296 Remarks 0)i ProJ'es&or li'aUaccs reply to B\ 



calls tlie attention of the American reader to more impor- 

 tant rvorks, particularly to the third volume of La Croix's 

 Calcul Differentiel et Integral, 2d edition, to which he says, 

 "I would refer for general information on these subjects, 

 and not to the Complement des Elemens d'Algebre, however 

 useful as a school book.''' Now upon looking over this vol- 

 ume of the Calcul Differentiel, and several otjier works 

 mentioned by Professor Wallace, nothing is to be found 

 relative to the point in question between him and B., which 

 is simply to ascertain the fact whether Euler did give, about 

 fifty years since, a demonstration of the binomial theorem, 

 upon principles exactly like those published by Professor 

 Wallace in his formulas i. ii. iii. iv. This was what B. as- 

 serted, and no more ; he said nothing about the application 

 of these formulas, o( Definite Integrals, of La Grange's Fonc- 

 tio7is Generatrices, of La Place's Tkeorie analytique des pro- 

 hahilitcs, of Wallis's Arilhmctica Injinitorxim, of Woodhouse's 

 Analytical Calculations, or Bishop Berkeley's Analyst, with 

 which Professor Wallace fills up the greater part of his 

 reply, though these works have no relation to the subject, 

 and the mention of them can serve no other purpose than icr 

 divert the attention and keep the main question out of sight* 

 Moreover it does not follow, though these important works 

 are thus quoted so readily, that they have all been .seen by Prof, 

 Wallace, His reply furnishes an instance to the contrary in 

 his reference to the Petersburgh Transactions: for in page 

 101, when speaking of Euler's labours on the Integral Cal- 

 culus, he refers to Vols. "XV. and XVL of the J\'ov. Comm, 

 Petrop. — S. 28,'' and to "■ Tom. V. des anciens memoires dc 

 Petersbourg, p. 44." Now there is nothing said about these 

 integrals in the first mentioned volume, and the other with 

 the French title is wrongly quoted. The title is in Latin, 

 being Commentarii Academim Scientianim Imperialis Petro- 

 politance, sometimes in familiar discourse and writing called 

 the ancient memoirs or commentaries, to distinguish them 

 from the new series of the same work. The same peculiar- 

 ity of quotation occurs in page 301, vol. L of Le Gendre's 

 Excrcices de Calcul Integral, where, in speaking of this last 

 volume, he uses the familiar reference of "Ibm. V. des anciens 

 memoires de Petersbourg,'''' which is literally copied in French, 

 by Professor Wallace. Le Gendre also refers to the article 

 28 of vol. XV'^L and to the page 44 of vol. V., instead of 

 ysing in both places the page or the ctrticle. This reference 



