[ 247 ] 
If, befides thefe examples that are obvious to ths 
naked eye, we extend the fame argument to the fmaller 
bility, that no two ftars of that brightnefs will be found, any 
where in the whole heavens, within the diftance of 3' from each 
other, will be reprefented by the fra&ion . l 8 . 75 ’ 5 — 
68 7 5- 5 1 
From twice the Log. of 6875.5 f 7*6746086] then, fubtradl twice 
the Log. of 3,33 See. [1.0457496] and the remainder 6.628859Q 
will be the Log. of the number of times, that 3.33 & c .* is contained 
in 
6875.5 1 v ‘ z * 4254603 times, and confequently 
4254602! 230X23° 
4254603! 
will be equivalent to the former fradfion. From the Log. of 
4254602, fubtradt the Log. of 4254603, and the remainder will 
be — .000000102, the proportional part for an unit in the number 
4254603: this multiplied into 230 times 230, or 52900, gives 
— *0053958, the Log. of the whoie quantity, which correfponda 
to the proportional part for an unit between 80 and 81 ; this quan- 
tity therefore is equivalent to the fraction nearly, the comple- 
ment of which to unity is 
8i* 
In the Pleiades, the five ftars Taygeta, Eledfra, Merope, Alcy- 
one, and Atlas are refpedtively at the diftances of 11, 19I, 
24 •§, 27, and 49 minutes from the liar Maia nearly. From 
7.6746086, twice the Log. of 6875.5, then, as before, fubtradt 
2.0827854, twice the Log. of 1 1 (the number of minutes between 
Taygeta and Maia) and the remainder 5.5918232 will be the 
Log. of the number of times, that 77 * is contained in 6875.5* VIZ> 
390682 times; and confequently a fradtion, whofe denominator 
is this number, and whofe numerator is this number lefs by an 
unit, multiplied into itfelf 1500 times, will reprefent the probabi- 
lity, that no liar out of 1500, fcattered by chance in the whole 
heavens, would he within the diftance of 11 minutes from the 
ftar Maia. From the Log. of 390681 therefore fubtradb the 
Log. of 390682, as in the former example, and the remainder will 
be — .00000111, the proportional part for an unit in the number 
390682, which multiplied by 1500 will give us — .0016650 for 
the Log. of the probability fought. In like manner from 
