132 NEWTON S PRINCIPIA. 



vance somewhat each revolution (as we before saw) ; and 

 it also increases the eccentricity of the orbit between qua 

 drature and syzygy, and diminishes that eccentricity be 

 tween syzygy and quadrature. So of the inclination of 

 the orbit, which is always diminished between quadrature 

 and syzygies, and increased between syzygy and qua 

 drature, and is at the minimum when the nodes are in 

 quadrature and the body itself in syzygy. 



We found before that the force L N was as oiv/p- 



The forces L N and N E are directly as the mass S, and 

 when S is very distant, the forces L N&quot; and N E vary as 



S 

 or inversely as the squares of the periodic times ; 



and if at a given distance the absolute disturbing force 

 be as the magnitude of the disturbing body, whose dia- 



rf? 



meter is d, these forces are as o -^3 ; or as the cube of the 



apparent diameter of S. Also if instead of one sa 

 tellite, M, moving round E, we have several whose orbits 

 are nearly of the same form or inclination (like the first 

 three of Jupiter), the mean motion of their apsides and 

 nodes each revolution are directly as the squares of their 

 periodic times, and inversely as the squares of the planet s 

 time, and the two motions (apsides and nodes) are to 

 one another in a given ratio. 



We now have one of those extraordinary instances which 

 abound in his writings, of Sir Isaac Newton s matchless 

 power of generalization ; of apprehending remote analogies, 

 and thereby extending the scope of his discoveries. Having 

 shown how the disturbing forces of bodies in a system act 

 upon their motions with respect to each other, he now 

 examines the effect of such forces upon the constitution 

 of the bodies themselves. He supposes, for example. 



