[ 417 ] 
By calculations fimilar to thefe may be determined 
univerfally, what expectations are warranted by any 
experiments, according to the different number of 
times in which they have fucceeded and failed; or 
what fhould be thought of the probability that any 
particular caufe in nature, with which we have any 
acquaintance, will or will not, in any fingle trial, 
produce an effeCt that has been conjoined with it. 
Molt perfons, probably, might expeCt that the 
chances in the fpecimen I have given would have been 
greater than I have found them. But this only fhews 
how liable we are to error when we judge on this 
fubjeCt independently of calculation. One thing, 
however, fhould be remembered here; and that 
is, the narrownefs of the interval between and 
™ or between i-° 4. ^ and -L° — ° Had 
this interval been taken a little larger, there would 
have been a confiderable difference in the refults of 
the calculations. Thus had it been taken double, or 
z — -5-t> it would have been found in the fourth in- 
flance that inflead of odds againft there were odds 
, for being right in judging that the probability of draw- 
ing a blank in a fingle trial lies between 4 4. -j- and 
10 1 
nr r TT* 
The foregoing calculations further fhew us the 
ufes and defeCts of the rules laid down in the effay. 
’Tis evident that the two laft rules do not give us 
the required chances within fuch narrow limits as 
could be wifhed. But here again it fhould be confi- 
dered, that thefe limits become narrower and narrow- 
er as q is taken larger in refpeCt of p ; and when p 
and q are equal, the exaCt folution is given in all cafes 
by the fecond rule. Thefe two rules therefore afford 
a direction 
1 
