along Wites and their Reflexion at the Oscillator. 147 



§ 3 be the throw when a "no-resistance" bridge is used at TT', 

 i. e., a piece of short thick copper wire, which therefore reflects 

 the waves without appreciable loss. Then it is required to 

 express the ratio 8 2 /^i as a function of the attenuation and 

 reflexion coefficients and then, from the experimental values 

 of the above ratio, to solve the resulting equations for the 

 coefficients sought. 



Let the maximum potential-difference of the two wires of 

 the line due to any wave be taken as the amplitude of that 

 wave, let p be the factor by which the amplitude of a wave is 

 affected on reflexion from S S' (fig. 1), and let e~ aX be the 

 attenuation factor by which the amplitude is affected in 

 traversing x cms. of the line. For convenience of actual 

 working 10~ w ' was substituted for the above, x' denoting 

 length traversed in metres, a was then deduced from 5. 



Now the throws of the electrometer are proportional to the 

 time-integral of the square of the amplitude of the passing 

 wave-train, i. e. } proportional to its energy: hence, if the 

 lengths of the line before and after the electrometer are l x and 

 l 2 respectively, and a wave-train of initial energy i leaves the 

 oscillator, we have with the {l absorber " at the end of the 

 line 



ie- 2l ^=kS } , (1) 



where k is the electrometer constant. 



Again, with the no-resistance bridge or short circuit at the 

 end, we have two series of impulses at the electrometer, the 

 energy of the forward waves being 



and that of the backward ones [e -4 ^ "] times the above, 



Hence we obtain 

 whence 





8 A= j— v^=»- say, .... (3) 



I being written for l x + 1 2 . 



Two experiments with different values of l x and t 2 furnish 

 two equations like (3) ; these are then cast in the form 



p^re-^ — i — 1— e~ il ^, (4) 



and p 2 eliminated between them. The result was an equation 

 in cr of the form 



Axe - *' 0- -I- ktfr * 1 + . . . = 0, 



or sa ? «=0. 



