3?8 NATURE AND MAN. 



well with the observed facts to suggest the existence of a real 

 &quot;law;&quot; but actually led to the prediction of a &quot;lost planet&quot; 

 between Mars and Jupiter, which has been verified by the 

 discovery of somewhere near two hundred &quot; asteroids,&quot; to say 

 nothing of streams of meteorites. The discovery of Neptune, how 

 ever, effectually demolished the credit of this &quot;law;&quot; the distance 

 of that planet from the sun proving to be nearly one-fourth less than 

 the formula would make it.* 



The first of the great achievements of Newton in relation to 

 our present subject, was a piece of purely geometrical reasoning. 

 Assuming two forces to act on a body, of which one should be 

 capable of imparting to it uniform motion in a straight line, whilst 

 the other should attract it towards a fixed point in accordance with 

 Galileo s law of terrestrial gravity, he demonstrated that the path 

 of the body would be deflected into a curve, which must be one of 

 the conic sections; and that, if the two forces are in near equivalence 

 the one to the other, the curve will be an ellipse. (Galileo had 

 already shown that the path of the projectile in which gravity 

 preponderates over the onward force, is a parabola). He proved, 

 moreover, that the motion of any body thus traversing an elliptical 

 orbit round a centre of attraction, must conform in its varying 

 rates to Kepler s second law. And further, he showed that if a 

 number of bodies be moving round the same centre of attraction 

 at different distances, the rates of their revolution must conform 

 to Kepler s third law. By assuming the existence of these two 

 balanced forces, therefore, he not only showed that all the observed 

 uniformities could be deduced from that one simple conception, 

 but furnished a rational basis for the assured expectation that the 

 like uniformities would prevail in every other case. And the 

 verification of this expectation by the discovery that even comets 



* It may not be uninstructive to note that in their mathematical search for 

 this stranger, \vliich manifested its presence by disturbing the motions of Uranus, 

 both Adams and Leverrier took Bode s formula as the basis of their computa 

 tion^, assuming its distance from the sun to be somewhat more than twice that 

 of Uranus. And it was by nothing more or less than a fortunate coincidence, 

 that the new planet was found in the place which they agreed in assigning to 

 it ; for if the search had been made a year earlier or a year later, iis actual 

 place would have been so far from its computed place, that it would probably 

 not have been found until new computations had been made on the basis of 

 some more lucky guess. 



