208 



Mr. G. J. Burch. On the Interpretation of [Feb. 11, 



the bundle, then it does not appear that sufficient data are afforded by 

 the electrometer records to discriminate between the effect of the non- 

 coincidence of the points of origin, and of the gradual development 

 and subsidence of the E.M.F. at any given point. 



Inasmuch, however, as it must not be assumed that the rate of 

 rise and rate of fall of E.M.F. are equal, i.e., that the potential gradient 

 at the wave-front is the same as that at the end of the wave, it becomes 

 necessary to find some mode of representing the time relations of 

 the variations of E.M.F. at any given point of a single linear con- 

 ductor. For this purpose the following device may serve : Let each 

 linear conductor be conceived as consisting of a number of parallel 

 elements which flash into complete activity in succession, and remain 

 active for a period not necessarily equal, after which each one in turn 

 passes suddenly into a condition of rest ; e.g., let the conductor 

 consist of parallel linear elements tt . . . . 77 n so that w\ — 7r is the 

 small interval of time that elapses before the second element comes 

 into action, and so on. 



Then the time at which a difference of potential is derived from 

 each of these elements in succession will be 



W = -b + mo)lv, U[ = (p 1 -b + VTr 1 )/v i etc., 



and the times at which these contributions to the total P.D. cease will 

 be respectively 



If h = 1 the formula represents an equal rate of rise and fall of 

 E.M.F. at each point of the conductor. 



If h < 1 the fall is more rapid than the rise. 

 If h > 1 the rise is more rapid than the fall. 



C. Effect upon the Variations of P.D. when the Conductors constituting 

 the Bundle are not all of the same Length. 



There yet remains a farther complication arising in the case of a 

 non-regular bundle, of which some of the constituent conductors do 

 not extend far enough to pass under both leads. 





1 1 



3 p.p, 









Pn 



Fig. 11. — As in Fig. 9. A, B, electrometer leads. Pj'. . . . P„, points of origin. 

 But some of the linear conductors do not reach from B to A. 



Let Q be the point at which a linear conductor ends, such that 

 OQ. = q, and following the notation hitherto employed, let q\, q- 2 .... q n 



