352 M. R. Riihlniann on the Alteration produced by Heat 



preferable dispersion-formula is troublesome*, I consider this 

 formula (7) to be sufficient ; and I believe I have by its means 

 sufficiently determined the alteration caused by heat in the velo- 

 city of the propagation of light in water. 



VI. On the relation between the Velocity of the Propagation of 

 Light and the Density. 



It is well known that the theory of emission has given the 

 following relation between the velocity of propagation of light 

 and the densityf, 



where v denotes the velocity of light in air, and k is a constant. 

 Hence the so-called refractive power (brechende Kraft) n 2 —l, 

 divided by the density, would be a constant quantity. It re- 

 mained necessarily impossible to discover a relation between the 

 optical conditions and the density of bodies as long as, in em- 

 ploying the vibration hypothesis, the mathematical theory, in 

 establishing the differential equations of the motion of the sether, 

 neglected the existence of material molecules and their action 

 upon the sether molecules. But an analytical solution of this 

 problem may be safely predicted now that it is almost univer- 

 sally admitted with CauchyJ, Redtenbacher§, Lorenz||, and 

 Briot^j, that in consequence of an attraction between the mate- 

 rial molecules and the sether molecules, and a reciprocal repul- 

 sive action between the aether molecules, there is in substances a 

 periodical arrangement of the sether molecules around the mate- 

 rial ones. A more exact discussion of the number of material 



* Christoffel, Beriuhte der Berliner Akademie fur 1861, vol. ii. pp. 906- 

 919 & 997-999. 



This formula, based certainly upon the insufficient foundation of Cauchy's 

 " Memoire sur la Dispersion," is quite as useful as Cauchy's formula as an 

 empirical expression, and allows a very interesting indication of the con- 

 stants n 2 and A . It is 



«„V2 



\Z l+ * + \A- 



where n is the index of refraction, X the undular length, and n and X two 

 constants dependent upon the nature of the medium. 



t Laplace, Mecanique Celeste, vol. iv. book 10. p. 264. 



% " Memoire sur les vibrations d'un double systeme de molecules, et de 

 Tether contenu dans un corps cristallise," Memoir es de VAcademie, vol. xxiv. 

 pp. 599-614 &c. 



§ Dynamidensystem, pp. 11-28. 



|| " TJeber die Theorie des Lichts," Pogg. Ann. vol. cxxi. p. 579. 



IT Essais sur la theorie mathematique de la lumiere. 



