and that opinion of its character and tendency which is 

 not yet quite exploded, was fixed in the general mind. 



Montmort, James Bernoulli, and perhaps others, had 

 made some slight attempts to overcome the mathema- 

 tical difficulty ; but De Moivre, one of the most pro- 

 found analysts of his day, was the first who made 

 decided progress in the removal of the necessity for 

 tedious operations. It was then very much the fashion, 

 and particularly in England, to publish results and con- 

 ceal methods ; by which we are left without the know- 

 ledge of the steps which led De Moivre to several of his 

 most brilliant results. These however exist, and when 

 we look at the intricate analysis by which Laplace ob- 

 tained the same, we feel that. we have lost some im- 

 portant links * in the chain of the history of discovery. 

 De Moivre, nevertheless, did not discover the inverse 

 method. This was first used by the Rev. T. Bayes, in 

 Phil. Trans, liii. 370. ; and the author, though now 

 almost forgotten, deserves the most honourable remem- 

 brance from all who treat the history of this science. 



Laplace, armed with the mathematical aid given by 

 De Moivre, Stirling, Euler, and others, and being in 

 possession of the inverse principle already mentioned, 

 succeeded both in the application of this theory to more 

 useful species of questions, and in so far reducing the dif- 

 ficulties of calculation that very complicated problems 

 may be put, as to method of solution, within the reach 

 of an ordinary arithmetician. His contribution to the 

 science was a general method (the analytical beauty and 

 power of which would alone be sufficient to give him a 

 high rank among mathematicians) for the solution of 



* The same may be said of several propositions given by Newton. 



