WILLIAM EMERSON. 34;3 



The formula explains itself; for the chance of throwing the 

 specified face at each throw is -, and the chance of not throwing 



71 — 1 



it is . Hence by the fundamental principles of the subject 



the chance of having the specified face just m times in p throws is 



I m \p — m \nj 



n 



Since the whole number of cases in the p throws is if, it follows 

 that the number of cases in which the required event can happen is 



P 



I m I p — m 



(n - 1) 



p-m . 



and the result had been previously given by Montmort in this 

 form : see his page 307. 



640. On the whole we may say that Mallet's memoir shews 

 the laborious industry of the writer, and his small acquaintance 

 with preceding works on the subject. 



641. William Emerson published in 1776 a volume entitled 

 Miscellanies, or a Miscellaneous Treatise ; containing several Mathe- 

 matical Subjects. 



The pages 1 — 48 are devoted to the Laws of Chance. These 

 pages form an outline of the subject, illustrated by thirty-four 

 problems. There is nothing remarkable about the work except 

 the fact that in many cases instead of exact solutions of the 

 problems Emerson gives only rude general reasoning which he 

 considers may serve for approximate solution. This he himself 

 admits ; he says on his page 47, 



It may be observed, that in many of these problems, to avoid more 

 intricate methods of calculation, I have contented myself with a more 

 lax method of calculating, by which I only approach near the truth. 



See also the Scholium on his page 21. 



Thus Emerson's work would be most dangerous for a beginner 

 and quite useless for a more advanced student. 



We may remark that pages 49 — 138 of the volume are devoted 

 to Annuities and Insurances. 



