616 APPENDIX. 



1057. The work which we have quoted at the beginning of 

 Art. 347 contains some remarks on onr subject; they form part 

 of the Introduction a la Philosopliie, and occur on pages 82 — 93 of 

 the second volume. It appears from page XLVII of the first volume 

 that this work was first published by 's Gravesande in 1736. The 

 remarks amount to an outline of the mathematical Theory of Pro- 

 bability. It is interesting to observe that 's Gravesande gives in 

 effect an example of the inverse use of James Bernoulli's theorem; 

 see his page 85 : the example is of the kind which we have used 

 for illustration in Art. 125. 



1058. The result attributed to Euler in Art. 131 is I find 

 really due to John Bernoulli. See Johannis Bernoulli... Opera 

 Omnia, Tomus Quartus, 1742, p. 22. He says, 



Atque ita satisfactum est ardenti desiclerio Fratris mei, qui agnoscens 

 summse liujus pervestigationem difficiliorem esse qiiam quis putaverit, 

 ingenue fassus est, omnem suam industriani fuisse elusam : Si quis in- 

 veniat, inquit, tiohisque commu7iicet, quod i7idustriam nostram elusit 

 hactenus, magna s de nobis gratias ft ret. Yid. Tractat. de Seriehus inji- 

 nitis, jD. 254:. Utinam Frater superstes esset. 



1059. An essay on Probability was written by the celebrated 

 Moses Mendelsohn ; it seems to have been published in his Phi- 

 losophische Schriften in 1761. I have read it in the edition of the 

 Philosophische Schriften which appeared at Berlin in 1771, in two 

 small volumes. The essay occupies pages 243 — 283 of the second 

 volume. 



Mendelsohn names as writers on the subject, Pascal, Format, 

 Huygens, Halley, Craig, Petty, Montmort, and De Moivre. Men- 

 delsohn cites a passage from the work of 's Gravesande, which 

 amounts to an example of James Bernoulli's theorem ; and Men- 

 delsohn gives what he -considers to be a demonstration of the 

 theorem, but it is merely brief general reasoning. 



The only point of interest in the memoir is the following. 

 Suppose an event A has happened simultaneously, or nearly so, 

 with an event B; we are then led to enquire whether the con- 

 currence is accidental or due to some causal connexion. Men- 



