104: IIki'okt .S.A.A. AbVAXcKMKN'i OF Science. 



yc'iirs ago, when railways were in their infancy. Quetelet says : 

 " How many statistical questions are connected with the establish- 

 ment of railways? Only to quote one example. There is a dependence 

 between the number of tra^■ellers transported each day and the fares 

 they have to pay : this dependence is sucli that the I'eceipts augment 

 or diminish according to the scale of fares. Every one can conceive 

 that if the fares were too low, the number of travellers, although more 

 considerable, would not be sufficient to pay the expenses of the enter- 

 pi'ise ; if, on the contrary, they were too high, the number of travellers 

 wuuld diminish, and the administration again would run the risk of a 

 loss. There is, then, a maximum which can be obtained, and which 

 can only be determined by the aid of good statistical documents. 



"Let us call ,«• the amount of the fare, and y the number of pas- 

 sengers corresponding to the fixing of this fare. There will be a 

 relation between x and y 



y =/{■'-')- 



The most simple hypothesis is to suppose that the number of passengers 

 increase in proportion as the fares diminish ; thus y = ', whence yx — a, 



which indicates an equilateral hyperbola referred to its asymptotes. 

 If x — u, y = infinity, that is to say, supposing the fare to be nothing, 

 the number of travellers will be infinitely great. On the other hand, 

 making ,t = infinity, y = o, that is to say, supposing the fare to be in- 

 finitely great, the number of travellers will be nil. We may conceive 

 that in most cases the curve will not differ much from an equilateral 

 hyperbola." 



