334 Mr. J. W. Gifford. [May 7, 



of angle, the indices are not quite the same at each angle, but if the 

 variations are in the same direction and not much greater for the extra- 

 ordinary than for the ordinary ray, we may assume that the optic axis 

 is very nearly perpendicular to the principal plane. Taking the three 

 angles as a, p, and y, the results are as follow (for line D) : — 



Ordinary ray. 

 oc. 1-5442550 

 p. 1-5442306 

 y. 1-5442765 



Quartz. 



Extraordinary ray. 



a. 1-5533605 

 p. 1-5533356 



y. 1-5533977 



Calcite. 



Ordinary ray. 

 ol. 1-6583705 

 P. 1-6583381 

 y. 1*6583595 



Extraordinary ray. 



a. 1 4864145 

 P. 1-4863865 



y. 1-4864062 



Thus it would seem that the differences in values of the extraordinary 

 indices are not greater than those for the ordinary ray. 



As further evidence of accuracy in observation, it may be mentioned 

 that the measurements for line D quartz, ordinary and extraordinary 

 ray recorded in the table, were made on March 4, 1900. On Decem- 

 ber 27, 1901, the prisms having been set up by mistake for a prism of 

 left-handed quartz, a complete independent series of measurements 

 were again made for both rays before the mistake was discovered. The 



two resulting indices follow :- 



March 4, 1900 



December 27, 1901 



Ordinary ray. 

 1-5442558 

 1-5442558 



Extraordinary ray. 

 1-5533662 

 1-5533673 



The difference of the two measurements of the ordinary ray begins 

 in the 8th decimal place and is not shown. 



8. Probable Accuracy of Indices. — These refractive indices maybe con- 

 sidered correct to the 5th decimal place ; the 6th is only approximately 

 correct, and the 7 th is of little value. But it is believed that in many 

 cases the error does not exceed unity in the 6th place. 



9. Interpolation. — The question of the relation between refractive 

 index and wave-length has not been gone into, but it may be said that 

 for the ultra-violet Cauchy's formula is not of great value, while for the 

 visual spectrum iVelson's formula is a nearer approximation, and takes 

 little time to work out,* while the graphical interpolation of devia- 

 tions by squares of reciprocals proposed by Dr. Marshall Watts f is not 



* See ' E,. M. S. Journal,' April, 1899, Presidential Address, 

 f ' Index of Spectra,' p. xii. 



