Professor Wallace in are the Remarks of B. 101 
manner, as Kramp has done by means of his Factoriels, (a 
name by which he designates series similar to Stainville's) 
and extended their application to definite i 
When a writer generalises too hastily it is “aificatt to 
form an idea of the truth or legitimacy of his conclusions, 
and that Euler had, in no small degree, this failing, will be 
evident to any one who reads his works. Lagrange (Le- 
gons sur le Calcul des fonctions, 1806, p. 409) speaking of 
takes as granted what he ought to prove. ‘Car (says he) 
Ja Démonstration qu’ on trouve dans le tome XV des Novt 
Commentarii de Petersbourg, est si compliquée, gee il - 
difficile de juger de sa justesse et de sa généralité.’ 
not this observation hold, in its full force, against Mir. °B. 
pra in asserting that, fa xfo=fia+) as deduced from 
particular and limited premises. 
If Euler has not been completely successful in the above 
and similar instances, still it wonld be an injustice to the 
memory of so great a man, not to acknowledge that he has 
contributed as much, if not more than any other individual 
of his time, to the modern improvements in almost en 
department of the new een In vols. oie and X 
of the Nov. Comm. Petrop. he has hed his Integral 
Calculus, in tom. XVI. of which Ss. 2, the integral fae 
(log. se Js, | is given, and ae tom. V. des 
anciens mémoires de Petersk - | 
fork dx=14/7 is of the same form hand is integrated be- 
we the limits r=o and c= @ ; Sghith shews that he had 
in possession of the germ of the theory of definite in- 
soley one of the most useful, though one of the most 
It, in the modern analysis, and which has since been 
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the Polytechnic School, by Herschel in the Phil. Tis. 
1814, and others who have pursued and still pursue this in- 
teresting investigation. Similar researches have been 
carried on by different authors, and under various denom- 
inations, and Laplace has further generalized these theo- 
ries in his Calcul des fonctions générailces, exhibited in vol. 
8. of the Journal of the Polytechnic School, and in his 
