76 THE INTERFEROMETRY OF 



large to converge both to the same point of the image, spectroscopically 

 resolved. If the wave-front ab is drawn and e' prolonged, it follows at once 

 that 



sin i+< sin 



cos 

 Hence 



/ , sin (i-\-(p) sin <p\ 



n\=2e[cos(i+<p)-} A 



V cos i I 



If i = o and $ very small, this becomes 



<A 

 / 





If in the first equation i is replaced by the angle of diffraction 6, the equation 

 for the diffracted fringes, as far as ^ 2 , may be reduced to 



= 2e\cos 6+<p sin ( - - 7 cos 0} 

 L 2 Vcos 6 / J 



so that <p sin 6 is the chief correction. 



Finally, the equation for the coarse fringes becomes 



f <>V 4 M 



n\ = 2e\ i cos 6 <p sin 0+ I 3+ n 7 cos 6} 

 I 2 \ cos v / J 



with a similar equation for the medium fringes. 



If we neglect the second order of small quantities (<p 2 ), the last equation 

 for the medium fringes may be put in another form, since 



2L 



2\/D = sin 6 and \/L = i cos 6 sin 6 = =L(I cos 6) 



u 



whence 



nL (n+n')L r 



i-2<pL/D i-2<pL'/D 



D being the grating space and X the wave-length. Hence if n be eliminated, 



LL' , LL' 



2 C fl f ft / / T-\ \/TT/ TT/\ '*" 



L-L'-(2<p/D}(LL'-LL 1 ) L-L' 



In other words, if <p is small so that <p- may be neglected, the relation of e and 

 n' is independent of <p ; or a slightly wedge-shaped air-film will show the same 

 result as a plane-parallel film. Experiments made by turning the adjust- 

 ment screws seem to bear this out, provided the mean thickness remains 

 unchanged. 



To give the whole subject further study, I have since half-silvered the 

 grating as specified, so that all the fringes may be seen by transmitted light, 

 preferably in the second order, since there is an abundance of light available. 

 The apparatus in such a case takes a good shape and is convenient for manip- 

 ulation. But these details will have to be given at some other time, and it 

 is the chief purpose of this paper to exhibit the phenomenon as a whole. 



