110 LECTURES 



The final verification of the law of gravity is, that it predicts the 

 disturbing effects which one body must have upon another. 



With this law in his hand the astronomer in his study has pre- 

 dicted inequalities in the planetary motions which no observer had 

 detected, and many which, though real, were too small to be detected 

 till they were pointed out and made the subject of special observation. 



The attention of Newton was particularly called to the law of gravi- 

 tation in 1665. The Principia, in which his discoveries v/ere given 

 to the world, was not published till 1687. The doctrines which he 

 announced were slow in winning their way to scientific favor. Out of 

 England, for a period of nearly forty years, they were either not known 

 or were known only to be rejected. The theory of vortices, as promul- 

 gated by Des Cartes, had obtained great popularity on the continent, 

 and was adopted by most of the eminent continental astronomers of 

 the age. 



Euyghens adopted the Newtonian doctrines only in part. Leibnitz 

 and John Bernouilli were conspicuous in opposition to them. Cassini 

 and Miraldi, to the end of their lives, were borne along by the vortices 

 of Des Cartes. "On the continent," says Grant, "all the great 

 mathematicians were unanimous in their hostility to the Newtonian 

 theory." At length, in 1732, forty-five years after the publication of 

 the Principia, and five alter the death of Newton, Maupertuis, of 

 the French Academy, was the first to adopt and defend the doctrines 

 of the Principia. But the writer who did most to commend the New- 

 tonian theory to favor in France was, probably, Voltaire, who, in 

 1738, published a brief, popular exposition of Newton's work, which 

 was widely circulated and did much to conciliate the favor of the 

 learned to the views of the great English philosopher. But if the 

 French astronomers in the first instance sinned against true science 

 in rejecting the doctrine of Newton, the labors of Clairault and La 

 Place have made ample atonement for it since. The theory of Newton 

 is universally received ; the vortices of Des Cartes survive only as a 

 memorable example of scientific error. 



Having given a sketch of the history of the law of gravitation, I 

 must content myself with adverting to two or three illustrations. 



1. What kind of a curve may a heavenly body describe, under the 

 action of this law? 



Newton showed that the curve might be a circle^ an ellipse, a par- 

 abola, or a hyperbola, being the four curves made by the section of a 

 cone, and it could not revolve in any other. Thus, in figure 8 let S 

 represent the place of the sun, and let A represent any body placed 

 at any given distance, as at A. Now suppose it receives an impulse in 

 a direction perpendicular to the radius- vector S A, the form of the 

 orbit which it will describe will depend upon the intensity of this 

 impulse. Any impulse in that direction will produce a cantrifugal 

 force. If this centrifugal force is exactly equal to the centripetal force 

 of the sun, the body will describe a circle, A C, about S as a centre ; 

 if it receives a less impulse it will describe an ellipse, as A E, of which 

 A is the aphelion and S the remoter focus ; if it receives a greater 

 impulse it will still describe an ellipse, as A E, of which A is the peri. 



