The instantaneous discharge is therefore [psi]/ak or the quantity which would be discharged by <s>an air<\s> a condenser of air of the equivalent thickness a, and it is <s>independent of<\s> unaffected by the want of perfect insulation. (88) Now let us suppose the connexion between the surfaces broken and the condenser left to itself and let us consider the gradual dissipation of the internal charges. Let [psi]' be the difference of potential of the extreme surfaces at any time t, then [psi]' = a<sub>1<\sub>k<sub>1<\sub>f<sub>1<\sub> + a<sub>2<\sub>k<sub>2<\sub>f<sub>2<\sub> + &c (56) but a<sub>1<\sub>k<sub>1<\sub>f<sub>1<\sub> = <s> a<sub>1<\sub>k<sub>1<\sub>e<sub>1<\sub><\s> =  r<sub>1<\sub> df<sub>1<\sub>/dt a<sub>2<\sub>k<sub>2<\sub>f<sub>2<\sub> =  r<sub>2<\sub> df<sub>2<\sub>/dt. Hence <s>a<sub>1<\sub>k<sub>1<\sub>f<sub>1<\sub><\s> f<sub>1<\sub> = A<sub>1<\sub> e<sup><s>a<sub>1<\sub>k<sub>1<\sub>/r<sub>1<\sub> t<\sup> f<sub>2<\sub> = A<sub>2<\sub> e<sup><s>a<sub>2<\sub>k<sub>2<\sub>/r<sub>2<\sub> t<\sup> &c and by referring to the values of e'<sub>1<\sub> e<sub>2<\sub> &c we find A<sub>1<\sub> = [psi]/r r<sub>1<\sub>/a<sub>1<\sub>k<sub>1<\sub>  [psi]/ak A<sub>2<\sub> = [psi]/r r<sub>2<\sub>/a<sub>2<\sub>k<sub>2<\sub>  [psi]/ak &c so that we find for the difference of extreme potentials at any time <s>[eqation]<\s> [equation] (89) It appears from this result that if all the layers are made of the same substance [psi]' will be zero always. I f they are of different substances, the order in which they are placed is indifferent, and the effect will be the same whether each substance consists of one layer or is divided into any number of thin layers and arranged in any order among thin layers of the other substances. Any substance, therefore the parts of which are not mathematically homogeneous, though they may be apparently so, may exhibit phenomena of absorption.
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Manuscript details
 Author
 James Clerk Maxwell
 Reference
 PT/72/7
 Series
 PT
 Date
 1864
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Cite as
J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’, 1864. From The Royal Society, PT/72/7
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