1896.] NEW YORK ACADEMY OF SCIENCES. 55 



tion, the rotation around b produces a similar change from 

 ascending to descending, with a turning point or emergence o 

 axis where the color is the red of first order, i. e., a = l>. With 

 rotation around a there is no such result. 



It ma}^ therefore be concluded from the behavior of the section 

 normal to <t. Fir.^t hy the reversal of the relation of phase ditfer- 

 ences during rotation around one of the extinction directions 

 that this direction is' (» and the other ( and similarly with the 

 section normal to C it may be proved that the axis of rotation 

 is h and the other tt. Second by rotation as far as the turning 

 point where the red of iirst order is re-established the angle be- 

 tween an optic axis and the plate normal may be measured from 

 which the character results from the rule that when the acute 

 bisectrix is C the sign is positive. 



lY. The von Federow Mica Wedge.* 



This is a simple inexpensive apparatus which can be used with 

 even greater ease than the quartz wedge either to determine the 

 character of the double refraction or to measure its strength. 



The wedge consists of fifteen superposed quarter undulation 

 mica plates, each about two mm. shorter than the one beneath it 

 and with their axes of elasticity parallel. The series is mounted 

 on a strip of glass and covered with a cover glass. 



The wave length of a middle color may be taken as 560 /^ f^ 

 (millionths of a millimeter) hence each quarter undulation mica 

 plate may be considered to possess a phase difference of 140 

 /« y- If then between the polarizer and analyzer we insert the 

 mica wedge so that its axis of least elasticity is at right angles 

 to that of the mineral under examination, we subtract from the 

 phase difference of the mineral an amount equal to n times 

 140 /' f- in which n represents the numbers of superposed mica 

 plates in the field. When the mineral appears dark the value evi- 

 dently corresponds closely to the phase diflerence of the mineral. 



From the expression A = eX. in which A is the phase differ- 

 ence, X the double refraction, and e the thickness in millionths 

 of millimeters, the thickness can be deduced when the double re- 

 fraction is known or vice versa. If a mineral of known double 

 refraction can be found in the section near the mineral under 

 investigationf the double refraction of the latter can be deduced 

 by measuring the phase difference of the known mineral whence 



»E. von Federow Zeit. /. Kryst, etc., v. 25, 1895, p. 349. 



t It is not safe to use minerals near the edge of the section as the thicknesses are apt 

 to be unequal. 



