Mr. A. Schuster's Electrical Notes. 17 



second terms. These terms are of some importance, for 

 Maxwell's expression cannot be made to satisfy the surface 

 conditions, while the surface integrals in the equations (15) 

 allow us to do so. 



The expression (Bn — Cm) may be considered as the com- 

 ponent of a current which must be imagined to be distributed 

 over the surfaces of separation of the two media. 



In order to determine the discontinuities of the differential 

 coefficients, let k x and k 2 be the magnetic susceptibility in the 

 two media, and let I, m, n be the direction-cosines of the 

 normal to the surface drawn towards the inside of the medium 

 to which the index 1 refers. The surface currents are then 

 given by 



id = m(K 1 y 1 — K 2 y 2 ) — nfjc^ — K 2 fi 2 ) , \ 



v' = n (/e^ — k 2 cc 2 ) — I {km - *vy 2 ) , > • . (16) 



IV'=1 (K l @i—K 2 /3) — ))l( K K l 0<. l —K 2 Ct 2 ). ) 



If the axis of z is taken in the direction of the normal, 

 iv' = 0, and we conclude: The first differential coefficients of 

 the normal component of the Vector Potential are continuous. 

 The differential coefficients of F and G in the directions a and 

 y must also be continuous, and the only ones which may be 



discontinuous are -=- and -=- . The discontinuities may be 

 dz dz J 



written down from (15) and (16), 



dF dF . , . 

 -^+ ^=4w(*i£,-tf 3 &). 



In this equation -y-is written for the differential coefficients 

 dz 2 



along the negative axis of z. But 



fii\dzi dx P 



1 / clF_dR\ 

 A*2 \ dz 2 dx )" 



Hence 



dz x + dz 2 " fju x \dz x dx ) fi 2 \dz 2 dx ) 



l^dF 1_<ZF/1 _ lY*l 

 /ju 1 dz 1 /Ag <fe 2 ~ V*i ^ 2 ) da' 



Phil. Mag. S. 5. Vol. 32. No. 194. July 1891. C 



^U- 



(17) 



