with the Aid of a Grating. 427 



which dd/dn (where 6 is the angle of diffraction corresponding 

 to the angle of incidence I, and n the order of interference} 

 is prominent. 



If e and y are constant, n } X, /j,, and R variable, the 

 differential coefficients may be reduced successively by the 

 following fundamental equations, D being the grating space, 

 fju and r corresponding to wave-length X and angle of dif- 

 fraction 6 : — 



<ffi=— tanR. dji/fi, .... (13) 



dk=—T> cos 0.d0, .... (14) 



d/jb//j,= —adX/X, (15) 



where (as a first approximation) a= "015 is an experimental 

 correction, interpolated for the given glass. Incorporating 

 these equations it is found that 



dd = X 2 cosR 



dn '2 D cos 6 e^—y cos 11 + ae^x (1 — tan 2 R) " 



If the path difference nX is annulled, 



d8 X 2 cos R 



dn XDcos ae\x{\. — tan 2 R) ; 



(17) 



which is the deviation per fringe, supposedly referred to the 

 centre of ellipses. 



These equations indicate the nature of the dependence of 

 the horizontal axes of ellipses on 1/D (hence also on the 

 order of the spectrum), l/e, 1/yu-, and 1/a, where the meaning 

 of a, here an important variable, is given in equation (15). 

 If instead of the path difference y the displacement N of 

 either opaque mirror is primarily considered (necessarily the 

 case in practice), the factor (1— tan 2 R) vanishes. 



Table III. contains a survey of data for equations (16) and 

 (17). The results for dOJdn would be plausible, as to order 

 of values. The data for d0/dn y however, are again neces- 

 sarily in error, as already instanced above, paragraph 8. 

 They do not show the maximum at E, and the A,-effect is 

 overwhelmingly large. 



Since equation (17) is clearly inapplicable, giving neither 

 maxima nor counting the fringes, it follows that in this 

 equation y>e/u,/cosH ; i.e., the centres of ellipses are not 

 in correspondence with the path difference zero. In other 

 words, the air-path difference is larger than the glass-path 

 difference in such a way that dO/dn is equal to co for centres 

 (here at the E line), but falls off rapidly toward both sides 

 of the spectrum. 



2 F 2 



