364 Dr. Barton and Mr. Lownds on Reflexion and 



simple relation is seen to be slightly modified by the 

 damping. 



Again, if the damping were not present, we should have 

 the simple result A 2 +13 2 -=l, as should be the case, showing 

 that the sum of the energies of the reflected and transmitted 

 wave-trains equals the energy of the incident one. To 

 effect the corresponding check for the damped waves, one 

 would need to take the time-integrals from zero to infinity 

 of the square of the amplitude for the incident, reflected, 

 and transmitted wave-trains, the exponential terms being no 

 longer ignored. 



As a further check it may be noted that the equation for 

 potential-difference at the condenser is always satisfied. For 

 the equation in question, viz.: ^ -f- (£' = <p- 2 , reduces to 

 l+a = h and h' = a', and by (8) this is an identity for all 

 values of k and y^. 



20. If the capacity of the condenser be imagined to in- 

 crease from zero to infinity, while the circuit and the incident 

 wave-train are maintained the same, we see by equations 

 (6) and (8) that the reflexion-coefficient A grows from zero 

 to unity, while the phase-difference a, but for the slight 



modification due to damping, changes from -=~ to — ir. 



Similarly, a reference to equations (7) and (8) shows that 

 as the capacity of the condenser changes from zero to infinity 

 the transmission-coefficient B changes from unity to zero, 

 while the phase- difference, but for the damping, changes from 



— 7T 



zero to -Tg— . 



21. These features for several sizes of condenser are 

 exhibited in Table I., and are graphically represented in figs. 2, 

 3, and 4, in which the dotted lines represent the values which 

 the coefficients would assume if there were no damping, and 

 the full lines the corresponding values for the damping 

 actually present in the experimental case in question. The 

 incident, reflected, and transmitted amplitudes are shown by 

 01, OR, and OT respectively. The curves in fig. 5 show at 



Fig. 2. — Reflexion and Transmission at Small Condenser. 



