226 Mr. J. Larmor. A Dynamical Theory [June 20, 



expression multiplied by (l /w~ 2 )> when the interface separates two 

 transparent media. 



The distinction between true current and total current is practically 

 immaterial, except in questions relating to electrical vibrations and to 

 optics. The remaining part of the theory is therefore developed more 

 particularly with a view to optical applications. At the end of the 

 previous paper a brief outline of the method of treating optical dis- 

 persion was given, and it was shown that the same principles led 

 directly to Fresnel's formula for the effect on the velocity of light 

 produced by motion, through, the eether, of the material medium 

 which transmits it. In the latter respect the theory is in agreement 

 with a more recent discussion by H. A. Lorentz, of the propagation 

 of electrical and optical effects through moving media. 



A detailed theory of optical propagation in transparent and opaque 

 ponderable media is given, on the basis that it is the contained 

 electrons that are efficient in modifying the mode of propagation 

 from that which obtains in free aether. The dispersive theory of 

 MacCullagh had been physically interpreted in the earlier part of 

 the previous paper ; but it appears from the same train of reasoning 

 as was there applied to Cauchy's theory, that molecular magnitudes 

 are too small compared with the wave-length to allow any consider- 

 able part of the actual dispersion to be accounted for statically 

 in that way. The rotatory dispersions, both natural and magnetic, 

 are, however, structural phenomena ; and this accounts for their 

 smallness compared with ordinary dispersion. 



As regards ordinary dispersion, a formula is obtained for the case 

 of perfectly non-conducting media, namely, p? = l + A/(/3 2 jp 2 ), where 

 '2iTTJp is the period, of the same type as one recently deduced by von 

 Helmholtz by an abstract process based on the principle of Least 

 Action combined with a theory of electrons, which, however, does not 

 correspond with the views here developed. That this formula is a 

 good representation of the experimental facts for ordinary trans- 

 parent media is generally recognised ; especially as it may, in case of 

 necessity, be modified by the inclusion of slight non-selective opacity, 

 due to drift of free electrons, after the manner of ordinary conduc- 

 tion. When this kind of general opacity is predominant, the result 

 obtained in the paper conforms to the main features of metallic pro- 

 pagation ; thus, with sufficient conductivity the real part of the square 

 of the refractive index becomes negative, and the real part of the 

 index itself may become less than unity, while the dispersion is 

 usually abnormal. 



When the phenomena of moving media are treated, dispersion may ? 

 for simplicity, be left out of account. It is shown that, if the view 

 described in the previous paper, that all the dynamical properties of 

 matter are to be derived from the relations of electrons, with or 



