428 Prof. J. H. Poynting on the Discharge 



as showing in a general way that heterogeneity would intro- 

 duce absorption phenomena ; and we cannot expectthe results 

 obtained on the supposition of such a special arrangement to 

 agree with those of experiment. We may regard the stra- 

 tified arrangement as giving a superior limit, as it were, this 

 being the constitution most favourable to the production of 

 the phenomena in the way supposed. The inferior limit would 

 be given by an arrangement in which each portion of the 

 substance of the same kind stretched from plate to plate with 

 the same cross section throughout. In this case there would 

 be no residual discharge produced. Using Maxwell's notation 

 (see below), the resistance per unit cross section may be 

 shown to be 



R/= (a 1 + q 2 + ...) 2 



instead of 



«i + «2 

 r x r 2 '" 



R=a 1 r 1 + a 2 ^2 + .. ., 



and R/ is always less than R. In any intermediate compo- 

 sition, in which portions of more conducting matter are insu- 

 lated from each other by less conducting matter, we shall have 

 residual discharge. 



It appears probable, from experiments of Dr. Schulze-Berge 

 ('Nature/ March 4, 1886, p. 432), that the resistance of 

 certain dielectrics is not proportional to the thickness, but is 

 much less for thin layers than might be expected. May this 

 not possibly arise from the size of the heterogeneous portions 

 being comparable with the thickness of the dielectric, so that 

 the more easily conducting portions may stretch in some parts 

 from plate to plate ? If so, we approximate more nearly to 

 the inferior limit.] 



The mathematical account of the residual discharge on this 

 hypothesis is practically the same as Maxwell's ; but it may 

 perhaps be worth while to give it with the necessary altera- 

 tions, as these seem to make it somewhat more straightforward 

 and evident. 



We shall suppose with Maxwell, " for the sake of simplicity, 

 that the dielectric consists of a number of plane strata of 

 different materials and of area unity/' and that the induction 

 is in the direction of the normal to the strata. 



Let a ly a 2 , &c, be the thickness of the different strata ; 



X 1; X 2 , &c, be the electric intensity within each stratum; 

 p l9 p 2 , &c, be the amount of decay of induction per 

 second in each stratum ; 



