequalities. In calculating them, astro- 

 nomers first suppose the case of one body revolving 

 about a second, and disturbed in its regular orbit 

 by a third ; this is what is called the problem of 

 the three bodies ; the disturbing effect of each 

 separate cause being thus found, the whole are 

 then combined. 



Masses of the Heavenly Bodies. The theory of 

 universal gravitation gives us the means of com- 

 paring the weights of the heavenly bodies, as if 

 they were weighed on a steelyard. Thus the fall 

 of the earth towards the sun in an hour can be 

 compared with the fall of the moon to the earth in 

 an hour ; and the two quantities, multiplied by the 

 squares of the two distances, will give the propor- 

 tion between the mass of the sun and the mass of 

 the earth, which is about 314,760 to i. When we 

 remember that the bulk of the sun exceeds that of 

 the earth more than a million of times, we see that 

 the matter of the sun is much lighter than the 

 material of the earth. In the same way, Jupiter's 

 mass is found to be 301 times that of the earth. 



To find the actual density or specific gravity of 

 the different bodies of the solar system, and com- 

 pare it with a fixed standard, such as water, it is 

 necessary to know the average density of the 

 whole earth. This has been sought by comparing 

 the attraction- of some known body with the 

 attraction of the globe. Thus, Dr Maskelyne 



attempted to calculate the attraction of a moun- 

 tain in Perthshire, by finding how far it made a 

 plumb-line to deviate from the perpendicular. In 

 this experiment the plumb-ball was supposed to 

 be attracted downwards by the general mass of 

 the earth, and sideways by the mountain ; and it 

 could thus be seen how many times the whole 

 earth surpassed the mountain in gravitating force. 

 If the mountain itself then were measured, and its 

 composition ascertained, so as to give the density 

 of its rocky material, the entire mass of the moun- 

 tain would be obtained, and from that the entire 

 mass of the earth. The result of this experiment 

 was, that the earth is, on an average, 5^ times 

 denser than water, or more than twice the density 

 of granite or sandstone rock. Other experiments, 

 of a different kind, have given much the same 

 determination. From this we can estimate the 

 densities of the sun, moon, planets, and satellites. 

 The Figures of the Heavenly Bodies, how caused. 

 It has already been seen that the sun and 

 planets are, in general, round masses, with a slight 

 flattening, which seems to be connected with the 

 rapidity of their whirl Now, both the general 

 roundness and the flattening can be shewn to 

 arise from ordinary mechanical laws, such as we 

 see operating on the earth, provided we suppose 

 that the planets were at one time soft, fluid masses. 

 If a fluid mass of attracting particles be left to 

 itself that is, if there be no external compulsion, 

 either attraction or pressure it will always assume 

 the round shape. 



But if such a body is whirled, the matter at 

 the surface acquires a tendency to fly off, so 

 as to oppose the general attraction towards the 

 centre. If the whirled body is soft or liquid, 

 it cannot remain at rest, or in equilibrium, in 

 its round form, inasmuch as the matter at the 

 equator, having a greater velocity than elsewhere, 

 is rendered lighter by its centrifugal tendency, 

 and is not a sufficient balance for the matter at 

 the poles. To restore the balance, there must 

 be a greater depth from the equator to the centre 

 than from the poles to the centre ; in other words, 

 the equatorial width must exceed the polar width, 

 which is what we actually find in all the revolving 

 bodies. The planets also that revolve the most 

 rapidly, as Jupiter and Saturn, are found to be the 

 most elliptical. 



Precession of the Equinoxes. It has been al- 

 ready explained in what this consists. The cause is 

 to be found in the combined action of the sun and 

 moon on the protuberant mass of matter accumu- 

 lated at the earth's equator. The exact nature of 

 this action is too complex for description here ; but 

 combined with the rotation of the earth on its 

 axis, the result is the regression of the equinoctial 

 points above mentioned ; while, as a necessary 

 consequence, the celestial pole describes, at the 

 same rate, a circle among the stars round the pole 

 of the ecliptic at a distance equal to the obliquity 

 of the ecliptic. Its motion, however, is not quite 

 uniform or straight, but in a waving line, alter- 

 nately approaching and receding from the pole of 

 the ecliptic. This secondary disturbance, which 

 is caused by the fluctuating position of the moon's 

 nodes, is known as the nutation of the earth's 

 axis. 



The poles of the earth do not, then, point always 

 to the same places among the stars. The present 

 position of the north pole is within a degree and 



