PROCEEDINGS 
OF 
THE ROYAL IRISH ACADEMY. 
1846-7. No. 58. 
December 14th, 1846. 
REV. HUMPHREY LLOYD, D.D., President, in the 
Chair. 
The Rev. William Reeves, M. B., was elected a Member 
of the Academy. 
The Rev. Charles Graves made some observations on the 
use of distributive signs of operation, both real and imaginary, 
in the construction of systems of algebra. 
1. An algebra with two distributive signs, one real and the 
other imaginary, might be framed in the following manner: 
We might define the sign + as standing for a distributive 
_ operation, such that the repetition of it any integer number of 
_ times is still equivalent merely to +. We might suppose the 
: _ nature of this operation known, and, on that account, call any 
_ quantity affected with the sign + a real quantity. Along 
; with this symbol we might employ a second, ++*, defining it 
_ as being the symbol of another distributive operation, such, 
Beha the twofold execution of it is equivalent to +. And the 
. nature of this operation, denoted by ++, might be supposed 
VOL. IIT. : 2z 
