238 



8. Hemimorphous substances are dependent on the opposite law 

 as to the dispersion of their optic axes. 



9. Whenever, according to Cauchy, the index of refraction 



T> 



^=A+ (A being the coefficient of refraction and B the coeffi- 

 X 



cient of dispersion), the relation between density D of the substances 

 and the coefficients A and B is expressed by the following formulae : 



fD=* fD=* 



2AdA=l MrfD 



*/limD=0 i/limD=0 



M and N remaining invariable quantities for every elementary sub- 

 stance. If M is made to signify specific power of refraction, and N 

 specific power of dispersion, their values may be found out by means 

 of the following equations : 



-rr =M > F 2=N - 



10. The consequence from 9 is, that the density of the ether 

 may be set in proportion to the density of the substances*. 



11. Not the elasticity, but rather the density is subject to varia- 

 tion (Fresnel's theory). 



12. The consequence of 9 is, that the propagation of light 

 may be equally conceived as being independent of the luminous ether, 

 and only in dependence on the substantial molecules. 



13. If Fresnel's formula is derived from the principle of conser- 



A 2 1 

 vation of vis viva, and ^ is substituted, a formula similar to 



Cauchy' s in structure is thus obtained. 



14. In consequence of 9, it appears possible to calculate the 

 density in the three dimensions of any crystal, and to bring this new 

 moment in connexion with the rest of the physical properties. 



15. The densities being proportional to the masses, and these to 

 the distance r of the molecules^ the coefficient of dispersion must be 

 subject to the general law of gravitation, and it would be admissible 



* Calcareous spar, Arragonite ; diamond, graphite, coal ; water, ice ; different 

 varieties of topaz, beryl, apatite, &c. ; and all the substances examined by Dale and 

 Gladstone may serve as evidences and exemplifications of the above propositions. 



