[ 29 6 ] 
LII. A Demonflr ation of the Second Rule in 
the EJfay towards the Solution of a Pro- 
blem in the DoElrme of Chances , publifhed 
in the Philofophical Traiif actions, Vol. LIII. 
Communicated by the Rev. Mr, Richard 
Price, in a Letter to Mr, John Canton, 
M.A.F.R.S . 
Dear Sir, Nov. 26, 1764. 
Read Dec. 6, T Send you the following Supplement to the 
1 76+ * JL ^[J a y 011 a Problem in the Doctrine of 
Chances , hoping that you may not think it improper to 
be communicated to the Royal Society. I Ihould not 
have troubled you again in this way had I not found 
that fome additions to my former papers were necelfary 
in order to explain fome paflages in them, and particular- 
ly what is hinted in the note at the end of the Appendix. 
“ I have firft given the deduction of Mr. Bayes’s fe- 
“ cond rule chiefly in his own words ; and then 
11 added, as briefly as poffible, the demonftrations of 
<c feveral propofitions, which feem to improve con- 
“ fiderably the folution of the problem, and to throw 
“ light on the nature of the curve by the quadrature 
“ of which this folution is obtained.” Perhaps, 
there is no reafon for being very anxious about pro- 
ceeding to further improvements. It would, how- 
ever, be very agreeable to me to fee a yet eafier and 
nearer approximation to the value of the two leries’s 
in the firfl: rule : but this I muft leave abler pcrlons 
to feek, chufing now entirely to drop this lubjed. 
The 
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