WRIGHT: MEASUREMENTS OF REFRACTIVE INDICES 539 



derived. Equation (6) is a convenient form to use for comput- 

 ing the third refractive index, provided the optic axial angle and 

 two of the refractive indices are known. 



Methods of measurement. The above equations express rela- 

 tions between certain quantities which can be measured as 

 follows: 



d, thickness of plate, measured either by a micrometer or a spherom- 

 eter or by one of the standard microscope methods. On thin plates 

 (a few hmidredths of a millimeter thick) the error may amount to 10 

 per cent; on thicker plates the percentage error is correspondingly 

 less. On many sections the thickness is best found by computation 

 from the interference fringes. The exact path-difference, k\, is ascer- 

 tained by direct comit of the interference bands. 



ni, n2, two of three principal refractive indices of the mineral measured 

 on the given plate either by the immersion method or other standard 

 method. Error should not exceed 0.001. 



/, the angle of incidence for the interference line selected, is measured 

 by use of the petiographic microscope equipped with Bertrand lens 

 and either a screw-micrometer ocular or a graduated scale in the eye- 

 piece. On sections of minerals of strong birefringence or on thick 

 plates the interference bands are sharp and the errors of reading should 

 be considerably less than 1°. With thin plates and minerals of medium 

 or weak birefringence the accuracy of the readings is less because of 

 the wide interference lines, but in this case the need for greater accuracy 

 decreases so that on nearly all plates the measurements should furnish 

 refractive index values which are adequate for most purposes. 



In certain cases the thickness is difficult to determine; also 

 the order, k, of the interference line may be uncertain, or only 

 one refractive may have been determined. These and other 

 problems can be solved by the measurement of several interfer- 

 ence lines. Thus in case the measurement of the thickness is 

 not feasible, we have on a section normal to a for two interference 

 bands, which can be measured, the equation 



ki _ 7 cos «i — /3 cos r^i 

 k2 7 cos rQ,2 — iS cos r^2 



(8) 



in which cos r„i and cos r^2 are the unknowns, depending on ix 

 and io and a. This equation is most readily solved by assuming 

 a value approximately correct for a; for this value of a, cos r^i 

 is computed by means of equation (5). The value of cos r„2 



