of Minerals in the Thin Section. 369 



graphic plat (fig. 1) Las been added with the standard stereo- 

 graphic plat to serve as a base for future plotting of similar 

 phenomena. 



(4) Plate II is intended to serve as a graphical base by 

 which to solve Mallard's formula, K sin E = D; also n 1 sin a x — 

 n 2 sin a 2 ; also <y' — a' =( r y — a) sin a x sin a 2 , a x and a„ being the 

 angles included between the given direction of wave propaga- 

 tion and the two optic axes respectively. 



( 5 ) The Mallard formula and method were tested by a new 

 method and the agreement of the formula with fact for the 

 special objective used and the particular precautions observed 

 found to be remarkable. It was evident that for each micro- 

 scopic objective similar tests should be made at intervals across 

 the entire held in order to insure accuracy and certainty in the 

 results obtained. 



(6) A disk-shaped type of the Becke drawing table was con- 

 structed in the Geophysical Laboratory and found satisfactory 

 in practice. 



(7) An improvement was made in the Fedorow-Fuess uni- 

 versal stage, consisting in the addition of two hinged graduated 

 circles on which to read the inclinations of the second vertical 

 circle Y 2 , and found to be of service in several methods. 



(8) A new form of condenser lens system which combines 

 the advantages of the ten Siethoff qualitative adjustable conden- 

 ser system with the exact movement of the universal stage, was 

 also described and applied to the examination of minute min- 

 eral sections, especially of artificial preparations. 



(9) A set of accurate drawings of the position of the dark 

 axial bar of the interference figure in convergent polarized 

 light for sections cut at various angles with one optic axis but 

 always so that the optic axis is still visible, has been prepared, 

 and the theoretically probable limits of error of determinations 

 of the optic axial angle by the different methods and for the 

 different sections established graphically. 



( 10 ) In the course of the investigation, several methods, 

 based solely on extinction angles for different faces,- were tried, 

 but without exception they were discarded because of the diffi- 

 culties in the measurement of the extinction angle and the 

 undue influence of small differences in extinction angle on the 

 value of the optic axial angle. 



Geophysical Laboratory, 

 Carnegie Institution of Washington, May 15, 1907. 



