to lie below measured ones for hulls of small prismatic coefficient, but to lie above 

 them for higher prismatic coefficients and to have much more pronounced humps and 

 (especially) hollows; these are shifted somewhat to the left of the observed ones. As 

 the Froude number becomes smaller than about 0.20 it becomes questionable whether 

 the residuary resistance should be compared with the calculated wave resistance. 



The discrepancies are generally ascribed to neglect of the effect of viscosity on 

 the wave formation, to the assumptions inherent in the linearization, and, of course, 

 to the difficulty of determining experimentally something which may be called the wave 

 resistance. There have been several attempts to take account of viscosity. An empirical 

 method of Wigley's [8], based upon damping of the bow wave, has been used to correct 

 the calculated curves in Figure 2. Havelock [9] has proposed computing the wave 

 resistance for a hull enlarged at each point by the amount of the displacement thickness 

 of the boundary layer at that point; a tail then follows the ship. This method has also 

 been considered by Okabe and Jinnaka [1], and by V. M. Lavrent'ev [1]. Although it 

 does damp out the oscillations at low Froude numbers in the calculated curve for C., c , 

 it does not shift the positions of the humps and hollows appreciably. Inui [1,3] intro- 

 duces an empirically determined shift in the stern wave to take account of this. The 

 empirical methods are perhaps objectionable because of their ad hoc character. On 

 the other hand, they do produce better agreement with experimental results and may 

 possibly give some idea as to where to look for reasons. Finding the causes for dis- 

 crepancies seems more important here than finding empirical curves to fit experimental 

 data. 



Attempts to go beyond the linearized theory have been made by Guilloton, 

 Okabe and Jinnaka [1] and by Inui [2]. In general, these attempts aim at trying to 

 satisfy exactly the boundary conditions (for a perfect fluid) on the hull while retaining 

 the linearized boundary condition on the free surface. We have commented earlier on 

 this in connection with the derivation of the linearized theory. It seems to the author 

 that an attempt at a complete second-order theory should be postponed temporarily. 

 The expressions involved will be so unwieldy for computation that it may be easier to 

 deal directly with the exact equations in machine computation. In addition, a too 

 refined perfect-fluid theory may be out of keeping with neglect of a more fundamental 

 treatment of the effect of viscosity. 



Proposals have been made for other methods of determining experimentally 

 the wave resistance. We mention especially one by Tulin [1]. 



These few remarks can not, of course, cover adequately the relation between 

 measured and calculated wave resistance. For a more comprehensive treatment one 

 should refer to Weinblum's excellent report [10], to Wigley [3], and to Birkhoff, Korvin- 

 Kroukovsky and Kotik [1]. However, the agreement seems good enough to give sup- 

 port to proposals of Weinblum, Guilloton and others that one should reverse the present 

 method of treating towing-test data by computing the wave resistance and considering 

 the difference as a Reynolds-number dependent frictional-plus-form resistance. The 

 current emphasis on methods of computing Michell's integral might seem misplaced 

 otherwise. However, the author is not aware of published comparisons of computation 

 and test for any ship forms in actual use. 



Relation Between Hull Form and Wave Resistance. Once it has been estab- 

 lished that the linearized theory gives a reasonable prediction of the wave resistance, 

 it is possible to use it to investigate in a qualitative way the effect of various changes 

 in hull shape, and even to try to find shapes of minimum wave resistance under certain 

 restrictions. This is perhaps an even more important use of the theory than calcula- 

 tions for special forms, and it has occupied a great part of the efforts of Havelock, 

 Weinblum, Wigley and others. 



There are a few immediate corollaries of Michell's integral: 1. R varies as the 

 square of the beam for a family of hulls related by 



?(x,y;0) = R{x,y;l). (51) 



120 



