LETTER TO GORDON. 171 



if Q is the weight of the suspended cable in the water, or the 

 weight of a piece of cable B D, hanging vertically downwards, 

 since A B . sin a = B D. 



If the force K is less than is necessary for equilibrium, 

 the cable slides back towards A, and the terminal velocity is 

 reached, when the friction in the water is equal to the lacking- 

 force. If on the contrary K is greater than necessary, the cable 

 acquires a velocity towards B, consequently the loss, i. e. the 

 difference of the lengths A B and A D is picked up again, and 

 the cable places itself in a straight line, thus without loss, on 

 the ground. The angle a is accordingly quite independent of 

 the amount of the force K. It simply indicates the proportion 

 of the velocity of sinking to the progressive motion of the ship. 

 For if the cable end B instead of being attached to the 

 weightless wire B C is carried over a pulley, and the pulley 

 moves with the ship from B to E, whilst the cable falls the 

 distance m T?, and finally if the cable is kept back with the 

 force K, there is no change at all in the conditions of equili- 

 brium. If the brake, which detains the cable, is so applied that 

 equilibrium is just attained, thus K=Q . sin , the cable has 

 no axial velocity whatever; it falls perpendicularly, and there 

 is the loss corresponding to the angle. If K is greater, the 

 cable is laid with little or no loss, if K is smaller, the loss may 

 be very great. The quicker in the latter case the motion of 

 the ship, the longer does A B become, the greater conse- 

 quently the friction in the water and the smaller the loss. If 

 on the other hand the force A' becomes greater than is ne- 

 cessary for equilibrium, the loss can easily be made up, and 

 the cable then forms a catenary curve. If the transitions are 

 rapid, the whole velocity, which the cable has acquired after 

 applying the brake on disturbance of the equilibrium, acts in 

 the direction A B, and tends to strain the cable. When one con- 

 siders the great mass of the suspended cable, it is clear that 

 these axial velocities of the cable may easily cause a fracture. 

 The only safe guide is the proportion of the ship's velocity to 

 the velocity of the cable. Moreover the ocean currents must 

 be taken into account, especially if they flow in various direc- 

 tions. If the current is everywhere equable, and extends to 



