J. W. Gibbs — Elastic and Electrical Theories of Light. 467 



Apt. XXXIY. — A Comparison of the Elastic and the Elec- 

 trical Theories of Light with respect to the Law of Double 

 Refraction and the Dispersion of Colors; by J. Willard 

 Gibbs. 



It is claimed for the electrical* theory of light that it is free 

 from serious difficulties, which beset the explanation of the 

 phenomena of light by the dynamics of elastic solids. Just 

 what these difficulties are, and why they do not occur in the 

 explanation of the same phenomena by the dynamics of electri- 

 city, has not perhaps been shown with all the simplicity and 

 generality which might be desired. Such a treatment of the 

 subject is however the more necessary on account of the ever- 

 increasing bulk of the literature on either side, and the confus- 

 ing multiplicity of the elastic theories. It is the object of this 

 paper to supply this want, so far as respects the propagation of 

 plane waves in transparent and- sensibly homogeneous media. 

 The simplicity of this part of the subject renders it appropriate 

 for the first test of any optical theory, while the precision of 

 which the experimental determinations are capable, renders the 

 test extremely rigorous. 



It is moreover, as the writer believes, an appropriate time 

 for the discussion proposed, since on one hand the experi- 

 mental verification of Fresnel's Law has recently been carried 

 to a degree of precision far exceeding anything which we have 

 had before, f and on the other, the discovery of a remarkable 

 theorem relating to the vibrations of a strained solid;}; has given 

 a new impulse to the study of the elastic theory of light. 



* The term electrical seems the most simple and appropriate to describe that 

 theory of light which makes it consist in electrical motions. The cases in which 

 any distinctively magnetic action is involved in the phenomena of light are so 

 exceptional, that it is -difficult to see any sufficient reason why the general theory 

 should be called electro-magnetic, unless we are to call all phenomena electro- 

 magnetic which depend on the motions of electricity. 



f In the recent experiments of Professor Hastings relating to the index of 

 refraction of the extraordinary ray in Iceland spar for the spectral line D 2 and a 

 wave-normal inclined at about 31° to the optic axis, the difference between the 

 observed and the calculated values was only two or three units in the sixth 

 decimal place (in the seventh significant figure), which was about the probable 

 error of the determinations. See page 60 of this volume. 



% Sir Wm. Thomson has shown that if an elastic incompressible solid in which 

 the potential energy of any homogeneous strain is proportional to the sum of the 

 squares of the reciprocals of the principal elongations minus three is subjected to 

 any homogeneous strain by forces applied to its surface, the transmission of plane 

 waves of distortion, superposed on this homogeneous strain, will follow exactly 

 Fresnel's law (including the direction of displacement), the three principal veloci- 

 ties being proportional to the reciprocals of the principal elongations. It must 

 be a surprise to mathematicians and physicists to learn that a theorem of such 

 simplicity and beauty has been waiting to be discovered in a field which has been 

 so carefully gleaned. See page 116 of the current volume (xxv) of the Philo- 

 sophical Magazine. 



