1895] MICROSCOPICAL JOURNAL. 167 



will rarely happen that coincidence of these values will 

 occur for all colors of the light employed, the dispersion 

 of the crystal and the liquid in general being dilferent. 

 So that although the values may be coincident for sodium 

 light, they would in all probability be different for other 

 colors. But if the observations are only conducted for 

 sodium light, a process which is frequently sufficient for 

 the purpose in view, then this objection entirely disap- 

 pears. Moreover, the errors introduced by the discrep- 

 ancy for different wave-lengths of light would not be 

 sufficiently large in most cases, if observations for other 

 colors were made, to materially reduce the value of the 

 method for the purposes for which it was designated. 



A consideration of the simple formula connecting the 

 optic axial angle with the beta refractive index and the 

 refractive index of an immersion liquid will at once ren- 

 der the value of the method, within the above specified 

 limits, clear. Representing as usual the real semi-acute 

 angle between the optic axes within the crystal by Va, 

 the semi-obtuse angle by Vo, and the apparent semi- 

 acute and obtuse angles in the immersion liquid by Ha 

 and Ho respectively, the refractive index of the medium 

 for light of the same wave-length being n, then : 



Sin Va equals j^JJ,^ sin Ha and Sin Vo equals ^J^ sin Ho. 



These two equations are of the same kind, for both 

 Va and Vo are less than 90 degrees ; and the only varia- 

 bles are n sin Ha and w sin Ho, for beta, sin Va, and sin 

 Vo are constant quantities for this wave-length of light. 

 If, now, the sum of the angles 2 Ha and 2 Ho is greater 

 than 180 degrees, the common factor 7i must, in order to 

 bring the sum of these angles down equal to 180 degrees, 

 be increased, that is, a liquid of higher refractive power 

 be employed. Conversely, if the sum is less then 180° 

 the refractive power of the liquid must be diminished in 

 order to bring the sum of the angles up to 180°. For 



