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An APPENDIX. 
CONTAINING 
An Application of the foregoing Rules to fome parti- 
cular Cafes. 
H E firft rule gives a dired and perfed folution 
in all cafes ; and the two following rules are 
only particular methods of approximating to the fo- 
lution given in the firft rule, when the labour of ap- 
plying it becomes too great. 
The firft rule may be uled in all cafes where either 
p or q are nothing or not large. The fecond rule 
may be ufed in all cafes where mz is lefs than Vy; 
and the 3d in all cafes where iti z is greater than 
1 and lefs than ^ , if n is an even number and very 
large. If n is not large this laft rule cannot be much 
wanted, becaufe, m decreafing continually as n is 
diminifhed, the value of z may in this cafe be taken 
large, (and therefore a confiderable interval had be- 
tween — —z and 4- z,) and yet the operation be 
n n 
carried on by the 2d rule; or mz not exceed \/y. 
But in order to fhew diftindly and fully the nature 
of the prefent problem, and how far Mr. Bayes has 
carried the folution of it ; I fhalJ give the refult of 
this folution in a few cafes, beginning with the loweft 
and moft fimple. 
Let 
