106 THE PRINCIPLES OF SCIENCE. 



(1) Is there any constant relation between the variable 

 and variant ? 



(2) What is the empirical formula expressing this re- 

 lation ? 



(3) What is the rational formula expressing the law of 

 nature involved \ 



Probable Connexion of Varying Quantities. 



We find it stated in Mr. Mill's System of Logic a that 

 * Whatever phenomenon varies in any manner whenever 

 another phenomenon varies in some particular manner, 

 is either a cause or an effect of that phenomenon, or is 

 connected with it through some fact of causation.' This 

 assertion may be considered true when it is interpreted 

 with sufficient caution ; but it might otherwise lead us into 

 great errors. There is nothing whatever in the nature of 

 things to prevent the existence of two variations which 

 should apparently follow the same law, and yet have no 

 connexion with each other. One binary star might be 

 going through a revolution which, so far as we could tell, 

 was of apparently equal period with that of another 

 binary star, and according to the above rule the motion 

 of one would be the cause of the motion of the other, 

 which would not be really the case. Two astronomical 

 clocks might conceivably be made so nearly perfect that, 

 for several years, no difference could be detected, and we 

 might then infer that the motion of one clock was the 

 cause or effect of the motion of the other. This matter 

 really requires the most careful discrimination. We must 

 always bear in mind that the continuous quantities of 

 space, time, force, &c., which we measure, are made up of 

 an infinite number of infinitely small units. We may 

 then meet with two variable phenomena which follow 



a Book iii. chap, viii, 6. 



