97 



40. There are six equivalent 60-valued functions, and no 

 more, of the 6th degree, of six terms each, made with six 

 letters. 



41. There are thirteen equivalent 60-valued functions, and 

 no more, each of twelve terms, of the 6 th degree, made with 

 six letters. 



42. There are four, and only four, equivalent 60-valued 

 functions, each of twelve terms, of the 4th degree, made 

 with six letters. 



43. There is one 60-valued function, and no more, of six 

 terms, of the 4th degree, made with six lettters. 



44. There are two 60-valued functions, and no more, of 

 the 3rd degree, one of six and the other of twelve terms, made 

 with six letters. 



45. There is only one 60*valued function, of the 2nd degree, 

 made with six letters. 



None of these 60-valued functions is reducible to the pro- 

 duct of two functions. 



All the above functions, and many others, are given in my 

 Memoir. 



The following Paper was also read : 



" On the Production of Graphite by the decomposition 

 of Cyanogen Compounds,'* by Dr. P. Pauli, communicated 

 by Professor RoscoE. 



The mother liquors obtained from the evaporation of a 

 solution of the so-called black ash are now commercially worked 

 for caustic alkali. 



These liquors contain the following compounds : — 



1. Chiefly hydrate of soda. 



2. Some quantity of carbonate of soda. 



3. Several sulphur compounds of sodium, viz. : sulphide of 

 sodium, hyposulphite of soda, sulphite of soda, and sulphate 

 of soda. 



