GALILEO AND HIS JUDGES. 151 



Now let us see how all this bears on the truth 

 of the Copernican system. Newton proved and I 

 may add that the improved methods of mathematics 

 which have been adopted since his day make the 

 proofs more simple and easy that if any body moves 

 in an ellipse, or indeed, in one of the other conic 

 sections, the law of force, tending to the focus, is that 

 of the inverse square of the distance.^ Conversely, 

 he proved that a body under the action of a central 

 force, varying in intensity as the inverse square of 

 the distance, will move in a conic section. 



Then if the Moon moved in an ellipse, as it was 

 easy to perceive that she did, and if her motion 

 corresponded precisely with what it would be on 

 the theory of universal gravitation ; if also, as seemed 

 evident, the planets revolved in ellipses, then the 

 inference that the law of gravitation, as stated by 

 Newton, was true became irresistible ; not sus- 

 ceptible, as before stated, of direct and absolute 

 proof, but established conclusively by a sound and 

 legitimate induction. 



* There are other laws, besides that of the inverse square of the 

 distance, which would cause a body to move in an ellipse, at least 

 if the force acting on it were placed, not in the focus, but in the 

 centre of the orbit. The question has been discussed with reference 

 to some of the binary stars which appear to move round one 

 another in ellipses. No doubt is thereby raised as to the pre- 

 valence of the law of the inverse square in our own solar system, 

 where it has been verified by long and careful observation; the 

 doubt (I think we may say a comparatively slight one) is whether 

 the same law extends to the whole stellar universe, where, of 

 course, accurate observation is impracticable. 



