THE MICROSCOPE BY MEANS OF THEIR OPTICAL CHARACTERS. 6()7 



a table or lithographic plate of the colours with the correspond- 

 ing relative retardations, but in determining colours so much 

 depends on the idiosyncrasy of the observer and the character 

 of the light that such estimates can only be relied on within very 

 wide limits. In the smoky atmosphere of a London winter, for 

 instance, the blue of the second order under crossed nicols appears, 

 as Mr. T. Crook pointed out to me, to pass directly into greenish 

 yellow without anything that could be definitely characterised 

 as green intervening. 



The birefringence may be denned as the relative retardation in 

 a unit of distance. The relative retardation is, accordingly, equal 

 to the product of the birefringence of the section and its thick- 

 ness, the distance traversed. It can be shown that, if the same 

 units are employed for both relative retardation and distance 

 traversed, the birefringence is equal to the difference between the 

 refractive indices of the two directions of vibration. 



If then k be the relative retardation, I the thickness of the 

 section, d the birefringence and /x and v the refractive indices 

 in the fast and slow directions, we have k = I d = I (v li). 



In the case of a section of quartz 21 microns thick, cut parallel 

 to the optic axis, the indices of refraction are 1*514 and 1'553 

 and the birefringence 0*009, which is the relative retardation in 

 microns after traversing one micron. Accordingly h = 21 x 0*009 

 = 0*189 of a micron. 



If, however, the relative retardation be expressed, as usual, in 

 micro-millimetres, it will, foi- the same thickness, be numerically 

 a thousandfold greater. This value of the relative retardation 

 may be denoted by K, and tne corresponding value of the bire- 

 fringence, that is to say the relative retardations in micro- 

 millimetres after traversing one micron, by D, which will be, in 

 the same manner, numerically a thousand times d, the value in 

 homogeneous units. D may be referred to as the birefringence 

 in millesims, where a millesim is a unit equal to 0*001. The 

 equation then becomes K = I D. In the special case which 

 has been taken, the birefringence is 9 millesims, so that K = 

 21 x 9 = 189 micro-millimetres. This procedure has the advan- 

 tage of avoiding small decimal amounts. 



The birefringence varies according to the direction in which 

 the section is cut in the crvstal. The value given in text-books 

 is the maximum birefringence, that found in sections cut parallel 



