484 THE PRINCIPLES OF SCIENCE. [CHAP 



Probable Connection of Varying Quantities. 



We find it stated by Mill, 1 that "Whatever pheno- 

 menon varies in any manner whenever another pheno- 

 menon 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 error. 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 connection with each other. 

 One binary star might be going through a revolution 

 which, so far as we could tell, was of 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 de- 

 tected, and we might then infer that the motion of one 

 clock was the cause or effect of the motion of the other. 

 This matter requires careful discrimination. We must 

 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 laws 

 so nearly the same, that in no part of the variations open 

 to our observation can any discrepancy be discovered. 

 I grant that if two clocks could be shown to have kept 

 exactly the same time during any finite interval, the pro- 

 bability would become infinitely high that there was a 

 connection between their motions. But we can never 

 absolutely prove such coincidences to exist. Allow that 

 we may observe a difference of one-tenth of a second in 

 their time, yet it is possible that they were independently 

 regulated so as to go together within less than that 

 quantity of time. In short, it would require either an in- 

 finitely long time of observation, or infinitely acute powers 

 ot measuring discrepancy, to decide positively whether 

 two clocks were or were not in relation with each other. 



1 System of Logic, bk. iii. chap. viii. 6. 



