338 MALLET. 



629. The memoir consists of the discussion of two problems r 

 the first is a problem given in the Ars Conjectandi of James Ber- 

 noulli ; the other relates to a lottery. 



630. The problem from the Ars Conjectandi is that which 

 is given on page 161 of the work ; we have given it in Art. 117. 



Mallet notices the fact that James Bernoulli in addition to 

 the correct solution gave another which led to a different result 

 and was therefore wrong, but which appeared plausible. Mallet 

 then says, 



Mr. Bernoulli s'etant contente d'indiquer cette singularity apparente, 

 sans en donner Texplication, j'ai cru qu'il ne seroit pas inutile d'entrer 

 dans un plus grand detail ladessus, pour eclaircir parfaitement cette 

 petite difficulte, on verra qu'on peut imaginer une infinite de cas sem- 

 hlables a celui de Mr. Bernoulli, dans la solution desquels il seroit aussi 

 aise d'etre induit en erreur. 



631. Mallet's remarks do not appear to offer any thing new or 

 important ; he is an obscure writer for want of sufficiently develop- 

 ing his ideas. The following illustration was suggested on reading 

 his memoir, and may be of service to a student. Suppose we 

 refer to the theory of duration of life. Let abscissae measured 

 from a fixed point denote years from a certain epoch, and the cor- 

 responding ordinates be proportional to the number of survivors 

 out of a large number born at the certain epoch. Now suppose we 

 wish to know whether it is more probable than not that a new 

 born infant will live more than n years. James Bernoulli's plausi- 

 ble but false solution amounts to saying that the event is more 

 probable than not, provided the abscissa of the centre of gravity of 

 the area is greater than n : the true solution takes instead of the 

 abscissa of the centre of gravity the abscissa which corresponds to 

 the ordinate bisecting the area of the curve. See Art. 485. 



632. We pass to Mallet's second problem which relates to a 

 certain lottery. 



The lottery is that which was called by Montmort la lotterie 

 de Loraine, and which he discussed in his work ; see his pages 

 257—260, 313, 317, 326, 346. The following is practically the 

 form of the lottery. The director of the lottery issues n tickets to 



