88 Mr. E. H. Barton. Electrical Interference [June 15, 



Q. Quantity of electricity per unit length of conductor. 

 L. Coefficient of self-induction ,, 



R. Resistance ,, 



i. Electric current. 



v. Velocity of propagation of the waves along the conductor. 

 X. Wave-length. 

 t. Time. 

 L, R, and v denote the values corresponding to the high fre- 



quencies used. 

 Take the conductor as the axis of x. 



For the normal parts of the conductor, namely, AB and CD, fig. 1, 

 the above symbols will be used with the subscript 1 ; for the 

 abnormal part BC they will be used with the subscript 2. 



8. When an electrical wave passes along a conductor we have at 



any point the E.M.F. = -~ -- L~-. But this also equals Rt. Thus, 



ox ot 



since i = Qv = C0v, we obtain the differential equation 



o ............ (1). 



x 



When and where 0=0, we have 



^ + ,CL^ = o or 



dx dt 



whence ^ 



the well known expression for the velocity of propagation of the 

 wave. 



9. ISTow R in equation (1) leads to a damping factor in the solution. 

 Since, however, we are now concerned simply with what occurs at 

 the point of reflection, this R will be omitted. Equation (1) then 

 becomes 



90 80 



and its solution 



J 



where /3/y3 = v = l/>/(CL), and/ 1? / 2 denote any functions. 



10. It will suffice for the case in question if we write for fi and / 2 

 sine functions with coefficients for the various amplitudes, and a 

 third term in the brackets to allow for a change of phase should 

 there be one. We may thus write for the original and reflected 

 waves in the first part of the conductor 



