260 BULLETIN OP THE UNIVERSITY OF WISCONSIN. 



dropping terms of higher order, he derived the following equa- 

 tion for the index of refraction : 



/ 7¥ = A 1 + -_r + 1 r+&ct. (9)> 



ChristofTel 1 showed that when Cauchy made his transforma- 

 tions to derive (9) from (8) he assumed A 2 to be small in com- 

 parison with A x and, hence, practically used only one constant. 

 ChristofTel devised a new method of solving equation (8) that 

 did not require the second assumption, and showed that the in- 

 dex of refraction can he represented by equation (10) : 



p o V7 



V -i -4- h + V 1 — h (10). 



1 1 



The problem of dispersion was also studied by Redtenbecker 2 

 and upon the supposition that each molecule is surrounded by a 

 dense ether shell he obtained the formula : 



1 



M 



- 2 = A + Xi + C A 3 (ii). 



The subject was next treated by Briot. 3 He considered the 

 assumptions made by Cauchy insufficient to explain dispersion, 

 inasmuch as a change in density alone could not give a different 

 order to the distances between the ether particles, and conse- 

 quently, if the wave length were a function of the velocity in- 

 side a material body the same must be true in free space. To 

 remedy this defect he assumed a direct action of the material 

 particles upon the velocity of the transmission of light and ex- 

 pressed this by adding a term KA. 2 to Cauchy's formula, thus: 



j 2 = K ,\» + A, + ~i + 4r + Act. jig). 



This formula he tested by the best experimental data obtainable 

 and found that the term KA 2 was small and in most cases could' 



) Christoffel, Pogg. Ann. CXVIL, p. 27, (1861). 



2 Redtenbecker, Dynamiden-System. Mannheim, (1857>. 



3 Briot, " Essai sur la theorie mathematique de la lumiere." Paris, 1863; Leipzig,. 

 1867: C. R. LVIL, p. 866. 



