C. Bancs — Use of Compensators. 303 



parallel to themselves, had no definite effect. Moving them 

 fore and aft together {D constant), produced results similar to 

 the above. The vertical lines of fig. 1 are liable to be sinuous, 

 or to resemble the grain of wood around a knot. 



If corresponding to fig. 1, the convex lens is kept fixed near 

 the grating and the concave lens gradually moved up to it, the 

 order of forms is reversed but not qrrite completely. They 

 usually terminate in long vertical ellipses, before reaching 

 which the wood-grained forms are sometimes passed. The 

 same is similarly true for the case of fig. 2. 



With cylindrical lenses (respectively convex and concave, 

 each one meter in focal distance), very little effect was observed 

 when the axes of the cylinders were parallel to the slit. With 

 the axes perpendicular to the slit the effects of spherical lenses 

 were virtually reproduced, except that the central fields par- 

 took of a more rectangular character. 



A variety of experiments were also made with strong lenses, 

 with similar results, the interferences being seen most clearly 

 in the principal focal plane of the telescope. 



5. 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 distance (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 = 2efi cos r/X or more generally 

 n = (ev>/X)f(y,r), (where e is the thickness of the plate, fi 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, r being 

 the angle of refraction at the plate of the grating. The pheno- 

 menon will thus be coarser for red light than for violet light 

 since /i decreases when X increases and for the present purposes 

 any two curves r and v, fig. 3, may be assumed as the loci of 

 the equation in question. If now horizontal lines be drawn for 

 n = 1, 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 normally, it must correspond to a maximum or a 

 minimum in n. These conditions are shown in the diagram 

 at M, where the maximum number of points or bands occurs, 

 and at m, where the reverse is true. The question is thus 

 referred to two sets of loci rr' and vv', or r'r" and v'v", etc. 

 In the former case e cos r varies with y in the same sense as 

 /i/X ; in the latter in the opposite sense and is preponderating 

 in amount. Both may vary at the same rates in the transi- 

 tional case, in which therefore the two curves r and v are at 

 the same distance apart for all values of y. 



Am. Jour. Sci. — Fourth Series, Vol. XL, No. 237. — September, 1915. 

 20 



