207 



II. " On the Specific Gravity of Alloys." By A. MATTHIESSEN, 

 Ph.D. Communicated by Professor WHEATSTONE. Re- 

 ceived November 17, 1859. 



This communication consists of a revised version of a Paper of the 

 author, having the same title, which was read on the 19th May, 

 and of which an abstract has been already given under that date 

 (page 12). 



III. " On an extended Form of the Index Symbol in the Cal- 

 culus of Operations." By WILLIAM SPOTTISWOODE, Esq., 

 M.A., F.R.S. Received November 24, 1859. 

 (Abstract.) 



In the case of two variables (the only one considered in the 

 present paper), the term Index Symbol means the operation 



=x^-+ 

 dx dy 



The new symbol is 



= L+ X !L 

 dx dy 



The symbols X, X l have the following meaning, 



dx dy 

 ,_ d 1 d 1 



dx dy 



where the accent indicates that in the combinations of #, *Bj the 

 differentiations are to affect the subject of operation alone, and not 

 x or y, so far as they appear explicit in the values of &, & r The 

 first object of the paper is to develope the relations between the 

 combinations of 88, X 1 and y Vi ; an d it is found that 



,= 



according as i is even or odd. 



