118 THE INTERFEROMETRY OF 



the interferences in the principal focal plane of the telescope are only just seen. 

 At D = 5 cm., however, the results are acceptable. When the concave lens is 

 nearest to the mirror and the convex lens toward the grating, the modified slit 

 image is smaller than the other. Adjustment is then easier and the usual 

 elliptic and hyperbolic forms may be observed without trouble. In both cases 

 the flickering of the arc lamp used passes the rays through different parts of 

 the lenses relatively to the center, and the adjustment is thus easily destroyed. 

 If the spectra from M and N, however, are observed, not in the principal 

 focal plane but in advance of it (toward the eye), interferences of great interest 

 will be observed, to be discussed in 69. 



67. Remarks. A few explanatory observations may here be inserted. The 

 occurrence of the elliptic or oval and the hyperbolic type of fringes may be 

 most easily exhibited by laying off the order of the fringe in terms of the dis- 

 tance (in arbitrary units) above and below the center of the image of the slit. 

 If we call the latter y and consider the allied colors of thin plates, for instance, 



n = 2en cos r/X or more generally n = (0ju A)/ (y, 



(where e is the thickness of the plate, /* its index of refraction, X the wave- 

 length of light in case of a dark locus of the order n) is to be expressed in terms 

 of y, which itself determines e cos r, r being the angle of refraction in the plate 

 of the grating. The phenomenon will thus be coarser for red light than for 

 violet light, since n decreases when X increases, and any two curves, r and v, 

 figure 84, may be assumed as the loci of the equation in question. If, now, 

 horizontal lines be drawn for n=i, 2, 3, etc., they will determine the number 

 of dark bands in the spectrum for any value of y. 



If the central ray is also a line of symmetry and intersects the grating nor- 

 mally, it must correspond to a maximum or a minimum of n. These conditions 

 are shown in the diagram at M, where the maximum number of bands occurs, 

 and at m, where the reverse is true. The question is thus referred to two sets 

 of loci, rr' and w', or r'r" and v'v", etc. In the former case e cos r varies with y 

 in the same sense as n/\ ; in the latter in the opposite sense and is preponder- 

 ating in amount. Both may vary at the same rates in the transitional case, in 

 which, therefore, the two curves r and v are at the same distance apart for all 

 values of y. 



Suppose, furthermore, that the same phenomenon is exhibited in terms of 

 wave-length X, as in the lower part of the diagram, the spectrum being now 

 equally wide for all values of y, while at any given y the upper diagram still 

 shows the number of dark points (bands) between r and v. If now, we suppose 

 that under any conditions these dark points are grouped symmetrically with 

 reference to any given color (which is probable, for a maximum or a minimum 

 of any value of y will be so for all values), and that the successive dark points 

 have been connected by a curve, the interference pattern will be of the elliptic 

 type in case of aa', a" a'", and of the hyperbolic in the case of a' a". 



The other features of the phenomenon are secondary and therefore left out 



