REVERSED AND NON-REVERSED SPECTRA. 147 



In the case where rings are counted, however, the center of ellipses leaves 

 the D line by a short distance, less than one-tenth of the interval between the 

 C and D lines. In such a case, if v & = A ti -\-b a ,/\ 2 for air and M 8 =<4g+&gA 2 

 for glass, the micrometer displacement to bring the ellipses back again from 

 X' to X should be 



and e g being the lengths of air and glass* in the beam. Here 



6 a = icr 14 Xi.65 ejo.. = icr 14 X33-5 

 e e = 2 cm. &g = io~ 12 X 48 e e b e = io- 



so that the effect of air, where 6 a is variable with pressure, is but 0.3 per cent 

 of the glass effect and may in the first approximation be neglected. The 

 equation may therefore be written : 



X 2 X 3 



If the mean data from series I be inserted (dN = 960 Xio" 6 when X refers to 

 the D line) 



_a = 9AoXio^X^Xo. 3 473 = IO _ 2Xa ^ 



For the case of the C and D lines 6XA = 3. 3 5/58. 9 = 0.05 7, roughly, about ten 

 times the preceding distance. 



In fact, the observations made for the estimate given in the preceding para- 

 graph (semi-displacement) , 



_AX , . = 2Xng i 

 X 2 58.9 



compared with the present 



$X_io- 8 Xo.34733JV_ 

 ~T = 576X10-" 



are quantities of the same order, though one would have expected closer 

 coincidence. 



The discrepancy observed between the method of measurement in terms 

 of the displacement (AN to bring the ellipses back to the fiducial position) 

 and the method of counting rings can not, therefore, be explained as the 

 result of a change of wave-length X in the latter case; i.e., the equation 



AA r =(w w)X/2 



where n n is the number of vanishing rings of the mean wave-length X, is 

 at fault for some other reason. Curiously enough, the ring method is essen- 

 tially simple, as it reduces to 7 = , / / \, if o and n are the number of rings 



* Thickness of glass plates of air-chamber, 1.3 cm.; of the plate of the grating, 0.7 cm. 



