534 Mr. J. Larmor. 



long, guided by a pair of parallel wires, was measured by interference 

 experiments when a part of Ihe circuit was surrounded by various 

 liquid dielectrics. The great length of the wave compared with the 

 section of the conductor ensures that it travels with its front sensibly 

 in the direction of propagation, and, therefore, that its velocity is 

 normal ; while the presence of the return wire limits its divergence 

 into space. Their results are expressed in the following table which 

 gives Kj*, the index of refraction m for light waves of length 6.10~ 7 

 metres, and the index of refraction m' for the observed waves of 

 about 6 metres long : 



K.4. M. m'. 



Castor oil 2'16 1'48 2'05 



Olive oil 1-75 1'47 1-71 



Xylene 1-53 Iv49 1'50 



Petroleum ] -44 1"45 1'40 



Thus the greatest, deviation from correspondence for the longer 

 waves is about 5 per cent. The- correspondence of these numbers 

 requires that the values of K t and, K 2 should be sensibly equal for 

 the substances tested, which can only be the .case in the limiting 

 form of the polarisation theory which constitutes Maxwell's dis- 

 placement theory. . In that case, as has been .seen, the currents are 

 all circuital; the Ampere-Neumann theory of electrodynamics 

 suffices for all purposes, and there is -no condensational wave. 



The stand- point from which the theory of dielectric polarisation 

 has been generalised in the theory here expounded is that of polar 

 elements attracting according to the law of inverse squares in the 

 manner of small magnets. In the results, however, this conception 

 disappears and the phenomena are all expressed iu the continuous 

 manner by means of partial differential equations! 



It is also possible, in Maxwell's manner, to ignore the attractions 

 of the elements from the beginning, and simply to define the displace- 

 ment as proportional to the. electric force. The statical theory of 

 condensers shows that in the dielectric the displacement must be 

 circuital, for the characteristic equation- of the potential must hold 

 good. The displacement constant assumed by Maxwell is equal to 

 the specific inductive capacity, in ordeT to ensure that the charging 

 current shall be continuous across the faces of a condenser. It might 

 be proposed to take a less restricted form for this constant, with the 

 result, of course, tliat the currents would be non-circuital. The in- 

 vestigation of this paper, however, proves that in all cases the velocity 

 of the waves of transverse displacement is specified iu terms of this 

 displacement constant ; and the experimental fact that in the simpler 

 media it is determined in the same manner by the specific inductive 

 capacity confines us to that value of the constant which is assumed 



