[ 244 ] 
whofe numerator would be to it’s denominator, as a 
circle of one degree radius, to a circle, whole radius 
is the diameter of a great circle (this lad quantity 
being equal to the whole furface of the fphere) that 
— - 2 
is, by the fraction . 60 — , or, reducing it to a 
^875-5' 
decimal form, .000076 1 54 (thatis, about 1 in 1 3 1 3 1 ) 
and thecomplement of this to unity, viz. .999923846, 
or the fraction 1 3 1 will reprefent the probability 
that it would not be fo. But, becaufe there is the 
lame chance for any one liar to be within the didance 
of one degree from any given dar, as for every other, 
multiplying this fradion into itfelf as many times 
as lhall be equivalent to the whole number of liars, 
of not lets brightnefs than thole in quedion, and 
putting n for this number, .999923846," or the fradior* 
1 3 1 3 Sl will reprefent the probability, that no one of 
13131 
the whole number of dars n would be within one. 
degree from the propofed given dar ; and the com- 
plement of this quantity to unity will reprefent the 
probability, that there would be fome one dar or 
more, out of the whole number n , within the didance 
of one degree from the given dar. And farther, 
becaufe the fame event is equally likely to happen to 
any one dar as to any other, and therefore any 
one of the whole number of dars n might as well 
have been taken for the given dar as any other, we 
mud again repeat the lad found chance n times, and 
confequently 
I 
