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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 6th 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. 
AH 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. 
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