QUANTITATIVE INDUCTION. 107 



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 one year, or any finite 

 interval of time, the probability would become infinitely 

 high that there was a connexion between their motions. 

 But it is apparent that we can never absolutely prove 

 such coincidences to exist. Allow that we may observe 

 a difference of one tenth or one hundredth of a second in 

 their time, yet it is just possible that they were independ- 

 ently 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 

 of measuring a discrepancy to decide positively whether 

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



A similar question actually occurs in the case of the 

 moon's motion. We have absolutely no record that any 

 other portion of the moon was ever visible to men than 

 such as we now see. This fact sufficiently proves that 

 within the historical period the rotation of the moon on its 

 own axis has coincided with its revolutions round the 

 earth. Does this coincidence prove a relation of cause 

 and effect to exist between these motions ? The answer 

 must be in the negative, because there might have been 

 so slight a discrepancy between the motions that there 

 has not yet been time to produce any appreciable effect. 

 There may nevertheless be a high probability of con- 

 nexion. 



The whole question of the relation of quantities thus 

 resolves itself into one of probability. When we can 

 only rudely measure a quantitative result, we can assign 

 but slight importance to any correspondence. Because 

 the brightness of two stars seems to vary in the same- 

 manner there is no appreciable probability that they have 

 any relation with each other. Could it be shown that 



