PLANETARY MOTIONS 31 



fore him had asked themselves the same queries, but 

 given them up as unanswerable conundrums. Newton, 

 however, did not. It occurred to him that, supposing the 

 moon at every mathematical point of her orbit to be di- 

 rected, with undiminishing velocity, tangentially forward, 

 she might still fall like the apple, but fall no farther than 

 just from the line of the tangent to the rim of the orbit. 

 The first time he made his calculation the result was so 

 far out that he gave up his hypothesis as unsound, and 

 charged his labors to profit and loss. Some years later, 

 however, as luck would have it, one of the chief data of 

 fact upon which he had relied, namely, the length of a 

 terrestrial degree, was found to be erroneous, and when 

 this corrected quantity was incorporated in his earlier 

 calculation the result came out satisfactory. His chief 

 doctrines are : 



1. Every body continues in its state of rest or of uni- 

 form motion in a straight line, unless it be compelled by 

 impressed force to change that state. 



2. Change of motion is proportional to the im- 

 pressed force, and takes place in the direction of the 



straight line in ivhich the force acts. 



3. To every action there is always an equal and con- 

 trary reaction, or the mutual actions of any two bodies 

 are always equal and oppositely directed. 



His law of gravitation is : Particles of matter attract 

 each other directly as the product of their masses and in- 

 versely as the square of the intervening distance. 



By way of a supplement to these laws, I quote a pass- 

 age from Young's work (Gen'l Astr., Art. 421) : 



Newton was not satisfied with merely showing that the prin- 

 cipal motions of the planets and the moon could be explained by 

 the law of gravitation ; but he went on to investigate the converse 

 problem, and to determine what must be the motions necessary 

 under that law. He found that the orbit of a body moving around 

 a central mass is not of necessity a circle, or even a nearly circu- 

 lar ellipse like the planetary orbits, but that it may be a conic sec- 

 tion of any eccentricity whatever a circle, ellipse, parabola, or 

 even an hyperbola, but it must be a conic. 



