CHANCE. 83 



not be continuous, since to very small variations of 

 the abscissa there would not correspond very small 

 variations of the ordinate. It would become impos- 

 sible to trace the curve with an ordinary pencil : that 

 is what I mean. 



What conclusion are we then to draw.? Lumen has 

 no right to say that the probability of the cause (that 

 of his cause, which is our effect) must necessarily be 

 represented by a continuous function. But if that be 

 so, why have we the right? It is because that state of 

 unstable equilibrium that I spoke of just now as initial, 

 is itself only the termination of a long anterior history. 

 In the course of this history complex causes have been 

 at work, and they have been at work for a long time. 

 They have contributed to bring about the mixture of 

 the elements, and they have tended to make everything 

 uniform, at least in a small space. They have rounded 

 off the corners, levelled the mountains, and filled up 

 the valleys. However capricious and irregular the 

 original curve they have been given, they have worked 

 so much to regularize it that they will finally give us 

 a continuous curve, and that is why we can quite con- 

 fidently admit its continuity. 



Lumen would not have the same reasons for drawing 

 this conclusion. P'or him complex causes would not 

 appear as agents of regularity and of levelling ; on the 

 contrary, they would only create differentiation and 

 inequality. He would see a more and more varied 

 world emerge from a sort of primitive chaos. The 

 changes he would observe would be for him unfore- 

 seen and impossible to foresee. They would seem 

 to him due to some caprice, but that caprice would 

 not be at all the same as our chance, since it would 



