LA YING DEEP-SEA CABLES. 447 



where p and q denote the velocities, transverse and 

 longitudinal, which would give frictions amounting 

 to the weight of the cable ; or, as we may call them 

 the transverse and longitudinal settling velocities. 

 We may use these equations merely as introducing 

 a convenient piece of notation for the components 

 of fluid friction, without assuming any hypothesis, 

 if we regard p and as each some unknown 

 function of/ and q. It is probable that p depends 

 to some degree on q, although chiefly on p ; and 

 vice versa, q to some degree on /, but chiefly on q. 

 It is almost certain, however, from experiments 

 such as those described in Beaufoy's Nautical 

 Experiments, that p and q are each very nearly 

 constant for all practical velocities. 



Eliminating/ and q between (i), (2), and (3), we 

 have 



which gives 



v sin i 



and 



(WD - T) sin i = WD 

 which gives 



These formulae apply to every case of uniform 

 towing of a rope under water, or hauling in, or 

 paying out, whether the lower end reaches the 

 bottom or not, provided always the lower end is 



