somewhat analogous to Newton s Rings. 71 



ing the abnormal part CB, then, and then only, would the theory 

 hitherto developed suffice. Clearly, however, these conditions are 

 not fulfilled. 



On the contrary, the waves go to and fro along the secondary, 

 suffering 



(a) Total reflexion with reversal of electrification at the short cir- 

 cuited end DD' (fig. 1), 



((3} Total reflexion without reversal of electrification at SS', and 

 (7) Partial reflexion and partial transmission at each incidence on 

 the abnormal part BC. 



We have, thus, a case of binary fission at each incidence of a train 

 on the abnormal part, each such fractional train returning to the ab- 

 normal part to be further, in like manner, subdivided. Theoretically, 

 this process continues ad infinitum. 



From these considerations it may easily be inferred that, to avoid 

 hopeless confusion, the distance from the. abnormal part to either end 

 of the secondary must exceed half the length of the train of electrical 

 waves, or in symbols : 



SB > JX and CE > JX (A), 



where X is the effective length of the wave-train, and the other 

 letters refer to fig. 1. 



It was also found necessary to avoid placing the abnormal part 

 midway between the two ends, S and D, of the secondary. For, in 

 that case, the two sets of waves respectively reflected at and trans- 

 mitted through the abnormal part would, after travelling to opposite 

 ends of the secondary, again meet at the middle and interfere with 

 each other. This disturbance was sufficiently obviated by fulfilling 

 the condition 



But when conditions (A) and (B) are both fulfilled, there is still a 

 residual disturbance. For, although the electrometer is placed to 

 receive the systems transmitted through the abnormal part, it, in 

 consequence of their repeating coursings to and fro, actually receives 

 also feebler systems of reflected waves. 



Thus, let tlie fraction of incident wave-energy transmitted by the 

 abnormal part be T, and let the ratio of the electrometer readings with 

 and without the abnormal part be T', then the author has shown that 

 T' is approximately given by the equation 



I -*- ~~~ S \ 02 / A \ 



v (4). 



where Si and s-> express the attenuation of energy suffered by the 



