CHANCE. 67 



mistake, since he is able to pay dividends to his 

 shareholders. These dividends would not vanish if 

 a very far-sighted and very indiscreet doctor came, 

 when once the policies were signed, and gave the 

 manager information on the chances of life of the 

 assured. The doctor would dissipate the ignorance 

 of the manager, but he would have no effect upon 

 the dividends, which are evidently not a result of 

 that ignorance. 



II. 



In order to find the best definition of chance, we 

 must examine some of the facts which it is agreed 

 to regard as fortuitous, to which the calculation of 

 probabilities seems to apply. We will then try to 

 find their common characteristics. 



We will select unstable equilibrium as our first 

 example. If a cone is balanced on its point, we know 

 very well that it will fall, but we do not know to 

 which side ; it seems that chance alone will decide. 

 If the cone were perfectly symmetrical, if its axis 

 were perfectly vertical, if it were subject to no other 

 force but gravity, it would not fall at all. But the 

 slightest defect of symmetry will make it lean slightly 

 to one side or other, and as soon as it leans, be it 

 ever so little, it will fall altogether to that side. 

 Even if the symmetry is perfect, a very slight trepida- 

 tion, or a breath of air, may make it incline a few 

 seconds of arc, and that will be enough to determine 

 its fall and even the direction of its fall, which will be 

 that of the original inclination. 



A very small cause which escapes our notice 

 determines a considerable effect that we cannot fail 

 to see, and then we say that that effect is due to 



