446 POPULAR LECTURES AND ADDRESSES. 



tively. These are balanced by 



P and T + Q -5- 



sin i sin i 



Hence 



P = W cos *, Q =(w -5) sin i. . . . (i.) 



To find the corresponding components of the 

 velocity of the cable through the water, which we 

 shall denote by/ and q, we have only to remark 

 that the actual velocity of any portion of the cable 

 in the water may be regarded as the resultant of 

 two velocities, one equal and parallel to that of 

 the ship forwards, and the other obliquely down- 

 wards along the line of the cable, equal to that of 

 the paying out, obliquely downwards along the 

 line of the cable (since if the cable were not paid out, 

 but simply dragged, while by any means kept in a 

 straight line at any constant inclination, its motion 

 would be simply that of the ship). Hence, if v be 

 the ship's velocity, and u the velocity at which the 

 cable is paid out from the ship, we have 



/ = v sin z, q u v cos *.,.... (2.) 



Now, as probably an approximate, and therefore 

 practically useful, hypothesis, we may suppose 

 each component of fluid friction to depend solely 

 on the corresponding component of the fluid 

 velocity, and to be proportional to its square. 

 Thus we may take 



P-W, Q = W . . . .(3.) 



