D'ALEMBERT. 431 



on which it rested, that the accumulation of matter at 

 the equator might be regarded as a belt of moons, that 

 its movement might be reckoned in the proportion of its 

 mass to that of the earth, and that the proportion of the 

 terrestrial axes is that of 229 to 230 ; that the earth is 

 homogeneous, and that the action of the sun and moon 

 ad mare movendum, are as one to four and a half nearly, 

 and in the same rate ad equinoctia movenda. Certainly 

 the three last suppositions have since Newton's time 

 been displaced by more accurate observations; the axes 

 being found, to be as 298 to 299, the earth not homoge- 

 neous, and the actions of the sun and moon on the tides 

 more nearly as one to three. But it has often been observed 

 and truly observed, that when D'Alembert came to dis- 

 cuss the subject, it would have been more becoming in 

 him to assign his reasons for denying the other hypothesis 

 on which the Newtonian investigation rests, than simply 

 to have pronounced it groundless. However, it is cer- 

 tain that he first gave a direct and satisfactory solution 

 of this great problem ; and that he investigated the Nuta- 

 tion with perfect success, showing it to be such that if it 

 subsisted alone, (i. e., if there were no precessional motion) 

 the pole of the equinoctial would described among the 

 stars a minute ellipse, having its longer axis about 

 18" and its shorter about 13", the longer being directed 

 towards the pole of the ecliptic, and the shorter of course 

 at right angles to it. He also discovered in his investi- 

 gations that the Precession is itself subject to a variation, 

 being in a revolution of the nodes, sometimes accelerated, 

 sometimes retarded, according to a law which he dis- 

 covered, giving the equation of correction. It was in 1 749 

 that he gave this admirable investigation ; and in 1755 



