\\M 



THE PROGRESS OF 



orbit, Newton determined the mean quantity of 

 this retrogradation, as well as the irregularities 

 ID \\hicli it is subject, and found both to agree, 

 corresponding very accurately with observation. 



The lunar inequality discovered by Tycho, 

 and called by him the Variation, which consist* 

 in the alternate acceleration and retardation of 

 the moon in each quarter of her revolution, wns 

 accurately determined from theory, such as it is 

 found by observation. The same remark applies 

 to the annual equation, which had been long 

 confounded with the equation of time. It does 

 not appear that Newton attempted an exact de- 

 termination of the other inequalities of the lunar 

 motion. He satisfied himself with the general 

 truth, that the principle of the sun's disturbing 

 force led to the supposition of inequalities of the 

 some kind with those actually observed. The 

 full knowledge of all these inequalities, and their 

 exact accordance with theory, was reserved for 

 a future period, when a more perfect state of the 

 calculus enabled philosophers to investigate the 

 whole subject 



The earth, in consequence of its rotation on its 

 axis, is influenced by a centrifugal force, which 

 must act most powerfully on the parts most dis- 

 tant from the axis. The amount of this centri- 

 fugal force is greatest at the equator ; and being 

 measured by the momentary recess of any point 

 from the tangent, which was known from the 

 earth's rotation, it could be compared with the 

 force of gravity at the same place, measured in 

 like manner by the descent of a heavy body in 

 the first moment of its fall. Newton found that 

 the centrifugal force at the equator is the 289th 

 part of gravitation, diminishing continually as 

 the cosine of the latitude, on going from the 

 equator to the poles, where it vanishes altogether. 

 From the combination of this force with that of 

 gravity, it follows that the plumb line cannot 

 tend exactly to the earth's centre, and that a 

 true horizontal line, such as is drawn by leveling, 

 if continued from either pole in the plane of a 

 meridian all round the earth, would not be a 

 circle but an ellipse, having its greater axis in 

 the plane of the equator, and its least in the 

 direction of the axis of the earth's rotation. Now 

 the surface of the ocean itself actually traces this 

 level, as it extends from the equator to the poles. 

 Hence it follows, that the figure of the earth is 

 an oblate spheroid, or a solid generated by the 

 revolution of the elliptic meridian about its 

 shorter axis. To determine the proportion of 

 the axis of this spheroid, Newton conceived that, 

 if tlie waters at the pole and at the equator were 

 to communicate by a canal through the interior 

 of the earth, one branch reaching from the pole 

 to the centre, and the other at right angles to it 

 from the centre to the circumference of the equa- 



tor, the water in this canal must be in equilibrio, 

 or the weight of the fluid in the one branch just 

 equal to that in the other. By a very subtle 

 process of reasoning, he found that the length of 

 the equatorial canal must be to that of the polar 

 as 230 to 229. It was demonstrated afterwards 

 by Maclaurin and Clairaut, that this is in fact 

 the ratio of the two diameters of the earth, sup- 

 posing its specific gravity to be homogeneous 

 from circumference to centre. If its specific 

 gravity increased from the circumference to the 

 centre, so as to be infinitely great at the centre, 

 then the difference between the two diameters 

 would be a minimum, and would amount only to 

 one 578th part. Mr Ivory has examined this 

 subject with his usual sagacity and profound 

 mathematical knowledge, and concludes that the 

 true difference between the length of the two 

 diameters is one 300th part. This determination, 

 we may safely assume, as exceedingly near the 

 truth. 



From the figure of the earth thus determined, 

 Newton showed that the intensity of gravity at 

 any point of the surface, is inversely as the dis- 

 tance of that point from the centre. Its increase, 

 therefore, in going from the equator to the poles, 

 is as the square of the sine of the latitude, the 

 same ratio in which the degrees of the meridian 

 increase. As gravity diminishes in going from 

 the poles to the equator, it follows that a pen- 

 dulum of a given length would vibrate slower 

 when carried from Europe to the torrid zone. 

 This had been already verified by the observa- 

 tions of Varin and De Hayes, made at Cayenne 

 and Martinique. 



What is called the precession of the equinoxes, 

 or the retrogradation of the equinoctial points, 

 had been long known. Its rate had been found 

 to amount nearly to 50" annually, so as to com- 

 plete an entire revolution of the heavens in 

 25,920 years. Nothing seemed more difficult to 

 explain than this phenomenon no preceding 

 astronomer had even thrown out a conjecture on 

 the subject. It was reserved for the sagacity of 

 Newton. He was directed by a certain analogy 

 between the precession of the equinoxes, and the 

 retrogradation of the moon's nodes, a phenomenon 

 to which his calculus had been already success- 

 fully applied. The spheroidal shell, or ring of 

 matter which surrounds the earth in the direc- 

 tion of the equator, being one half above the 

 plane of the ecliptic, and one half below, is sub- 

 jected to the action of the solar force, the tend- 

 ency of which is to make this ring turn on the 

 line of its intersection with the ecliptic, so as 

 ultimately to coincide with the plane of that 

 circle. This would have happened long since it 

 the earth had not turned on its axis. The effect 

 of the rotation of the spheroidal ring from west 



