Waves produced by the Rolling of a Ship. 414 
value would lie between 1 and 2, but the modification is not worth while 
at this stage. 
Both the energy method and the present calculation are no more than 
first approximations, and therefore we may not attach any great 
accuracy to the estimates by either method ; nevertheless, it is interesting 
that both methods give results of the same order of magnitude. On the 
theoretical side the problem should be treated as three-dimensional, 
and also the boundary conditions at the surface of the ship satisfied 
more closely ; in addition, the actual motion of the ship and its axis 
of rotation are important factors in a more detailed investigation. On 
the other hand, it would be desirable to have experiments on models 
of suitable form designed to provide better estimates of frictional and 
eddy-making resistance to rolling, and so to afford more reliable knowledge 
of the amount left to be accounted for by wave propagation. 
Summary. 
Expressions are obtained for the surface disturbance produced by a 
cylinder, of elliptic cross-section, submerged in water and making small 
oscillations. A simple form of these results is used as a first approxi- 
mation for the height of the waves, supposed two-dimensional, sent out 
on either side by a rolling ship. Numerical calculations are made 
for cases for which a similar estimate has been made by an energy method 
due to W. Froude ; the results by the two methods are of the same order 
of magnitude. 
References. 
G. S. Baker, Trans. Nav. Arch. lvi. p. 238 (1914); also Trans. N.E. Coast 
Inst. Eng. and Ship. vol. 56, p. 25 (1939). 
W. Froude, ‘Naval Science,’ i. p. 411 (1872) ; also iii. p. 312 (1874). 
T. H. Havelock, Proc. Roy. Soc. A, xciii. p. 522 (1917). 
L. Spears, Trans. Soc. Nav. Arch. and Mar. Eng. (N. Y.), vi. p. 21 (1898). 
W. White, Trans. Nav. Arch. xxxvi. p. 145 ([895). 
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