VOL. LXIX.] PHILOSOPHICAL TRANSACTIONS. 577 



proportion of the diameters of the earth, determined on the false supposition of 

 an entire fluidity, cannot differ much from the truth. 



'^ 2. But the precession of the equinoxes, which depends on the unequal ac- 

 tions of the sun and moon on the protuberant parts of the earth at the equator, 

 will not be the same in these different hypotheses; at least we can never be cer- 

 tain that it will be so till we have computed their effects, and the computation it- 

 self must proceed on different principles. Suppose the earth to be fluid under 

 the form of an oblate spheroid; or, what is more simple, suppose the region of 

 the equator to be surrounded with a ring of fluid matter; then the unequal ac- 

 tion of the sun will disturb the figure of the ring, and communicate a motion 

 to its parts. Suppose we knew the precise disturbing force of the sun on any 

 one particle of this ring, according to its situation; in that case we could easily 

 find the velocity which would be communicated to such a particle in any given 

 time; but the mutual actions of the fluid particles on each other could never be 

 exactly estimated, much less their effects in endeavouring to turn the whole earth 

 round its centre. However, it is easy to see, that in the case of a hard ring of 

 matter cohering close to the surface of the earth at the equator, both the law by 

 which the particles act on each other, and on the whole mass of the earth, will 

 be widely different from the case of fluidity, and the effects much greater in 

 altering the position of the axis of rotation. 



To explain this by an easy example, let a, b, c, fig. 1, pi. 6, represent 3 small 

 bodies in the same horizontal line ae. Suppose a to descend by any accelerating 

 force, as gravity; b to descend by the same force, a less or a greater; and c not 

 to be acted on at all: in every one of these cases the bodies a and b will descend 

 with their respective velocities, and the body c will preserve its situation. If a 

 and B are small particles of fluid of any form, and c a hard one, and if the par- 

 ticle A be placed in contact with b, and have its centre of gravity a little above 

 the centre of gravity of b, and is acted on by the greater accelerating force; in 

 this case we may conceive how the action of a may disturb the motion of b, and 

 in the same way how the hard particle c may receive a small motion from the 

 actions of a and b. This motion must be extremely little, compared with the 

 whole motions of a or b, and still a great deal less if c be strongly connected 

 with a string of hard particles along the line ce, so that c cannot be moved 

 without the whole line ce turning round the immoveable centre e. Now if a, 

 B, c, be supposed hard particles, firmly connected to the lever ae; then it is 

 plain that the velocity of c, whatever it is, must be in proportion to that of a 

 and B as their respective distances from e the centre of motion, and this, wiiat- 

 ever the impulsive forces are with which a and b are urged in their respective 

 directions. 



The body c being still supposed void of gravity, let the bodies A and b be 



YOL. XIV. 4 E 



