412 bowen: anthophyllite 



dices by the method of minimum deviation, and by this method 

 the writer obtained exactly the same values as Penfield: 7 = 

 1.6404, a = 1. 6301. The method is so thoroughly dependable 

 that there is no reason for doubting the value of /3 so obtained. 

 The other value of /S given by Penfield was calculated from 

 measurements of the optic axial angle on oriented plates in an 

 immersion medium. The relation between the angles so ob- 

 served and the true angle is given by the equations 



and 



sin //„ = — sin V 



sin /f o = — sin (90 - V) 



whence by dividing one obtains the relation 



sin Ha 



= tan V. 



sin Hg 



Therefore, by measuring both the obtuse and the acute optic 

 axial angle in an immersion medium one can calculate the true 

 angle without any knowledge of the index of the immersion 

 medium. The method is very accurate and there is no reason 

 for questioning the value of 2 F so obtained. On the other hand, 

 if one wishes to calculate ii from such measurements, an accurate 

 knowledge of the refractive index of the immersion medium is 

 required. The liquid used by Penfield was potassium mercuric 

 iodide solution, and though he gives the index of his solution, 

 the assumption that this was in error, since it may change so 

 readily by evaporation, is the most reasonable method of ac- 

 counting for the great discrepancy between the value of (3 so 

 calculated (1.6353) ^-^d that measured by minimum deviation 

 (1.6301). Penfield evidently placed greater dependence upon 

 the former value (1.6353), for he used it in calculating a, ob- 

 taining the result 1.6288. On the other hand, if the latter value 

 of ( 1. 6301) is used, the calculated value of a is 1.6 195. The 

 whole question can best be decided by direct measurement of a. 

 This was done in immersion liquids with Na light on a rather 

 thick cleavage plate ||oio, under which conditions the method 



