418 D'ALEMBERT. 



solution of the problem concerning the Precession; the 

 Nutation had only been by his unrivalled sagacity con- 

 jectured a priori, and was proved by the observations 

 of Bradley. The solution of the Precession had not 

 proved satisfactory; and objections were taken to the 

 hypotheses 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 ratio ad equi- 

 noctia movenda. Certainly the three last suppositions 

 have since Newton's time been displaced by more ac- 

 curate observations; the axes being found, to be as 

 298 to 299, the earth not homogeneous, and the ac- 

 tions 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 discuss 

 the subjectj 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 certain that he first gave a direct and satisfactory 

 solution of this great problem; and that he investi- 

 gated the Nutation 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 describe among the stars a minute ellipse, hav- 

 ing 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 investigations that the Pre- 

 cession is itself subject to a variation, being in a revo- 

 lution of the nodes, sometimes accelerated, sometimes 

 retarded, according to a law which he discovered, 

 giving the equation of correction. It was in 1749 that 



