Page:Philosophical Transactions - Volume 053.djvu/437

 circumtances, it has happened a certain number of times, and failed a certain other number of times. He adds, that he oon perceived that it would not be very difficult to do this, provided ome rule could be found according to which we ought to etimate the chance that the probability for the happening of an event perfectly unknown, hould lie between any two named degrees of probability, antecedently to any experiments made about it; and that it appeared to him that the rule mut be to uppoe the chance the ame that it hould lie between any two equidifferent degrees; which, if it were allowed, all the ret might be eaily calculated in the common method of proceeding in the doctrine of chances. Accordingly, I find among his papers a very ingenious olution of this problem in this way. But he afterwards conidered, that the potulate on which he had argued might not perhaps be looked upon by all as reaonable; and therefore he choe to lay down in another form the propoition in which he thought the olution of the problem is contained, and in a cholium to ubjoin the reaons why he thought o, rather than to take into his mathematical reaoning any thing that might admit dipute. This, you will oberve, is the method which he has purued in this eay.

Every judicious peron will be enible that the problem now mentioned is by no means merely a curious peculation in the doctrine of chances, but neceary to be olved in order to a ure foundation for all our reaonings concerning pat facts, and what is likely to be hereafter. Common ene is indeed ufficient to hew us that, from the obervation of what has in former intances been the conequence of a certain