202 ADVANCED ELECTRICITY AND MAGNETISM. 



ing it towards the center of curvature of the bent tube at p) 



T 

 equal to -ds*\ and if the string is not moving this force is 



exerted against the side d of the tube. 



If, however, the string is moving at a velocity v which satisfies 

 the equation: 



v 2 T 



m -ds = ds 

 r r 



or, if: 



.-> (3) bis 



then the radial force (in the direction of r) due to the tension 

 of the string is just sufficient to produce the necessary accelera- 

 tion, and no force at all is exerted on the string by the guiding 

 tube. Under these conditions the guiding tube might be removed 

 and the bend would continue to stand in a fixed position on the 

 traveling string, or if the string were standing still the bend would 

 travel along the string at velocity v. 



1 1 6. Differential equations of electrical wave motion on a 

 transmission line. The theory of electrical wave motion is 

 usually developed in terms of electric and magnetic field intensi- 

 ties in space,! and the equations are not easy to understand, 

 especially by the electrical engineer who is accustomed to express 

 everything in terms of voltage and current. Therefore the fol- 

 lowing discussion of electric wave motion on a transmission line 

 is expressed in terms of voltage and current. 



Throughout the following discussion the resistance of the line 

 wires is assumed to be negligible and the line wires are assumed 

 to be perfectly insulated. 



* See Franklin, MacNutt and Charles's Calculus, Art. 51, page 72. 



t A very simple development of this general theory is given on pages 186-195 

 of Franklin's Electric Waves, The Macmillan Co., 1909. The student must be 

 familiar with the elements of vector analysis to be able to understand this electro- 

 magnetic theory. See Electric Waves, pages 158-185, or see Franklin, MacNutt 

 and Charles's Calculus, pages 210-253. 



