13 



tests are valuable from the viewpoint of obtaining reliable comparative re- 

 sults for various forms. Accurate absolute values of wave resistance cannot 

 be obtained by Proude's method for low speeds, but we can hope to obtain (by- 

 using great care) consistent differences In wave resistance corresponding to 

 definite changes in form; much is achieved when we can rely on the sign of the 

 result. Unfortunately, the same doubts as to the absolute values apply to the 

 calculated wave resistance in this range. Our main task will be, therefore, 

 to establish whether changes in the calculated wave resistance do correspond 

 to the experimental values with respect to the general trend and range, not so 

 much with respect to the absolute values, although the agreement in the latter 

 sometimes is also very satisfactory. 



3. GENERATION OP BODIES BY SINGULARITIES AS BASIS POR 

 CALCULATING WAVE RESISTANCE 



The representation of ship forms by algebraic expressions enables 

 us to calculate the wave resistance comparatively easily for the limiting case 

 of a slender body, the so-called "Michell's ship." The assumption is made 

 that the slope of the hull to the vertical center plane expressed by f|,^. 

 is everywhere small. 



While the condition for the longitudinal slope £^ is not unreason- 

 able for most normal ship forms, the condition^ is very seldom satisfied. 

 Let us investigate, at least superficially, the assumptions on which the the- 

 ory is based . 



Lord Kelvin^* substituted for the ship a pressure concentrated at 

 a point and applied to the surface which he designated by "forcive." He suc- 

 ceeded in explaining the main features of the wave pattern created by a ship. 

 His work was widely extended by E. Hogner-"-* who gave a general formula for the 

 wave resistance of pressure systems, which enables us to calculate the resist- 

 ance of bodies with negligible draft, especially gliding craft, when the pres- 

 sure distribution is known. 



For normal ship forms the approach by the usual singularities— 

 sources, sinks and doublets— has proved to be more appropriate. The genera- 

 tion of bodies by sources and sinks (doublets), proposed by Ranklne,®^ should 

 -always form a basic study in theoretical naval architecture. Before discus- 

 sing bodies floating on the surface, we will investigate wholly submerged bod- 

 ies in an unbounded fluid (the free surface is very far away from the body). 



It is well known that under appropriate conditions, closed slender 

 bodies of revolution are generated by sources and sinks (doublets) located 



