xxii JOSIAH WILLABD GIBBS. 



at equations somewhat different from those of Maxwell in that they 

 do not contain explicitly the dielectric constant and conductivity as 

 measured electrically, thus avoiding certain difficulties (especially in 

 regard to metallic reflection) which the theory as originally stated had 

 encountered ; and it is made clear that " a point of view more in 

 accordance with what we know of the molecular constitution of 

 bodies will give that part of the ordinary theory which is verified 

 by experiment, without including that part which is in opposition 

 to observed facts." Some experiments of Professor C. S. Hastings 

 in 1888 (which showed that the double refraction in Iceland spar 

 conformed to Huyghens's law to a degree of precision far exceeding 

 that of any previous verification) again led Professor Gibbs to take 

 up the subject of optical theories in a paper which shows, in a 

 remarkably simple manner, from elementary considerations, that this 

 result and also the general character of the facts of dispersion are in 

 strict accord with the electrical theory, while no one of the elastic 

 theories which had, at that time, been proposed could be reconciled 

 with these experimental results. A few months later upon the publi- 

 cation of Sir William Thomson's theory of an infinitely compressible 

 ether, it became necessary to supplement the comparison by taking 

 account of this theory also. It is not subject to the insuperable 

 difficulties which beset the other elastic theories, since its equations 

 and surface conditions for perfectly homogeneous and transparent 

 media are identical in form with those of the electrical theory, and 

 lead in an equally direct manner to Fresnel's construction for doubly- 

 refracting media, and to the proper values for the intensities of the 

 reflected and refracted light. But Gibbs shows that, in the case of 

 a fine-grained medium, Thomson's theory does not lead to the known 

 facts of dispersion without unnatural and forced hypotheses, and that 

 in the case of metallic reflection it is subject to similar difficulties; 

 while, on the other hand, "it may be said for the electrical theory 

 that it is not obliged to invent hypotheses, but only to apply the 

 laws furnished by the science of electricity, and that it is difficult to 

 account for the coincidences between the electrical and optical pro- 

 perties of media unless we regard the motions of light as electrical." 

 Of all the arguments (from theoretical- grounds alone) for excluding 

 all other theories of light except the electrical, these papers furnish 

 the simplest, most philosophical, and most conclusive with which the 

 present writer is acquainted; and it seems likely that the con- 

 siderations advanced in them would have sufficed to firmly establish 

 this theory even if the experimental discoveries of Hertz had not 

 supplied a more direct proof of its validity. 



In his last work, Elementary Principles in Statistical Mechanics, 



