196 T. H. Havelock 
before decreasing to zero; with decreasing width of the channel, this maxi- 
mum increases in amount and occurs at a higher value of the ratio b’/a’. 
SUMMARY 
The paper gives a new treatment of the problem of a flat plate in a stream 
bounded by plane parallel walls, including circulation round the plate. The 
plate is considered as the limiting case of the elliptic cylinder; an integral 
equation is obtained, whose solution by continued approximation leads to 
expansions for the lift and moment on the plate. The solution is modified 
to give similar results when the stream is bounded by parallel free surfaces, 
taking the condition at a free surface in an approximate form; and a further 
modification gives the case when one boundary of the stream is a:plane wall 
and the other is a free surface. The problem of the elliptic cylinder in general 
is also considered with reference to the moment of the forces when the 
stream is bounded by plane walls and when there is no circulation. 
REFERENCES 
Tomotika, S. 1933 Rep. Aero. Res. Inst. Tokio, 7, 357-93. 
1934 Rep. Aero. Res. Inst. Tokio, 8, 157—227. 
Reprinted from ‘Proceedings of the Royal Society of London’ 
Series A No. 925 vol. 166 pp. 178-196 May 1938 
PRINTED IN GREAT BRITAIN BY W. LEWIS, M.A., AT THE CAMBRIDGE UNIVERSITY PRESS 
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