[ 85 ] 
Now, to find from hence the fiim of all the 
chances whereby the excefs of the pofitive errors 
above the negative ones can amount, precifely, to a 
given number w, it will be fufficient (infiead of mul- 
tiplying the former feries by the whole of the latter) 
to multiply by fuch terms of the latter, only, as are 
neceflary to the production of the given exponent 
in queftion. Thus, the firft term of the 
former feries is to be multiplied by that term of the 
fecond, whofe exponent is nv-\-m^ in order that the 
power of r, in the produCt, rriay be r”. But it is 
plain, from the law of the feries, that the coeffi- 
cient of this term (putting m = q) will be 
” (y)j q being the number of faCtors j and 
^ 3 
I 
confequently, that the produCt under confideration 
will be Again, the fecond term 
of the former feries being — the exponent 
of the correfponding _ term of the latter will be 
— w nv m (=y — w), and therefore the term 
itfelf equal to 
n n-\~l »4-2 
(q — w) X : which, 
j • ^ „ . n »-j-i «+2 / X 
drawn into — gives (y — “zejjx — 
12.3 
for the fecond term required. 
In like manner, the third term, of the prod uCl, 
whofe exponent is w, will be found 
n n-\-\ n -}-2 
(y — iw) 
n n — 
X 
I 2 
r” : and the fum of all the terms having the 
fame given exponent (/«) will confequently be 
