536 A Dynamical Theory of the Electromagnetic Field. [Dec. 8, 



The theory does not attempt to give a mechanical explanation of the 

 nature of magnetic disturbance or of electric displacement, it only asserts 

 the identity of these phenomena, as observed at our leisure in magnetic and 

 electric experiments, with what occurs in the rapid vibrations of light, in a 

 portion of time inconceivably minute. 



This paper is already too long to follow out the application of the elec- 

 tromagnetic theory to the different phenomena already explained by the 

 undulatory theory. It discloses a relation between the inductive capacity 

 of a dielectric and its index of refraction. The theory of double refraction 

 in crystals is expressed very simply in terms of the electromagnetic theory. 

 The non-existence of normal vibrations and the ordinary refraction of rays 

 polarized in a principal plane are shown to be capable of explanation ; but 

 the verification of the theory is difficult at present, for want of accurate 

 data concerning the dielectric capacity of crystals in different directions. 



The propagation of vibrations in a conducting medium is then considered, 

 and it is shown that the light is absorbed at a rate depending on the con- 

 ducting-power of the medium. This result is so far confirmed by the 

 opacity of all good conductors, but the transparency of electrolytes shows 

 that in certain cases vibrations of short period and amplitude are not ab- 

 sorbed as those of long period would be. 



The transparency of thin leaves of gold, silver, and platinum cannot be 

 explained without some such hypothesis. 



The actual value of the maximum electromotive force which is called 

 into play during the vibrations of strong sunlight is calculated from 

 Pouillet's data, and found to be about 60,000,000, or about GOO Daniell's 

 cells per metre. 



The maximum magnetic force during such vibrations is ' 1 93, or about -{^ 

 of the horizontal magnetic force at London. . - 



Methods are then given for applying the general equations to the calcu- 

 lation of the coefficient of mutual -induction of two circuits, and in parti- 

 cular of two circles the distance of whose circumferences is small compared 

 with the radius of either. 



The coefficient of self-reduction of a coil of rectangular section is found 

 and applied to the case of the coil used by the Committee of the British 

 Association on Electrical Standards. The results of calculation are com- 

 pared with the value deduced from a comparison of experiments in which 

 this coefficient enters as a correction, and also with the results of direct 

 experiments with the electric balance. 



