Wave Resistance of an Ellipsoid. 486 
Comparing (14) and (26), we see how the latter approximates to the former 
when 6 and ¢ are small compared with a. We have, for instance, a difference 
which is independent of the velocity in that the factor (2 — «,»)?(a? — b2)3? in 
(14) is replaced by 4a° in (26) ; this makes the value of R calculated from (14) 
greater than that found from (26) in a certain ratio. To give a few numerical 
examples :—When a = 5b, c= 6, the ratio is 1-2; when a=5b, c= 4b, it 
is 1-12; while for a= 106, c=6, it is about 1-05. Again, comparing the 
integrals in (14) and (26) the quantity a=\{(b2 —c2)/(a2— b2)tis re- 
placed by 8 =6 Va2—62. From the considerations given in § 5, it 
appears that this difference would have only a slight effect upon the 
character of the resistance-velocity curve for a body with proportions 
like those of a ship. 
7. For a ship model with fine ends and the usual ratios of length to beam 
and draught, experimental results have shown that the theoretical expressions 
form at least a good first approximation. A more exact solution of the 
theoretical problem for a surface ship of simple form moving in a frictionless 
liquid is desirable, but it presents considerable difficulties. As regards com- 
parison with experimental results, such a solution would probably not improve 
the present position appreciably, on account of the effects of fluid friction in 
the actual problem. So far as the ship problem is concerned, it seems that the 
approximate theory might be supplemented by semi-empirical assumptions of 
a suitable nature, possibly as regards the effective distribution equivalent 
to a ship under actual conditions. 
