29 



ing to the adoption is based on the fact that above a certain value 



(about 0.5) of the ratio, the value of the term tanh -y- appearing in 



the Gerstner and Laplace-Auy equations of wave motion approaches 

 very closely to unity. It should, however, be noted that the dis- 

 tinction of deep- or shallow-water waves made on this basis is arbitrary 

 and, as far as the Stokes' theories are concerned, may have practically 

 no significance. In fact, Stokes defines the deep-water wave as one 

 for which "the depth of the fluid is very great compared with the 

 length of a wave", when we may without sensible error suppose the 

 depth to be infinite. 



In reality, as an examination of the formulae in Section 6 will show, 



the ratio y is effective as a parameter in Stokes' theory until large 



values of the ratio are reached. If the comparison of shallow-water 

 wave theory with experimental results shows Stokes' theory to be 

 most nearly applicable to the waves studied, it would appear, there- 

 fore, that the present arbitrary distinction between deep- and shallow- 

 water waves should be revised to be more in accord with the principles 

 on which Stokes makes the distinction. 



Considering first the results of section 5, the comparison of wave 

 lengths and wave velocities (all comparisons are understood to be 

 between measured and theoretical values, unless specifically stated 

 otherwise) indicates agreement of experiment with both of the theories 

 studied within the limits of experimental error, the closer agreement 

 being with the Gerstner theory. 



The comparison of the proportions of wave height above still water 

 level indicates agreement with both theories within the limits of the 



experimental error, for values of j less than about 0.05. Above this 



value the measured percentages tend to be higher than those predicted 

 by either theory. 



It should be noted in this connection, and also with respect to the 

 wave profiles, that the experimental values are susceptible to con- 

 siderable error by reason of a phenomenon of reflection from the wave 

 absorber. The first waves generated from water at rest had smooth, 

 flowing profiles. As soon as these first waves reached the absorber it 

 was noticed that small, short waves appeared to be superimposed on 

 the generated waves, until after a short time the initial smooth wave 

 surface became a surface of more or less irregular outline. This 

 condition is shown clearly in figures 3 to 5. Furthermore the fact that 

 the generated waves had not attained a stable form before measure- 

 ment probably had an appreciable effect on the shape measurements. 



With respect to the wave profiles there is little evidence to show 

 agreement with either of the theories investigated. 



