THE DIELECTRIC 



107 



medium. We may see the necessity for this by supposing two 

 fluid dielectrics in contact along a surface AB, Fig. 73. Now 

 imagine a small charge taken along CD in one medium close to 

 and parallel to AB, and then across to E, back along EF in the 

 other medium, close to and parallel to DC, and than across to C. 

 We may neglect the work done along DE and FC by making them 

 small enough. If the intensity along CD were greater than that 

 along EF, then, on the whole, work would be obtained from the 

 cycle, and repetition of the cycle would lead to discharge of the 



FIG. 73. 



energy of the system without altering the charges, and such dis- 

 charge is contradicted by experience. Hence the intensity parallel 

 to AB and close to it is the same in each medium, or the potential 

 i> continuous. 



We may describe the second condition as (2) continuity of strain. 

 The equality of the opposite charges in an electrified system is not 

 affected by the presence of dielectrics of different capacities, and 

 we have every reason to suppose that if we draw unit tubes, each 

 starting from +1, they will end each on 1, whatever dielectrics 

 thi-y P.-INN through. If then ABCD, Fig. 74, represents a unit 



K, 



FIG. 74. 



tube in a medium with dielectric constant K r continued as CDEF 

 in another ini-diiim with constant K 2 , CDEF is also a unit tube. 

 If the area of the surface cut out by each tube is a, and if the two 

 tubes make angles O t 2 with the normal, the cross-section of ABCD 

 i- a CM ffj, while the cross-section of CDEF is a cos r If the 

 strains on the two sides of CD are D x and D 2 , the equality of the 

 total strain in the two tubes gives 



