INAUGWRAL ADDRESS 
OF THE 
CHAIRMAN OF THE MATHEMATICAL SECTION, 
By AsApH HALL. 
GENTLEMEN OF THE MATHEMATICAL SECTION: 
I thank you for the honor you have conferred on me by my 
election as Chairman of this Section, and the best return that I can 
make is to do my utmost to render our meetings as interesting and 
successful as possible. 
Although my duties have been such that I have not been able to 
take a very active part in the proceedings of the Philosophical So- 
ciety, it is easy to understand how a need has been felt for a more 
full and frequent discussion of mathematical questions. Mathe- 
matics has indeed been called the queen of the sciences, but the 
rigor and dryness of its methods make it distasteful to many. 
The fact seems to be that as any branch of knowledge advances 
and finally is reduced to law, it loses in a large degree its attractive- 
ness and popularity. Then, it is only with the indefinite outlines 
and the obscure boundaries of this science that most people like to 
deal; and this may be natural and right, since nearly all advance- 
ment originates in speculation and doubt, which lead to investiga- 
tion, and which, by a variety of motives, spur men on to labor. 
But the science of mathematics, though old, is yet young and vigo- 
rous. We have now six journals of the highest rank, which are 
devoted almost exclusively to pure mathematics—two in Germany, 
two in France, one in England, and, I am glad to say, one in our 
own country. These journals are devoted to the discussion of the 
highest conceptions of space and number, treating chiefly of the 
laws and forms of analytical expressions, and generally they touch 
lightly on any practical application of the science. Such discus- 
sions prepare the way, however, for better and more general prac- 
tical methods, and in our own country they have, I think, another 
value. For one, I can hardly accept the doctrine, advocated in 
some quarters, that the American scientific man of the future should 
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