lOS Barus — Use of the Grating in Interferometry. 

 No. 0. Zero. 



7. 



<( 



9. Aa;=— 2ju,(?/ cos ^=2-2'=' 

 10. =— 2|u,e/cos 6=:2-2'' 



Here /a is the index of refraction and e the thickness of the 

 ghiss plate of tlie grating, and excess of path for the M ray 

 IS reckoned positive. These paths must be compensated by 

 corresponding decrements and increments respectively of the 

 air paths GM and GN. Ordinarily, these path differences in 

 glass being fixed for the given angles 6, would fall away ; but 

 they vary essentially with color, and hence the degree of com- 

 pensation is never the same for all colors. 



Furthermore, although the wave fronts of the two rays are 

 the same on emergence, this does not imply coincidence of 

 phase even in such cases as numbers 1 and 2, for instance: the 

 absolute lengths of paths in glass are quite different, although 

 their differences are the same. Consequently the cases 1 and 

 2 would again interfere if superimposed, one case being first 

 diffracted and the other first refracted.* The path differences 

 are respectively, 



No. 1,2: Aa;=e (—^ ~ (tan r— tan 0) sin 61' ) =^ 2-P™ 



\cos d cos r ^ ' / 



No. 2,1: =:e (— ^+-^4- (tanr— tan {d%mO'\=z 2-3'"" 

 ' \cos r cos $ ^ ^ / 



If the grating is moved As cm. parallel to itself to be equal 

 to these increments A x, at an angle 90° — ^' to the grating, 



2 A 2 = A a; cos 6 



remembering that A a? and As are passed over twice. 



Thus it is not surpi-ising that so many cases were identified. 

 It is also apparent that the air compensations are very different 

 and hence identification is facilitated. Finally, since a vertical 

 slit and collimator are used, the section of a beam of light 

 passing through the grating by a horizontal plane consists of 

 parallel rays ; the section by a vertical plane, however, is 

 convergent. 



It is interesting to find the numerical data for the above 

 equations, assuming that i = 45°, 6' = 32° 39', e = •eS'^™, /a = 

 1"53 (estimated), X/D= '1677, for the sodium line of the 

 spectrum. The results are given with the equations. Their 

 mean value is about 2'3™', which is equivalent to a displace- 

 ment of grating As= '6'^"', the value actually found. 



It follows, moreover, that the center of the ring system 

 order, ?i = 0, must move from red to violet or the reverse, 



* A glasB plate with identical gratings on both sides is here in question. 



