[ 8 ? ] 
^deration, that the chances for throwing precifely 
the number w, with n dice, whereof the faces, of 
each, are numbered — ‘u 3, — 2, — i, o, 
+ muft be the very fame as 
’ the chances whereby the pofitive errors can exceed 
the negative ones by that precife number ; which laft 
are, evidently, the fame as the chances for throwing 
precifely the number [ov n-\-q) with 
the fame n dice, when they are numbered in the com- 
mon way, with the terms of the natural progreffion 
I, a, 3,4, y, ^c . : becaufe the number upon each 
face being, here, increafed by -u + i , the whole in- 
creafe upon all the h faces will be expreffed by 
•v-\- i.n-y fo that there will be now the very fame 
chance for the number as there was 
before for the number m ; fince the chances for 
throwing any faces affigned will continue the fame, 
however thofe faces are numbered. 
Proposition II. 
Suppofing the refpedlive chances, for the different 
errors which any fingle obfervation can admit 
of, to be expreffed by the terrns of the feries 
r~^ -j- -h 
(whereof the coefficients, 
from the middle one (*1;+ i), decfeafe, both ways, 
according to the terms of an arithmetical progref- 
fion) : ’tis propofed to determine the probability, 
or odds, that the error, by taking the Mean of a 
given number (/) of obfervaiions, exceeds not a 
• • I 
given quantity I y j. 
Purfuing 
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