NATURE 719 



mate than the second? In any case it is not the definition that tells 

 us. We are therefore bound to complete the definition by saying, 

 " ... to the total number of possible cases, provided the cases are 

 equally probable." So we are compelled to define the probable by 

 the probable. How can we know that two possible cases are equally 

 probable ? Will it be by a convention ? If we insert at the beginning 

 of every problem an explicit convention, well and good! We then 

 have nothing to do but to apply the rules of arithmetic and algebra, 

 and we complete our calculation, when our result cannot be called in 

 question. But if we wish to make the slightest application of this 

 result, we must prove that our convention is legitimate, and we shall 

 find ourselves in the presence of the very difficulty we thought we had 

 avoided. It may be said that common-sense is enough to show us the 

 convention that should be adopted. Alas ! M. Bertrand has amused 

 himself by discussing the following simple problem : " What is the 

 probability that a chord of a circle may be greater than the side of 

 the inscribed equilateral triangle ? " The illustrious geometer suc- 

 cessively adopted two conventions which seemed to be equally impera- 

 tive in the eyes of common-sense, and with one convention he finds 

 1-2, and with the other 1-3. The conclusion which seems to follow 

 from this is that the calculus of probabilities is a useless science, that 

 the obscure instinct which we call common-sense, and to which we 

 appeal for the legitimization of our conventions, must be distrusted. 

 But to this conclusion we can no longer subscribe. We cannot do 

 without that obscure instinct. Without it, science would be impos- 

 sible, and without it we could neither discover nor apply a law. 

 Have we any right, for instance, to enunciate Newton's law? No 

 doubt numerous observations are in agreement with it, but is not that 

 a simple fact of chance? and how do we know, besides, that this law 

 which has been true for so many generations will not be untrue in the 

 next? To this objection the only answer you can give is: It is very 

 improbable. But grant the law. By means of it I can calculate the 

 position of Jupiter in a year from now. Yet have I any right to say 

 this? Who can tell if a gigantic mass of enormous velocity is not 

 going to pass near the solar system and produce unforeseen perturba- 

 tions? Here again the only answer is: It is very improbable. From 

 this point of view all the sciences would only be unconscious applica- 

 tions of the calculus of probabilities. And if this calculus be con- 

 demned, then the whole of the sciences must also be condemned. 

 I shall not dwell at length on scientific problems in which the inter- 

 vention of the calculus of probabilities is more evident. In the fore- 

 front of these is the problem of interpolation, in which, knowing a 

 certain number of values of a function, we try to discover the inter- 

 mediary values. I may also mention the celebrated theory of errors 

 of observation, to which I shall return later; the kinetic theory of 



