398 On Waves due to a Travelling Disturbance. 



Ekman's experiments showed, in fact, that the resistance 

 was greatly increased when the bottom of his model boat 

 approached or penetrated the surface of separation. 



As regards the actual magnitude of the resistance, an 

 estimate, necessarily somewhat vague, can be made in a 

 certain case as follows : It has been computed * that the 

 wave-resistance to a horizontal cylinder of radius a towed 

 .at right angles to its length with velocity c, at a depth h in 

 ■homogeneous fluid, is 



R = 4:TT 2 gpaWe- 2Kl \ • • . • (86) 



■where K l —g/c 2 ns before. If we assume that when the 

 cylinder is towed along the interface the wave-resistance 

 at the interface bears to that at the upper surface the ratio 

 .of R 2 ' to R/, as found from (82) and (83), we get 



K= -t 9 — . • , % T ■ . 47rWV . • . (87) 



To make the formulae more comparable, we have put /> = 0, 

 which involves an under-estimate, and leads to no difficulty 

 for values of c in the neighbourhood of ^c . Thus if we put 

 jc 2 h~'2, and /i = 250 cm,, which was the estimated thickness 

 of the freshwater layer in one of Hansen's experiences, we 

 find 



R = -lla 4 , . ...... (88) 



in grammes per centimetre of length of the cylinder. This 

 corresponds to a speed 



c= "49800= 39 cm./sec.-, 



-or about 1/4 kilometres per hour. 



Considering the somewhat precarious nature of the above 

 comparison, no importance can be attached to the precise 

 numerical value obtained for R ; but the order of magnitude 

 of the result (which almost certainly errs in defect) seems 

 decidedly to support the adequacy of the theory advanced 

 by Bjerknes and Ekman. 



* Anncdi di matematica (3) vol. xxi. p. 327 (1913). 



