to a Travelling Disturbance. 397 



sources, and an account of tank experiments made in 

 verification of the above explanation. There are also some 

 indications of mathematical theory. A fuller publication 

 was promised : but I do not know whether this has taken 

 place. 



From the theoretical point of view the matter is not 

 altogether a simple one. The difference of densities is 

 actually very small, and although interfacial waves of con- 

 siderable amplitude may be readily generated, their energy 

 for given amplitude is relatively slight. It is obvious, in 

 fact, that if the difference be small enough no appreciable 

 effect of the kind contemplated could be expected, since the 

 case would be practically that of a homogeneous fluid. It 

 is difficult to devise a case which shall admit of mathe- 

 matical treatment, and at the same time be comparable with 

 actual conditions; but in default of this we may examine 

 whether any indications can be gathered from the precedino- 

 formulse. 



In the phenomena referred to the ratio [p —p)'p has some 

 such value as ^y. The expressions 



p + (j>'- p)e~ 2 ^\ p+(p- p)e- 2 *i\ 



which occur in our formulae, may therefore be replaced 

 without sensible error by p. The values of B^ and R/ in 

 (80) and (82) are therefore practically the same as if the 

 fluid had been homogeneous. 



Since fj 2 jc i = K l 2 , we have from (80) and (81) 



R t - p 2(c-V 2 )\ Kl be-^ b ) e '* * {b ^> 



approximately. A glance at the numerical table at the end 

 of this paper, wdiich is calculated on the basis of (p — p)/p = -^$, 

 shows that for values of c in the neighbourhood of ^c this 

 ratio may be enormous, in spite of the smallness of the first 

 factor, if b be at all comparable with h. That is, even 

 when the disturbing pressure acts on the upper surface, the- 

 resistance due to the interfacial waves may greatly exceed 

 that (in itself very small) due to the waves on the upper 

 surface. 



When the disturbing forces act at the interface this 

 resistance is again greatly increased; thus from (81) and 

 (83) 



