33 



It was found that in principle resistance effects due to the verti- 

 cal and longitucllnal distribution of displacement cannot be separated; fortu- 

 nately, however, it is possible to derive a great number of characteristic 

 properties of ship forms without considering the shape of sections and the 

 draft, which together determine the vertical distribution. 



In the light of this knowledge, the basic item is the sectional-area 

 curve; it is therefore natural to begin with the well studied elementary 

 shapes given by 



V = X(f) Z(0 [12] 



which embody a given sectional-area curve in the simplest way. Later, more > 

 complicated forms will be investigated. 



The present most important chapter of the paper is perforce present- 

 ed in a rather rudimentary state, since numerous lengthy computations needed 

 for a rigorous discussion are not yet completed. Thus, instead of calculated 

 resistance curves some simple intermediate functions are used as a basis of 

 our analysis. 



This analysis uses systematic geometrical variations of ship lines. 

 In principle, a more elegant way would consist in minimizing the resistance 

 integral. The latter procedure yields forms of least resistance which are 

 basic results in themselves. Besides, when trying to establish simplified 

 useful relations between important form parameters and resistance properties 

 it is generally favorable to investigate good forms, since because of the pos- 

 sibly complicated actual relations the results may depend upon the selection 

 of the forms. However, the method of minimization has not yet lead to a satis- 

 factory solution; hence, the approach of geometrical variation adopted here 

 appears to be the only one suitable. 



It is pertinent to mention here why so many "mathematical models" 

 have been tested which bear little resemblance to actual ship forms, since the 

 erroneous opinion is widely held that theory can deal only with oversimplified 

 models: 



a. Simplicity of mathematical expressions v;as aimed at in earlier work 

 when methods of computation were not developed and the physical bearing of the 

 theory was unknown. 



b. Variations in form for basic research must sometimes be made not 

 with the purpose of improving forms, but of obtaining pronounced changes in 

 resistance. 



