Indices of Doubly -refracting Crystals. 831 



of incidence % in the position given by BB, and the centre of 

 ellipses is then returned to the same fiducial line D o£ the 

 spectrum, by moving the opaque mirror on the micrometer 

 over a distance AN, nothing has been changed at the grating, 

 and the first term of the right-hand member of equation (1) 

 remains unchanged. It therefore vanishes so far as AN is 

 concerned. Hence we may write 



as fig. 2 shows. For not only has the path e been increased, 

 by the introduction of the oblique plate, but the air-path is 

 also longer. On removing ey a 



/AN cosy >. \ 2b /0 . 



^ =/ H — e~ " + cos ( l ~ r V~ \2 • • • ( 3 ) 



In this equation the quantities /i, r, refer to the same fiducial 

 spectrum line of wave-length \, to which the centre of 

 ellipses is always to be restored by moving the micrometer. 

 Whenever the incidence at the plate is normal, z = r=0, 



"=M— +1 )-v> w 



an equation more generally useful and particularly so in 

 case of long columns. 



If the dispersion of air cannot be disregarded, fi a must be 

 replaced by p a (l + 2b" \\ 2 }ia) > p a and b" referring to a plenum 

 of air. Equation (3) is then modified by replacing the last 

 term by 



-2(b-b")l\ 2 (5) 



Since fjL cos r = y/ y? — sin 2 i, equation (3) is essentially of 

 the fourth degree and can be solved only by approximation. 

 This, however, is rapid; for ft— 1, nearly, is computed in 

 terms of //,, which is always relatively more accurate than 

 fjL — 1. In Table I. the values of the micrometer displace- 

 ments AN are given under varying conditions of illumi- 

 nation, but all under normal incidence, i = r = 0. It is 

 probable that the differences of value of AN found are 

 owing simply to the distortion of the ellipses in the different 

 cases. 



3 12 



