50 Messrs. C. and M. Barus on Interference of 



where y is the index of refraction of the glass, found to be 

 equal to 1*5265 for sodium light, by breaking- off a small 

 corner of the glass of the grating and using Kohlrausch's 

 total reflectometer. 



If the wave fronts be taken in the glass plate ffgg, the 

 equations become 



nk = 2ey cos r, (6) 



nX = 2ey cos U (7) 



n\— 2ey(cosr—GOs6i) .... (8) 



with three other corresponding forms for 6 < r. 



For an air space between yg and M the equations wouM be 



n\ = 2e cos /, 



n\ = 2c cos Q\ 



nX = 2e(cos6'— cos?!); &c. 



4. Differential Equations. 



The quantity measured on the spectrometer is essentially 

 angular and preferably dO'/dn, the angular distance apart of 

 the fringes, in radians. Later we shall measure Be or the 

 linear displacement of the parallel faces per fringe. In any 

 measurement, however, we meet with embarrassment, inas- 

 much as n, X, y, r, 0, 6' ', are all variable. The angle % and 

 the thickness e and the grating space D are alone given. 

 Among these the variation of r with y and X must be found 

 by experiment. Fortunately, in case of the interferometer, 

 all these variables are eliminated and e alone changes subject 

 to a given i and 0'. The y used need not be known. 

 See § 7. 



For the present purpose, as the variation of y enters only 

 as a correction, we haA r e been satisfied with the usual results 

 in physical tables. If from the C to the D line 



(dy/y)/(d\/\)=-'016, 

 and from the B to the C line, = — '013, we may write 



-^=■015^, 

 y X 



and therefore 



We shall abbreviate q = 'Qlb, h = l + a. 



