[ 86 ] 
, n W-4-I «4-2/ \ 
[q) X r" 
‘ I 2 -2 
n w— |— I w-f-2 / \ . 
(q-^w)%nr^ 
12 2 ' 
n n-\-i n-\-7. 
« « — r 
I 2 3 
H W— |— I W— }— 2 /■ \ ft—i tl" 
- -I—. (q — 7W) X -• •— 
12 2\.2*5/I2 
&C. 
From which general expreflion, by expounding 
7n by o, 4-1, — I, 4-2, — 2, &c. fucceffively, the 
fum of all the chances, whereby the difference of 
the politive and negative errors can fall within the 
propofed limits, will be found i which, divided by 
X X 1 — r|~”, will give the true meafure 
of the probability required: .from whence the ad- 
vantage of taking the Mean of feveral obfervations 
might be Ihewn : but this I fhall exemplify in the 
next propolition j which is better adapted to the 
purpofe, and to which this is premif^d, as a Lemma. 
Remark. 
If r be taken = i, or the chances for the errors in 
excefs and defedl be fuppofed exadlly the fame ; 
then our expreflion, by expunging the powers of r , 
will become the very fame- with that (hewing the 
chances for throwing « -b y points with « dice j each 
die having as many faces (w), as the refult of any 
one Angle obfervation, can come out different ways. 
Which may be otherwife made to appear, indepen- 
dent of any kind of calculation, from the bare con- 
fider- 
