Rays, inCrystals 'with one and tiuoAxes of DoubleRefraction. 1 43 



The ray which in emerging from the plate deviates accord- 

 ing to the law of Descartes (Snellius), takes a direction with- 

 out, making with the normal of the plate an angle \ i, which 

 is calculated by the formula sin ^ i = 11" sin \ «. 



The following are the values of i for the different colours. 

 Apparent Inclination of the Optical Axes. 



from the observed inclination. Notwithstanding the difficulty 

 of taking this angle with precision, the difference of 2° is still 

 too great. I cannot tell the cause, unless the two rays, which, 

 within the plate, pass along the same optical axes, separate at 

 their egress. 



The preceding experiments having demonstrated that the 

 ratio of the indices of refraction varies in the three spectra 

 with the colours, the true ratio between the elasticities of the 

 vibrating medium along the three axes of crystallization cannot 

 be determined. If we take the elasticity of the vibrating me- 

 dium in air to be unity, the elasticity along the axis A will be 



= — 73r, along B = — 7T7T , and along C = —777- ; since the velo- 



cities being — j, —jjj-, and —^ in the system of undulations are 



as the square roots of the elasticity. But when the ratios 



n'2 n'^ 



—fi^^ and —fj^ change with the colours, they do not express 



exactly the ratios of the elasticity along the three axes of cry- 

 stallization. However, in taking the elasticity along the axis 

 A as unity, and calculating the above ratios for one of the 

 middle rays of the spectrum, such as F, we shall have the fol- 

 lowing elasticities for Arragonite. 



A B C 



1 0-81975 0-82424 



And for calcareous spar, 



Along Axis. Perpendicular to Axis. 



1 0-79874 



Colourless Topaz. — The prisms of this mineral were cut in 

 the same manner as those of arragonite. As the two spectra 

 always cover one another, I used a plate o^ tourmaline to 



