56 DYNAMICAL PRINCIPLE. 



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 accurate observa- 

 tions ; the axes being found, to be as 298 to 299, the earth not 

 homogeneous, 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 

 discuss the subject, it would have been more becoming in him 

 to assign his reasons for denying the other hypothesis on 

 which the Newtonian investigation i-ests, 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 investigated 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, 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 

 investigations that the Precession is itself subject to a varia- 

 tion, being in a revolution of the nodes, sometimes accelerated, 

 sometimes retarded, according to a law which he discovered, 

 giving the equation of correction. It was in 1749 that he 

 gave this admirable investigation ; and in 1755 he followed it 

 up with another first attempted by him, namely, the variation 

 which might occur to the former results, if the earth, instead 

 of being a sphere oblate at the poles, were an elliptic spheroid, 

 whose axes were different. He added an investigation of the 

 Precession on the supposition of the form being any other 

 curve approaching the circle. This is an investigation of as 

 great difficulty perhaps as ever engaged the attention of 

 analysts. It remains to add that Euler, in 1750, entered on 

 the same inquiries concerning Precession and Nutation ; and 

 with his wonted candour, he declared that he had read 

 D'Alembert's memoir before he began the investigation.* 



* This Tract is from ' Lives of the Philosophers 'Life of D'Alembert. 



