THE INDUCTIVE OR INVERSE METHOD. 301 



are symptoms of disturbance which would prevent our 

 placing much reliance on any inference from the prevailing 

 order of the known planets to those undiscovered ones 

 which may possibly exist at great distances. These and 

 all like complications in no way invalidate the theoretic 

 truth of the formula, but render their sound application 

 much more difficult. 



Erroneous objections have been raised to the theory of 

 probability, on the ground that we ought not to trust to 

 our a priori conceptions of what is likely to happen, but 

 should always endeavour to obtain precise experimental 

 data to guide us e . This course, however, is perfectly in 

 accordance with the theory, which is our best and only 

 guide, whatever data we possess. We ought to be always 

 applying the inverse method of probabilities so as to take 

 into account all additional information. When we throw 

 up a coin for the first time, we are probably quite ignorant 

 whether it tends more to fall head or tail upwards, and 

 we must therefore assume the probability of each event 

 as -^. But if it shows head, for instance, in the first throw, 

 we now have very slight experimental evidence in favour 

 of a tendency to show head. The chance of two heads is 

 now slightly greater than ^, which it appeared to be at 

 first f , and as we go on throwing the coin time after time, 

 the probability of head appearing next time constantly 

 varies in a slight degree according to the character of our 

 previous experience. As Laplace remarks, we ought 

 always to have regard to such considerations in common 

 life. Events when closely scrutinized will hardly ever 

 prove to be quite independent, and the slightest pre- 

 ponderance one way or the other is some evidence of 

 connexion, and in the absence of better evidence should 

 be taken into account. 



e J. S. Mill, ' System of Logic,' 5th Edition, bk. iii. chap, xviii. 3. 

 f Todhunter's 'History,' pp. 472, 598. 



