Transparent Inactive Crystal Plates. 1205 



observations were made by using the cross grating ocular as 

 shown in the microphotograph fig. 15. The observed coordi- 

 nated values were reduced to their angular equivalents by use 

 of the apertometer and these in turn reduced to the corre- 

 sponding crystal angles by means of the sine formula and the 

 refractive index ft. The use of the refractive index ft for all 

 direction introduces an error, but experience has shown that 

 this error is not great and in general may be disregarded. 



Points were located as accurately as possible along each 

 axial bar and. then plotted in projection (indicated by small 

 circles, figs. 14a, 146). Although the axial bars were not 

 perfectly sharp they were well defined and the points were 

 taken along the central line of the bar, the position of each 

 point being determinable to within about 1°, or less for certain 

 positions. In fig. 14a, the results which were obtained from 

 an unmounted cleavage plate are represented ; in fig. 145, the 

 interference figure is that from the same plate mounted in 

 Canada balsam between cover glass and object glass. In each 

 of these figures, the positions of the line of vibration were 

 determined graphically, both by the method of Professor 

 Becke (indicated by small crosses) and by that of the writer 

 (indicated by small circles). A comparison of the relative 

 positions of these small circles and crosses relative to the dot- 

 ted line which represents the position of extinguishing plane 

 of the upper nicol shows that in a few instances the points 

 as determined by Professor Becke's method are slightly 

 more accurate than the equivalent points of the writer's 

 method ; in the majority of instances, however, the small 

 circles are more nearly correct than the small crosses. 

 As a general rule, it may be stated that the order of accuracy 

 of the two methods is about the same, the writer's method 

 having the single advantage of greater simplicity. 



A critical comparison of the results of observation on 

 mounted flakes with those on unmounted flakes show clearly 

 the effect of rotation by the glass surface, causing the axial 

 bars and axes to shift slightly, so that the direct reading of the 

 optic axial angle is not quite the same in the two cases. The 

 difference is not great, but it is noticeable, and is sufficient to 

 make it advisable to use unmounted plates wherever possible, in 

 optic axial measurements, if results of the highest accuracy are 

 desired. Ordinarily, however, this precaution is unnecessary, 

 since such accuracy is not required. 



A rotation of the crossed nicols through 90° also generally 

 produces a slight shift of the axial bars from mounted plates, 

 as indicated by fig. 16, which is a direct record to scale of the 

 observed phenomena. In each case the points along the cen- 

 tral line of the axial bar were plotted. The position of this 



Am. Jour. Sci.— Fourth Series, Vol. XXXI, No. 183.— March, 1911. 

 15 



