for the solution of which we may take 



Here dS denotes an element of volume situated at a distance r 

 from the point for which we wish to calculate 51 and O., and the 



I means that, in the expressions representing ^'g and S^^ 



r 



for that element of volume, t is to be replaced by t . 



V 



The algebraic sign of v is left indeterminate by (17). We shall 

 choose it in such a way that our formulae represent a propagation 

 of vibrations issuing from the elements of volume in which (£'e and S?g 

 are applied. 



For aether vv^e have q = l and, as may easily be show^ii -=zin, v=zc. 



§ 4. We have next to establish the equation of energy. The calcu- 

 lations required for this purpose, as well as those we shall have 

 to perform later on, may be much simplified, if we replace all 

 discontinuities at the limit of two bodies by a gradual transition 

 from one to the other; this may be done without loss of generality , 

 because, in our final results, the thickness of the boundary layers 

 may be made to become infinitel}^ small. A further simplification is 

 obtained by leaving out of consideration the imaginary magnetomotive 

 forces, and by supposing the coefficients (i and q to be real. The 

 coefficients p^^,p^^ etc. however will always be considered as complex 

 quantities. We shall decompose them into their real parts, which 

 we shall denote by «„, <^fi3, etc., and their imaginary parts, for which 

 we shall write — i(i^^, — i{^^^, etc., so that /^n = «n — M^n, etc. 



28 



Proceedings Royal Acad. Amsterdam. Vol. VIII. 



