Page:Philosophical Transactions - Volume 053.djvu/438

 caue or action, one may make a judgment what is likely to be the conequence of it another time, and that the larger number of experiments we have to upport a concluion, o much the more reaon we have to take it for granted. But it is certain that we cannot determine, at leat not to any nicety, in what degree repeated experiments confirm a concluion, without the particular dicuion of the beforementioned problem; which, therefore, is neceary to be conidered by any one who would give a clear account o the trength of analogical or inductve reaoning; concerning, which at preent, we eem to know little more than that it does ometimes in fact convince us, and at other times not; and that, as it is the means of cquainting us with many truths, of which otherwie we mut have been ignorant; o it is, in all probability, the ource of many errors, which perhaps might in ome meaure be avoided, if the force that this ort of reaoning ought to have with us were more ditinctly and clearly undertood.

Thee obervations prove that the problem enquired after in this eay is no les important than it is curious. It may be afely added, I fancy, that it is alo a problem that has never before been olved. Mr. De Moivre, indeed, the great improver of this part of mathematics, has in his Laws of chance, after Bernoulli, and to a greater degree of exactnes, given rules to find the probability there is, that if a very great number of trials be made concerning any event,