12 The Rev. B. Bronwin on the Inverse Calculus 



same purposes as this cotton, and if it be notoriously known 

 that what is now called pyroxyloidine was not brought before 

 the French Academy and the scientific world until towards 

 the middle of last November, the idea of attributing to France 

 the discovery of gun-cotton cannot be seriously entertained, 

 or of assigning to me merely a practical application of that 

 which another would have discovered. 



I appeal to the justice of Frenchmen, to decide the point to 

 whom belongs the honour of not only being the first to apply 

 the new substance in question, but also of having first pre- 

 pared it — to MM. Braconnot and Pelouze, or myself. I 

 must, moreover, add expressly, that it was not xyloidine even 

 which led to my discovery, however intimate may be its rela- 

 tion with gun-cotton ; it was theoretical ideas, possibly very 

 erroneous ones, but which are peculiarly my own, as well as 

 some facts which I was also the first to discover. Suum cuique 

 is a principle of morality on which society at large rests ; 

 why should it not be strictly respected in the republic of sci- 

 ence? M. Pelouze is a distinguished chemist, and already 

 possesses a sufficiently high reputation not to require to ele- 

 vate his pretensions on the merits of others ; and I am fully 

 persuaded that this estimable chemist, of well-known truth 

 of character, will, appreciating with impartiality the circum- 

 stances which have occurred, freely render me the justice to 

 which I consider myself entitled. 



Bale, Dec 28,1846. 



III. On the Inverse Calculus of Definite Integrals. 

 ^ By the Rev. Biiice Bronwin*. 



"T^HIS paper contains several very simple and easy methods 

 ■■ in the inverse calculus of definite integrals; and they 

 show that the function under the sign of integration may have 

 more than one form. The exponents n and p are always 

 positive, and n+p = i an integer. 



First, let (p{x)='ZAmX"^i an ascending series. Then 



=2A;„a'"+'* /" x'^-^dx{\^x)'^ 



= r(w)2;A^«-+« r^^'^^^^j) =4'(«) suppose. 

 * Communicated by the Author. 



