[ 373 ] 
the proportion of the number of times it will hap- 
pen, to the number of times it will fail in thofe tri- 
als, fhould differ lefs than by fmall aligned limits 
from the proportion of the probability of its happen- 
ing to the probability of its failing in one fingle trial. 
But I know of no perfon who has fhewn how to de- 
duce the folution of the converfe problem to this ; 
namely, “ the number of times an unknown event 
“ has happened and failed being given, to find the 
“ chance that the probability of its happening fhould 
« lie fomewhere between any two named degrees of 
« probability.” What Mr. De Moivre has done 
therefore cannot be thought fufficient to make the 
confideration of this point unneceffary : efpecially, as 
the rules he has given are not pretended to be rigo- 
roufly exadt, except on fuppofition that the number 
of trials made are infinite ; from whence it is not ob- 
vious how large the number of trials muff be in or- 
der to make them exadt enough to be depended on 
in pradtice. 
Mr. De Moivre calls the problem he has thus folv- 
ed, the hardeft that can be propofed on the fubjedt 
of chance. His folution he has applied to a very 
important purpofe, and thereby fhewn that thofe 
a remuch miftaken who have infinuated that the Doc- 
trine of Chances in mathematics is of trivial confe- 
quence, and cannot have a place in any ferious enqui- 
ry *. The purpofe I mean is, to fhew what reafon 
we have for believing that there are in the conftitution 
of things fixt laws according to which events happen, 
and that, therefore, the frame of the world muft be 
* See his Doctrine of Chances, p. 252, &c. 
Vol. LIII. Ccc 
the 
