500 



less be found to be diacid, like the diamiues derived from ethylene. 

 Even now the group of diacid diamines is represented in the naphtyl 

 series : 



Naphtylamine V N monoacid. 



H 



(C 10 H 6 )" 1 



Naphtylenediamine H 2 I N diacid. 

 H, J 



The body which I designate by the term Naphtylenediamine, is the 

 base which Zinin obtained by the final action of sulphide of ammo- 

 nium upon dinitronaphtaline. This substance, originally designated 

 seminaphtalidam, and subsequently described as naphtalidine, com- 

 bines, according to Zinin's experiments, with 2 equivalents of hydro- 

 chloric acid*. 



II. "On the Formula investigated by Dr. BRINKLEY for the 

 general Term in the Development of LAGRANGE'S Ex- 

 pression for the Summation of Series and 'for successive 

 Integration." By Sir J. F. W. HERSCHEL, Bart., F.R.S. 

 &c. Received April 26, 1860. 



(Abstract.) 



In the Philosophical Transactions for the year 1807, Dr. Brinkley 

 has investigated an expression of the general term of the series of 

 Lagrange and Laplace for the finite differences and integrals of any 

 function u in terms of its differential coefficients and common inte- 

 grals of successive orders ad infinitum, which is in effect equivalent 

 to the development of the functions (e* l) n and (e f I )~ n in powers 

 of t. The demonstration of the formulae arrived at, as there stated, 

 is circuitous and extremely difficult to follow ; so much so as to ren- 

 der a simpler and easier one a desideratum in analysis, as there are 

 probably few who have had the patience to follow it out to its con- 

 clusion. 



More recently (Philosophical Transactions, 1816), the author of the 

 present paper arrived at a general and extremely simple expression 



* Licbig's Annalen, vol. Ixxxv. p. 328. 



