262 BULLETIN OF THE UNIVERSITY OF WISCONSIN. 



It is noteworthy that Lord Kelvin 1 in a paper read' before the 

 Koyal Society of Edinburgh, February 6th, 1899, on the ab- 

 sorption line of sodium vapors, used Sellmeier's formula. 



Kelvin's 2 theory is quite similar to that of Sellmeier, the 

 chief peculiarity being the conception of concentric spherical 

 shells, connected by zigzag springs, to represent a molecule hav- 

 ing more than one natural period of vibration. 



Under the assumption of a diatomic molecule of this form he 

 writes the equation thus : 



/V 2 \ 2 m T 8 m, T» 



YV\/ = X + T 2 — K 2 + T s — K^ ( 14 >- 



Where T equals period of vibration of ether light wave. 

 Where K equals natural period of vibration of one shell. 

 Where K x equals natural period of vibration of the other shell. 

 Where m equals density of 1st shell, using ether as unity. 

 Where mj equals density of 2nd shell, using ether as unity. 



This theory of mutual reaction between matter and ether was 

 next developed by Helmholtz. 3 Let u, v, w, be the displace- 

 ments of the ether particles of density m, in an element of 

 volume dv; U, V, W, the displacements of the material parti- 

 cles of density m'; then, considering the forces along X axis 

 only, he forms two equations of motion, thus : 



u 



m 



m 



dt 8 



dHJ 

 dt 8 



= X+X' + A+&ct. (15a). 



= X x + X', + A, + Act. (isb). 



Where X equals action of ether particles external to dv ; 



Where X' equals external impressed force on m. 



Where A equals direct action of the material particle in dv on 



the ether ; 

 Where X x equals action of matter external to element dv. 

 Where X' x equals external impressed force on m. 

 Where A x equals direct action of the ether in dv on the material 



particles. ___^ 



i Kelvin, Phil. Mag. XLVII., p. 302. 

 2 Kelvin, Baltimore Lectures, 1884. 

 ■ Helmholtz, Pogg. Ann. CLIV., p. 582. 



