112 REVERSED AND NON-REVERSED SPECTRA. 



from which B may be obtained without further measurements. If greater 

 approximation is necessary, so that two constants, B and C, enter the disper- 

 sion equation, 



(4) 



so that observations at three spectrum lines, X, X', X", would be necessary. 



The amount of displacement corresponding to the thickness e of glass is, 

 at a given spectrum line X, 



where 2J5/X 2 is constant for all values of e, or 



^ 



It is therefore not possible to obviate the term in B, determined as shown, 

 if /z is to be measured. 



If equal distances are cut off at M and N, the interference pattern, of course, 

 remains stationary in the spectrum. It is interesting to inquire to what degree 

 this may be guaranteed. Equation (3) is available for the purpose, and, since 

 X and X' are nearly the same, X' X = 5X and 



6eB ., 



Let 5X be the width of the sodium lines: 

 5X = 6Xicr 8 cm. X = sgXicr 6 cm. e = 0.68 cm. 



data for the above grating and sodium light. Hence 



6Xo.68X4-6Xio- H X6Xio- s 



(59)'Xio- - .SXio-o cm. 



i.e., about a half of lo" 4 cm. This would be equivalent to the space on a grating 

 with about 20,000 lines to the centimeter, or 50,000 to the inch. The ellipses 

 can not be set as closely as this, but the order of sensitiveness is within that 

 of a good micrometer. 



It is interesting to inquire whether the sensitiveness will change markedly 

 for larger angles of incidence /. If n is the index of refraction, the largest 

 angle R obtainable at grazing incidence, 1 = 90, would be sin RI/H. It 

 may then be shown that 



d\ X 3 

 Putting (JL= 1.5 and the other data as above, where d\ = 6X io~ s cm., 



_ i.34X46X.o- 9 . aX . y "/(59)'X.o-"+4.S _ x IO , cm . 

 (59) 3 Xio- 18 1. 12 



The datum is of the same order as above, so that the sensitiveness changes 

 but very little for different angles of incidence. Thus there is no disadvan- 

 tage in using I = o. 



