NOTICES AND ABSTRACTS 
OF 
MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. 
MATHEMATICS AND PHYSICS. 
MATHEMATICS. 
Address of the President, Professor W. J. Macavorn Ranxryz, FERS. 
Tue President, on taking the chair, said that the quantity of business before 
the Section was so great that the utmost economy of time would be necessary in 
order to dispatch that business in a satisfactory manner. For that reason the 
Committee had instructed him to recommend to the Section the observance of the 
following rules in conducting discussions :—That immediately after the reading of 
any paper, members should put such questions to the author as they might con- 
sider desirable for the purpose of making clear the meaning of the paper; that the 
author should answer those questions one by one; that after all the questions had 
been answered, such members as chose to make remarks on the subject of the paper 
should address the Section, each member being at liberty to speak once only on one 
paper; and that after all those remarks had been made, the author should reply to 
the whole discussion in one address. He trusted that the members of the Section 
would approve of the rules recommended by the Committee, and would support 
him in taking care that those rules should, as far as practicable, be observed. 
On a certain Class of Mathematical Symbols. 
By W. H. L. Russert, A.B., FBS. 
In general, a mathematical symbol acting on a function of a variable gives rise to 
another function of that variable. Thus = F@),AF@), M3 dx f (x), and many other 
expressions, are all functions of (x). But there are certain symbols which, in their 
action on a function of a variable, produce expressions which, from their essential 
nature, are independent of that variable. Such is the symbol used by Cauchy in his 
‘Exercices’ to denote the aggregate result obtained by multiplying a function 
of (x) successively by those simple factors which, equated to zero, make it infinite, 
and then substituting for x) the values obtained by equating those factors to zero. 
Such also is the symbol @ used by Professor Boole in his researches on the com- 
parison of transcendents, denoting the result obtained by subtracting from the 
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