144 
sults of Mr. Galbraith’s analyses. Having had occasion to 
analyze the water of the river Liffey above King’s Bridge, in 
order to ascertain the quantity of alkalies contained in it, he 
found distinct evidence of the presence of potash, and none 
whatever of the presence of soda. And as this river takes its 
rise in the granite platform of the Wicklow hills, and might 
be said to contain the washings of that district, the presence 
of potash strongly confirms the opinion maintained by Mr. 
Galbraith, that the felspar of the Dublin and Wicklow hills 
was potash felspar. 
Mr. Galbraith explained, that he had used the terms orthose 
and albite in the sense in which Sir R. Kane had used them, 
although he did not consider it quite exact, as his object was 
to confine himself exclusively to the consideration of the rela- 
tive numerical quantities of potash and soda in the Wicklow 
felspars. 
The Rev. Professor Graves continued the reading of his 
Paper on the principles which regulate the interchange of 
symbols in certain symbolic equations. 
Let 7 and p be two distributive symbols of operation, which 
combine according to the law expressed by the equation, 
pw =7p+a, (1) 
a being a constant, or at least a symbol of distributive opera- 
tion commutative with both 7 and p. 
In this fundamental equation, if we change 7 into p and p 
into —7, it becomes 
—Tp=—pT+a, 
or (2) 
pT =T7P Ta, 
the same as before. From this it follows, that in any symbo- 
lical equation, 
p (x; p)=9, (3) 
which has been directly deduced from the fundamental equa- 
