428 C. Barns — Interference of Reversed Spectra. 



This explanation shows why the original phenomenon, con- 

 sisting of single lines, cannot be manifolded by increasing the 

 width of slit. It vanishes for a wide slit into a flickering 

 shadow. The phenomenon is a strip cut across an enormous 

 black or bright horizontal fringe, by the occurrence of a nar- 

 row slit. Moreover the scintillations variously interpreted 

 above are now seen to be due to tremors, however different 

 from such an effect they at first appear ; i. e., the enormously 

 broad horizontal fringe changes from dark to bright, as a 

 whole, by any half wave length displacement of any part of the 

 apparatus. 



To be quite sure that the concave grating G' had no funda- 

 mental bearing on the phenomenon, I again replaced it by the 

 Michelson plane reflecting grating with similar results. 



8. .Equations. — An attempt must now be made to describe 

 the phenomena, or at least the interferometer part of them, by 

 equations. This may be done for the method of two gratings 

 at once, as the result, if the distance apart of the gratings is 

 (7=0, includes the method with one grating; i.e., the more 

 complicated figure 10, where G is the transmitting and G' the 

 reflecting grating, resolves itself into a case of figure 11 with 

 but one grating, G. 31 and M' are the two opaque mirrors, 

 1 the normally incident homogeneous ray. Supposing, for 

 simplicity, that the grating planes, G and G' , are parallel and 

 symmetrically placed relatively to the mirrors 3f and 31' , as in 

 the figure, the ray Y diffracted at the angle #, is reflected into 

 .Z"at an angle 8 — # 2 — #, and diffracted into Z normally, at an 

 angle 0„, on both sides. Under the condition of symmetry 

 assumed 



X + Y-{X' + Y')=0 



or without path difference. Let N be the normal from I to 

 31, and n the normal from 1' to 31, with a similar notation on 

 the other side. Hence if 1 be given an inclination, di, 8 } is 

 incremented by dd t , Y +X passes into y y + y + x, Y' + X' 

 into y' + x' + x', decremented at an angle d0/, while both are 

 diffracted into Z ' . Since generally 



sin l — sin i = Xj D 

 cos 6 l d6 l = cos 0/ tf0/ 



for homogeneous light and the same di. Hence dO x = dd x '=d6. 

 If 



s = e s - $„ a- = e 2 + e, 



the auxiliary equations 



X+ Y= c sin6 i + sing « 



sin 8 



and 



