42] ROYAL ASTRONOMICAL SOCIETY TO M. PETERS. 311 



with those which would be occasioned by precession, and he made allowance 

 for this by employing in the reduction of his observations the changes 

 deduced from the observations themselves. 



No sooner, therefore, had Bradley determined the law and the cause 

 of aberration, than a new subject of investigation presented itself, requiring 

 a much longer course of observations for its complete examination. Com- 

 paring his observations of different stars, he found that their changes of 

 declination were such as might be attributed to a real motion of the 

 Earth's axis, and he was not slow in perceiving that the varying action 

 of the Moon upon the equatoreal parts of the Earth, according to the 

 different positions of the nodes of the lunar orbit, was the probable cause 

 of this motion. During the course of the observations, Bradley communi- 

 cated what he had observed to Machin, who was then "employed in 

 considering the theory of gravity and its consequences with regard to the 

 celestial motions," mentioning at the same time what he suspected to be 

 the cause of these phenomena. 



Machin confirmed this supposition, and shewed that the observed 

 motions might be very nearly accounted for, by supposing that the pole 

 of the equator described a small circle about its mean position as centre, 

 during a period of the Moon's nodes. 



Bradley remarked that his observations would be more completely 

 represented by supposing the true pole to move about the mean pole in 

 an ellipse instead of in a circle, the major axis being in the solstitial 

 colure ; and this conclusion is perfectly true, the minor axis being, however, 

 a little smaller than he made it. 



Bradley continued the observations during an entire revolution of the 

 Moon's nodes, and then published an account of his discovery in the 

 Philosophical Transactions for 1748, in a paper which is a perfect model 

 of lucid statement and strict inductive reasoning. 



In the following year, D'Alembert succeeded in determining the true 

 motion of the Earth's axis by means of analysis, in his "Recherches sur 

 la Precession des Equinoxes et sur la Nutation de 1'Axe de la Terre," 

 and since that time the subject has been repeatedly treated of by physical 

 astronomers. The most complete and elegant theoretical investigation, how- 

 ever, of the motion of the Earth about its centre of gravity is that given 

 by Poisson in the seventh volume of the Memoir es de I'Institut. The 

 theoretical investigations with respect to nutation leave nothing to be 

 determined by observation, except the value of one constant. This is 



