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PHILOSOPHICAL SOCIETY OF WASHINGTON. 
rewards of life. So long as we assume that an act of Congress can regulate 
everything it seems impossible for us to understand that we are placed in 
a world where universal laws have been established which we ought to 
learn and to which we should conform our conduct. No wonder we are 
told that mathematics should be studied only to “ discipline the mind ”— 
that is, to make us sharp and cunning in the affairs of life. Perhaps it is 
the influence of this sentiment that makes so much of the mathematical 
learning that we have tend to become quibbling and intolerant. The best 
corrective for this condition is the study of the real questions of nature. 
Whenever we undertake to solve a question of this kind we are sure to 
find things so different from the questions of the books that our eyes are 
opened to a wider world. . If we call a thing by a different name, or repre¬ 
sent it by a new symbol, it does not help much. The real difficulty must 
be met. 
From my own experience I find that solving a few problems now and 
then is a good exercise. Even if they are mere hook-questions, the prac¬ 
tice serves to keep one’s knowledge bright; hut if a question he thoroughly 
worked it will generally give some instruction, and can he used to illus¬ 
trate a theory. In this respect mathematics has a great advantage over 
most of the natural sciences, in which the investigator seems like a hoy 
picking up stones on a New England farm—the work must be repeated 
every time the land is plowed. 
45th Meeting. October 17, 1880. 
The Chairman presided. 
Present, eleven members and guests. 
In the absence of the Secretary, Mr. A. S. Flint was elected 
secretary pro tem. 
Mr. C. H. Kummell read a paper on Some Fundamental 
Theorems in Mensuration in One, Two, and Three Dimensions. 
This paper was published in full in No. 4, vol. iv, of the 
Annals of Mathematics, University of Virginia, Va., 1888. 
The remainder of the evening was devoted to a discussion of 
the paper of Mr. A. Hall on Problem-Solving, read at the 44th 
meeting. 
