102 Professor Wallace in Reply to the Remarks of B. 
analytique “e probabilités, 1814. These theories,as 
is "well Ped are applied with singular success in the 
most abstruse physical researches, whilst in the works of 
— wpretrges e scarcely a word, relative to them, 
ngiven. Lately, however, in the Phil. ‘Trans. and 
paedhe few other works of less note, several have distinguish- 
ed themselves in these investigations. In calling the at- 
tention of the American reader to those important — 
ries, it is to these works, and also to La Croix’s work o 
the Differential and Integral Calculus, 2d. Ed. stiniculeddy 
the 3d. vol. published in 1819, that I would refer —— 
information on these subjects, and not to the 
des Eléméns @ orp however useful as a wihel nye 
To those who take a pleasure in proceeding from the most 
elementary principles to the most remote conclusions,” it 
ss be highly interesting to discover the different ways 
n which the same truths may be established, and to pur- 
sue those methods, which from the most ee principles 
d to to the most general results. e 
ations, it is eee 
e merits age a 
all» nents in the modern analysis 
principally depend on the developement and application 
of series. Hence Lagrange gives Fermat the honour of first 
exhibiting the germ of the new Calculus (Calcul des fone- 
tions p. 325.) whilst Laplace gives almost the whole merit 
to Wallis. In his Théorie analytique des probabilités (2d. 
Ed. 1814,) one of the most profound and elegant analyti- 
cal performances in existence, speaking, in the preface to 
this work, of the 4rithmetic of Infinities of Wallis, he says, 
at itis “ I’ un des ouvrages qui ont le plus contribué 
au progrés de I’ analyse, et ou /’ on trouve le Germe de la 
théorie des intégrales définies, ? une des bases de ce nou- 
veau calcul des probabilités.” Wallis published his Arith- 
metica Infinitorum in 1657. (He was born in 1616, ninety- 
ann ab before Euler existed.) Laplace gives his re- 
ble theorem in p. 465. of the additions to his Theory 
of Probabilities, where he shews how nearly it is connect- 
ed with the modern calculus, particularly the theory of 
