42 THE INTERFEROMETRY OF 



It was here, with the ocular thrown much to the right (near M), that I 

 again encountered the arrow-shaped fringes of figure 2, D, Chapter I. Though 

 they are rarely quiet, the observation can not be an illusion. As seen with 

 white light and a fine slit they are merely an indication of fringes which, when 

 viewed with a broad slit and homogeneous light, will be horizontal. 



Rotation around a horizontal axis parallel to the face of the grating must 

 also destroy the parallelism of the rulings. The usual effect was to change the 

 size of fringes (distance apart, etc.) ; but I was not able to get any consistent 

 results on rotating G', owing to subsidiary difficulties. On rotating the grating 

 G, however, a case in which fine rotation around a horizontal axis was more 

 fully guaranteed, the fringes passed with continuous rotation through a 

 vertical maximum, as in figure 22. 



In figure 26, the central region a of the grating G' is found, on inspection, 

 to be yellow in the position G', red in the position G'\, and green in the posi- 

 tion G' z . The slit in this case must be very fine. For a wide slit and homo- 

 geneous light, the continuous change in the obliquity of pencils is equivalent 

 to the continuous change of wave-length in the former case. It is therefore 

 interesting to make an estimate of the results to be expected, if the vertical 

 fringes for the cases bb r or cc' were Fresnellian interferences, superposed on 

 whatever phase-difference arrives at these points. In the usual notation, if 

 c is the effective width at the concave grating, F its principal focal distance, 

 x the deviation per fringe, dd the corresponding angle of deviation, X the 



wave-length of light, 



x = \F/c ord9 = \/c 



If c=i.6 cm., X = 6Xicr 5 cm., then d0 = 3.7Xio- 5 , or about 7" of arc. 



The corresponding deviation ddD equivalent to d\D of the DiD 2 lines would 

 be (if the grating space is .D=i 73X10-" cm., 6 = 20, nearly, the normal 

 deviations for yellow light), 



. d\ D 6XICT 8 _ _ _4 



^ == --- 3 - 7> 



Thus -77:- = 0.1, or, in this special case, there would be ten hair lines to the 

 duo 



DiD 2 space. As c is smaller or larger, there would be more or less lines. 

 This is about the actual state of the case as observed. Finally, if c is very 

 small, the fringes are large, since 



dd _\D cos 6 

 dB D cd\o 



Thus conditions for practical interferometry would actually appear, the 

 fringes being of DiP 2 width for c = 0.17 cm., provided a wide slit and homo- 

 geneous light of at least D\ or D 2 grade is used. Such an interferometer 

 seems to differ from other forms, inasmuch as the fringes remain of the same 

 size and distribution, from their entrance into the field to their exit ; or for a 

 motion of the opaque mirror M of about 6 mm. 



