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caufe or a&icn, one may make a judgment what Is 
likely to be the confequence of it another time, and 
that the larger number of experiments we have to 
lupport a conclufion, fo much the more reafon we 
have to take it for granted. But it is certain that we 
cannot determine, . at lead not to any nicety, in what 
degree repeated experiments confirm a conclufion, 
without the particular difeuffion of the beforementi- 
oned problem ; which, therefore, is neceflary to be con- 
lidered by any one who would give a clear account ot 
the ftrength of analogical or indaSUve reafoning ; con- 
cerning, which at prefent, we feem to know little more 
than that it does fometirrtes in find convince us, and 
at other times not ; and that, as it is the means ot 
cquainting us with many truths, of which otherwife 
we muft have been ignorant ; fo it is, in all proba- 
bility, the fource of many errors, which perhaps 
might in fome meafure be avoided, if the force that 
this fort of reafoning ought to have with us were more 
diftindtly and clearly underftood. 
Thefe obfervations prove that the problem enquired 
after in this etfay is no lefs important than it is curi- 
ous. It may be fafely added, I fancy, that it is alfo 
a problem that has never before been folved. Mr. 
De Moivre, indeed, the great improver of this part 
of mathematics, has in his Laws of chance *, after Ber- 
noulli, and to a greater degree of exadtnefs, given 
rules to find the probability there is, that if a very 
great number of trials be made concerning any event, 
* See Mr. De Moivre’s Doftrinc of Chances , p. 243, &c. He 
has omitted the demonftrations of his rules, but thefe have been 
fince fupplied by Mr. Simpfon at the conclufion of his treatife 
on The Nature and Laws of Chance . 
the 
