TRAXSACTIOXS OF THE SECTIOXS. 47 



e being the elasticity nnd d the density of luminous ether ; but there were no 

 means of giving a physical and numerical interpretation of the elasticity and density 

 of ether in certain retracting media. 



The index of refraction n is, according to the law of Brewster, equal to the tan- 

 gent of the angle of polarization-maximum (3 ; hence 



tan 



/3=M = \/fi. 



Conceiving the luminous phenomena as produced by molecular vibrations, the 

 densitj' of tlie luminous ether must be represented by the density or distance of 

 atoms (»•), or be a function of it, viz. 



It is a fact, confirmed by vai-ious experiments, that by mechanical pressure, by 

 imequal heating, and by other means augmenting or diminishing the distance of 

 atoms, the velocity of light undergoes a sensible change, isotropical refractive media 

 becoming even doubly refracting. This confirms the supposition that the velocity 

 of light is in connexion with the atomic distances. 



It is obvious that there can be no great difference of elasticity in the case of a more 

 rapid vibratoiy motion than heat is; and if we suppose the elasticity of atoms to be 

 the same in both cases for the propagation of light and heat, there can be no essential 

 error in that hypothesis as to the value or amount of elasticity. Supposing, therefore, 

 elasticity of atoms to be proportional to, or identical with, the specific heat for light 

 and heat, we get 



V s 



where s denotes the specific heat of the chemical element, v the velocity, and n the 

 index of refraction of light. 



As to the form of the function r, the simplest supposition may be tried ; putting 

 therefore 



f(r)=r, 



we have to try the accordance of that supposition with the data of observation in 

 the equation 



M = -=V — 

 V S 



J' 



According to the law of Dulong and Petit, the product of atomic weight m and of 

 specific heat s is a constant, 



ms = C, 



Hence we get, if iv denotes the specific weight, 



- 3 



1 mJ 

 w=-=-i r> 



or 1 „ m* 



M=- = C . — r. 



The specific heats and densities of chemical elements are referred to water as unit, 

 but the atomic weight 2V commonly to hydrogen as unit. 



Dividing, therefore, the atomic weight by the weight of water, HO = 9, it .is 

 brought to the same imit as the specific heat and the specific weight «'. - 



We obtain thus 



^1^ Cm* 



log M=iog C-f 1(4 log w— log w— log 9), 

 log « =0-5795202 -l-f- 1 log m-} log n: 



