72 FROM NEBULA TO NEBULA 



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 inits 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. 



In investigating the laws of circulating bodies, it has 

 been customary from the time of Newton to take, as the 

 typical case, that of the earth and the moon, and from 

 that to generalize as to all. Let us follow their example ; 

 but let us first seek to familiarize ourselves with the 

 nature and the difficulties of our problem. 



Most people imagine that it is an easy matter to draw 

 a perfectly straight Une. Such a thing is not possible for 

 any human being, and even if it were accidentally accom- 

 plished, there would be no available standard by which 



