244 THE PRINCIPLES OF SCIENCE. [CHAP. 



before we have any comprehension of the principle in its 

 general form. It is easy to see, too, that it is the rule 

 which will, out of a great multitude of cases, lead us most 

 often to the truth, since the most probable cause of an 

 event really means that cause which in the greatest 

 number of cases produces the event. Donkin and Boole 

 have given demonstrations of this principle, but the one 

 most easy to comprehend is that of Poisson. He imagines 

 each possible ca,use of an event to be represented by a 

 distinct ballot-box, containing black and white balls, in 

 such a ratio that the probability of a white ball being 

 drawn is equal to that of the event happening. He further 

 supposes that each box, as is possible, contains the same 

 total number of balls, black and white ; then, mixing all 

 the contents of the boxes together, he shows that if a 

 white ball be drawn from the aggregate ballot-box thus 

 formed, the probability that it proceeded from any par- 

 ticular ballot-box is represented by the number of white 

 balls in that particular box, divided by the total number 

 of white balls in all the boxes. This result corresponds to 

 that given by the principle in question. 1 



Thus, if there be three boxes, each containing ten balls 

 in all, and respectively containing seven, four, and three 

 white balls, then on mixing all the balls together we have 

 fourteen white ones ; and if we draw a white ball, that is 

 if the event happens, the probability that it came out of 



the first box is ^; which is exactly equal to -j ^r 3 ' 



T <T + 1 (T + f 7 



the fraction given by the rule of the Inverse Method. 



Simple Applications of the Inverse Method. 



In many cases of scientific induction we may apply the 

 principle of the inverse method in a simple manner. If 

 only two, or at the most a few hypotheses, may be made 

 as to the origin of certain phenomena, we may sometimes 

 sasily calculate the respective probabilities. It was thus 

 that Biinsen and Kirchhoff established, with a probability 

 ittle short of certainty, that iron exists in the sun. On 

 comparing the spectra of sunlight and of the light proceed- 



1 Poisson, Recherches sur la ProlaUHte (Us Jugements, Paris, 1837, 

 PP 82, 83. 



