ADDITIONS TO THE NEWTONIAN THEORY. 267 



few years' observations showed Bradley the effect 

 of this change 9 ; and long before the half cycle of 

 nine years had elapsed, he had connected it in his 

 mind with the true cause, the motion of the moon's 

 nodes. Machin was then secretary to the Royal 

 Society 10 , and was " employed in considering the 

 theory of gravity, and its consequences with re- 

 gard to the celestial motions:" to him Bradley 

 communicated his conjectures ; from him he soon 

 received a Table containing the results of his cal- 

 culations ; and the law was found to be the same in 

 the Table and in observation, though the quanti- 

 ties were somewhat different. It appeared by both, 

 that the earth's pole, besides the motion which 

 the precession of the equinoxes gives it, moves, 

 in eighteen years, through a small circle; or 

 rather, as was afterwards found by Bradley, an 

 ellipse, of which the axes are nineteen and fourteen 

 seconds 11 . 



For the rigorous establishment of the mecha- 

 nical theory of that effect of the moon's attraction 

 from which the phenomena of Nutation flow, Brad- 

 ley rightly and prudently invited the assistance of 

 the great mathematicians of his time. D'Alembert, 

 Thomas Simpson, Euler, and others, answered this 

 call, and the result was, as we have already said 

 in the last chapter, that this investigation added 

 another to the recondite and profound evidences of 

 the doctrine of universal gravitation. 



9 Rigaud, Ixiv. 10 Ib. 25. " Ib. Ixvi. 



