PROCEEDINGS 



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, 

 that the twofold execution of it is equivalent to +. And the 

 nature of this operation, denoted by +% might be supposed 



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