74 Mr. R. Appleyard on the Formation of 



In Case I. /3=o0y=12, and A=l-26 g-^B ; 

 Case II. /3 = 18 7= 6, and A=l-07 e- 12 *C ; 

 Case III. /3= 9 7 = 3, and A= -57 £" 12 -E ; 

 Case IV. J3= 6 y= 2, and A= -31 <?- 12ir G. 



Thus the effect of each successive subdivision is to further 

 reduce the amplitude of the received current. 



§11. Returning to the equation of § 2 for determining fiv, 

 viz. : — 



mnrr'x 2 —x{m + nv' + mv\ + 1 = 0, 

 write in this 



- =7, -,—i, -=k, -=k', and7 + 7 / = r, 

 r ' r m n ' 



so that 7, y' are the conductivities of the two conductors, k, k' 

 the rigidities to electrostatic stress of the two dielectrics, and 

 F the total conductivity of the two conductors. 

 The equation becomes 



X- — X{yk + Tk' } + ryy'kk' = 0, 



and the roots of this equation represent the signalling speeds 

 of the two equivalent cables. 



If k be very small, x = Yk' or 0. Hence if the layer of 

 dielectric between the conductors be very thin, though at 

 the same time perfectly insulating, the speed through the 

 central conductor, however small its section may be, is the 

 same as if the whole of the two conductors were solid, and the 

 whole used for the conducting circuit. 



IX. The Formation of Mercury Films by an Electrical Process. 

 By Rollo Appleyakd*. 



IF a sheet of gelatine, damp leather, or similar permeable 

 substance is used as a separating diaphragm between two 

 bodies of mercury, and a current is sent through it, a film of 

 mercury is deposited upon the surface connected to the 

 positive pole of the battery. And the film remains on the 

 diaphragm after removal from the apparatus. 



If the diaphragm is replaced in the apparatus and subjected 

 to a current in the reverse direction, the film vanishes from 

 that surface, and a second film appears on the other side. 

 That is to say, the film is always on the side of the diaphragm 

 connected to the positive pole of the battery, and there is no 

 film on the negative surface. 



* Communicated by the Physical Society : read May 14, 1897. 



