480 Royal Society : — 



§ 3. The optical axes of elasticity, coinciding with the diagonal of 

 the prism of 60°, are nearly equal to each other, and (a and /3 

 being axes of elasticity and a and b crystallographical axes) if limit 



t is supposed to be = v''3, then a=/3. 



§ 4. "Whenever a prism of 60° is extant in the prismatic system, 

 the first median line (" bissectrice de Tangle aigu") is perpendicular 

 to its diagonal*. 



§ 5. Whenever a number of prisms of G0° are extant (110, Oil, 

 101), the first median line stands perpendicular to the diagonals of 

 one of these prisms, and simultaneously to the plane of cleavage. 



§ 6. The first median line is generally perpendicular to the dia- 

 gonal of prisms, whose limit may be expressed by simpler proportions, 

 as 1 : a/2 : a/3 : a/5 : a//. 



§ 7. The dispersion of the optical axes in the prismatic system is 

 dependent on the magnitude of the crystallographical axis, with 

 which the middle axis of elasticity is coincident. 



(A) If the crystallographical axes (d 2m being a crystallographical 

 axis, with which coincides the second median line dp, with this the 

 medial axis of elasticity being coincident) are to each other as limit 

 of the square roots of odd numbers, then for 



dp > d 2m is p > v, 

 dp < d 2m is p < v. 



(B) If the same axes are to each other as the square roots of even 

 numbers to the odd, then the law of dispersion becomes the reverse 

 of what it was under the first supposition (A). 



§ 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 



yu= A H — - (A being the coefficient of refraction and B the coefn- 



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

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



2A</A= I MdD, 



c/iimD=0 JlimD = 



| e?B= I 2NDtfD, 



JlimD=0 J]imD = o 



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 : — 



* The totality of the substances belonging to the prismatic system, as far as 

 they have been hitherto objects of optical investigation, may stand in proof and 

 as exemplifications of the propositions enounced here. 



