10 INTRODUCTION. 



regulates, which are sometimes called arbitrary 

 magnitudes. 



If the attraction of the sun upon the planets 

 did not vary inversely as the square of the dis- 

 tance, theybrm of the law of gravitation would 

 be changed; if this attraction were, at the earth's 

 orbit, of a different value from its present one, 

 the arbitrary magnitude would be changed ; and 

 it will appear, in a subsequent part of this work, 

 that either change would, so far as we can trace 

 its consequences, be detrimental. The form of 

 the law determines in what manner the facts 

 shall take place ; the arbitrary magnitude deter- 

 mines how fast, how far, how soon ; the one gives 

 a model, the other a measure of the phenomenon ; 

 the one draws the plan, the other gives the scale 

 on which it is to be executed ; the one gives the 

 rule, the other the rate. If either were wrongly 

 taken, the result would be wrong too. 



