THE INDUCTIVE OR INVERSE METHOD. 281 



happening. He further supposes that each box, as is 

 possible, contains the same total number of balls, black 

 and white ; and 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 particular ballot-box is represented 

 by the number of white balls in that particular box, 

 divided by that total number of white balls in all the 

 boxes. This result corresponds to that given by the 

 principle in question c . 



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

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

 w T hite balls, then on mixing all the balls together we have 

 fourteen Avhite 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 T 7 T ; which is exactly equal to ^ ^-,the 



Tff + T& + T(&amp;gt; 



fraction given by the rule of the Inverse Method. 



Simple Applications of the Inverse Method. 



In many cases of scientific induction w T e 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, or the connection of 

 one phenomenon with another, we may sometimes easily 

 calculate the respective probabilities of these hypotheses. 

 It was thus that Professors Bunsen and Kirchhoff esta 

 blished, with a probability little short of certainty, that 

 iron exists in the sun. On comparing the spectra of sun 

 light and of the light proceeding from the incandescent 

 vapour of iron, it became apparent that at least sixty 

 bright lines in the spectrum of iron coincided with dark 



c Poisson, Rechcrclies sur la Probability cles Jugcmcnts, Paris, 1837, 

 pp. 82, 83. 



