[ 4i6 ] 
2 Y 
and lefs than 1-2 E at bi - 2 E «/’ bq, E being «+• 1 
n 
n 
ipq 
P A 
xE ^ p xmz- 
m z 
, ??-2 m 
+ X — 
2 n 5 
2; 
&C. 
V n ' 3 
By making here 1000 =/> ioorrr:^ noo = ?z 
,-U = s, ct=— ’= i.o 4 83o 8.E<A? = _ x £T. h 
pj 2 %/ K y 
being the ratio whofe hyperbolic logarithm is T ' T X 
1 1 1 1 1 
— - - X - 
n P q 360 rp 
I I 
— 7- X — 
x 260 « 1 * 3 * 5 
1 --&C. 
*>* ? S 
and K the ratio of the quadrantal arc to radius; the 
former of thefe expreffions will be found to be .7953, 
and the latter .9405 &c. The chance enquired after, 
therefore, is greater than .7953, and lefs than .9405. 
That is; there will be an odds lor being right in gueff- 
ing that the proportion of blanks to prizes lies nearly 
between 9 to 1 and 1 1 to 1, (or exactly between 9 to 
1 and 1 11 1 to 99) which is greater than 4 to 1, 
and lefs than 16 to 1. 
Suppofe, again, that no more is known than that 
blanks have been drawn 10,000 times and prizes 1000 
times in 11000 trials; what will the chance now 
mentioned be? 
Here the fecond gs well as the firft rule becomes 
ufelefs, the value of m z being fo great as to render 
it fcarcely poffible to calculate diredtly the feries ;nz - 
4 -t —1 x ?, LJL - &c. The third rule, therefore, 
3 2 \n 5 
mull; be -aTed ; and the information it gives us is, that 
the required chajice is greater than .97421, or more 
than an odds of 40 to 1. 
