82 SCIENCE AND METHOD. 



inch in the cause produces a difference of a mile in 

 the effect. If I am to win in case the effect corre- 

 sponds with a mile bearing an even number, my 

 probability of winning will be |. Why is this ? 

 Because, in order that it should be so, the cause must 

 correspond with an inch bearing an even number. 

 Now, according to all appearance, the probability 

 that the cause will vary between certain limits is 

 proportional to the distance of those limits, provided 

 that distance is very small. If this hypothesis be not 

 admitted, there would no longer be any means of 

 representing the probability by a continuous function. 

 Now what will happen when great causes produce 

 small effects ? This is the case in which we shall not 

 attribute the phenomenon to chance, and in which 

 Lumen, on the contrary, would attribute it to chance. 

 A difference of a mile in the cause corresponds to 

 a difference of an inch in the effect. Will the 

 probability that the cause will be comprised between 

 two limits n miles apart still be proportional to n ? 

 We have no reason to suppose it, since this dis- 

 tance of n miles is great. But the probability that 

 the effect will be comprised between two limits n 

 inches apart will be precisely the same, and ac- 

 cordingly it will not be proportional to n, and that 

 notwithstanding the fact that this distance of n 

 inches is small. There is, then, no means of repre- 

 senting the law of probability of the effects by a 

 continuous curve. I do not mean to say that the 

 curve may not remain continuous in the analytical 

 sense of the word. To iiifmitely small variations 

 of the abscissa there will correspond infinitely small 

 variations of the ordinate. But practically it would 



