negligible, and both the cable and the stream are uniform— so that each ele- 

 ment of the cable has the same equilibrium position, it is clear that the con- 

 figuration of the cable must be such a straight line. The external forces 

 acting upon the cable are: 1 ) The hydrodynamic force and 2) the weight of 

 the cable in water. If the direction of the cable is measured and the weight 

 of the cable is known, the components of the hydrodynamic force that are nor- 

 mal to the cable can be found, since these must balance the corresponding com- 

 ponents of the weight of the cable. Thus the cable acts as a balance, weigh- 

 ing the normal components of the hydrodynamic force. Unfortunately, the 

 weight of the cable is fixed so that the only method of changing the angle of 

 the cable is to vary the speed of the stream. Hence, it is an inevitable con- 

 sequence of this method that the force acting upon the cable at each angle of 

 the cable to the stream is investigated at a different Reynolds number. 



The component of the hydrodynamic force that is parallel to the ca- 

 ble can be determined through a knowledge of the tension in the cable at the 

 upper end. This tension can in turn best be found by measuring the drag of 

 the cable. 



The problem of choice of axes requires some attention. There are 

 three directions that are intrinsically involved in the physical situation: 

 1) The direction of the stream, 2) the direction of gravity, and 3) the 

 direction of the cable. Since stranded cables assume an angle of sraw when 

 freely trailed these three directions will not be coplanar. The direction of 

 the stream and the direction of gravity are of course perpendicular and the 

 most convenient fixed reference frame, for the purpose of making measurements, 

 is the set of these two directions and their mutual perpendicular. Thus, let 

 X, y, and z represent displacements and i, J, k represent unit vectors re- 

 spectively in the direction of the stream, in the direction of gravity and In 

 the direction of the mutual perpendicular— which is chosen so as to complete 

 a set of right-handed rectangular Cartesian axes. Call this system Reference 

 Frame I. 



When studying the hydrodynamic force acting upon the cable it must 

 be remembered that in so far as the hydrodjmamic situation is concerned the 

 direction of gravity is entirely extraneous. The only directions that can af- 

 fect the hydrodynamic force are the directions of the stream and the direction 

 of the cable. The hydrodynamic forces should be related to the angle, <t> , be- 

 tween these two directions and any error of relating the hydrodynamic force 

 to the projection of this angle of the cable in the x-y plane must be avoided. 

 For the purpose of resolving the hydrodynamic force into components in a mean- 

 ingful way a new reference frame is needed. Such a reference frame is formed 

 in the following manner: Let f be a unit vector in the direction of the cable. 



