of Minerals in the Thin Section. 327 



D = — 7 . sin E, 



n . k 



an equation which can be simplified to 



D = K sin E (4) 



P 



by replacing - — , an expression consisting entirely of con- 



stants, by K, the Mallard constant of the microscope for the 

 given fixed position of microscopic lens system. The constant 

 K can be determined once for all by ascertaining the D for 

 any known angle E. The method usually employed to deter- 

 mine this constant K is to measure, on a section of a biaxial 

 mineral of known optic axial angle and cut normal to the acute 

 bisectrix, the distances between the apices of the dark hyper- 

 bolic bars of the interference figure in the diagonal position ; 

 this distance is 2D, and the optic axial angle measured is 2E. 



This method, however, does not furnish a check on the value 

 of K, thus obtained, and its validity verified for other angles E, 

 unless many similar sections of different biaxial minerals be 

 taken and the K of the microscope for each angle E be ascer- 

 tained. The formula, D = K sin E, of Mallard assumes that 

 the loci of the focal points of waves entering in all directions 

 lie on a perfect spherical surface, an assumption which actual 

 microscopic objective lens systems in the strict sense of the 

 word do not fulfill. 



To test the validity of the formula for the microscopic field 

 of a given objective (No. 9, Fuess, with Amici-Bertrand lens, 

 system 7-9, and movable screw micrometer ocular with Rams- 

 den ocular), two polished plates of calcite were used, the one 

 cut after 0001 and the second at an angle of 23° 17' with 0001 

 as measured on a two-circled goniometer, the adjustment on the 

 goniometer having been accomplished by means of fresh cleav- 

 age faces along the edge of the plate. These plates were placed 

 successively on a carefully adjusted Fedorow-Fuess universal 

 stage (large model) and the positions of the optic axis meas- 

 ured on the micrometer ocular screws as the stage was turned 

 about its horizontal axis from degree to degree on both sides 

 from the horizontal position. By means of the two plates, a 

 continuous set of readings was obtained for D for angles E 

 ranging from 0° to 47°. These values were ascertained for 

 both scales (horizontal and vertical) of the double screw microm- 

 eter ocular described on page 336, and are listed in Table I. 



The values for D listed under the heading " calculated " in 

 this table were figured by Mallard's formula by taking the 

 average value of K for both the horizontal and vertical scales 

 of the double micrometer ocular ; for the vertical micrometer 



