A FEW QUESTIONS IN HYDRODYNAMICS. 
BY 
R. A. Harris. 
[Read before the Society February 16, 1901.] 
Owing to the comprehensiveness of the subject of hydro¬ 
dynamics and to its already numerous divisions and subdi¬ 
visions, it would be a difficult matter to ascertain and report 
upon the recent progress made in the various directions. 
The treatises of Lamb and Basset show the nature of the 
problems which have engaged the attention of workers, and 
indicate to some degree how far such labors have been suc¬ 
cessful. The reports of Challis, Stokes, and Hicks found in 
the British Association Reports for 1833, 1846, 1881 and 
1882 (and particularly the one by Hicks), give surveys of 
the subject as then developed. A brief account of some of 
the more recent work is given by E. W. Brown in the Amer¬ 
ican Association Report for 1898. As implied in the above 
title, no attempt will here be made to give a review of the 
subject as a whole or of any branch of it. The aim will be 
to briefly consider a few questions in liquid wave motion 
which have a considerable practical interest. 
As in other and kindred branches of physics, the state¬ 
ment of several classes of these problems is not difficult, 
and for this we have to thank such analysts as Lagrange, 
D’Alembert, and Fourier; but the real difficulty comes 
from the inability of mathematics to solve the problems thus 
set forth. Speaking of vibrating systems in general, Ray¬ 
leigh says: 
“The rigorous determination of the periods and types of vibration of 
a given system is usually a matter of great difficulty, arising from the 
fact that the functions necessary to express the modes of vibration of 
14—Bull. Phil. Soc., Wash., Vol. 14. 
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