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PHYSICS: C. BARUS 615 
of the same order but different wave lengths, X and X', respectively, 
that for the given position of G and G', only the rays a a' issue coinci- 
dently at T. The rays cd, c'd! issue at ^i, e'l and though brought to 
the identical focus by the telescope, the distance ex e\ may be too large 
to admit of appreciable interference. Hence the colored strip within 
which interferences occur will comprise those wave lengths which lie 
very near X, whereas the colors lying near X', etc., will be free from 
interference. 
If the mirror M is displaced parallel to itself to by the microm- 
eter screw, the rays c'' and c' d' will now coincide at e'l, whereas 
the rays from a h and a'h' will no longer issue coincidently and may not 
interfere. Thus the interferences are transferred as a group from rays 
lying near X to rays lying near X'. It is obvious therefore that with 
the displacement of M, the strip carrying interferences will shift through 
the spectrum and that a relatively enormous play of the micrometer 
slide at M will be available without the loss of interferences. In fact 
a displacement, e, of over 3 cm. of M normal to itself, produced no 
appreciable change in the size or form of fringes, but they passed from 
the green region into the red. The fringes as seen with a fine sht were 
straight parallel strong Hues. They did not thin out to hair lines at 
their ends, nor show curvature, as one would be inclined to anticipate. 
On the contrary, they terminated rather abruptly at the edges of a 
strip occupying about one-fourth of the visible length of the spectrum. 
It follows, from figure 1, that the displacement of M does not change 
the lengths of rays; for they are enclosed between parallel planes, as 
it were. Since the double angle of reflection is here 5 = 180° — 20, 
where B is the angle of diffraction of G and G' , the displacements of M 
over a normal distance e will shorten the path at M in accordance with 
the equation 
n \ = 2e cos 5/2 = 2e sin 6 (1) 
where n is the number of fringes passing at wave length X. 
This equation^ is not obvious, as for constant X, the distance between 
G and G' measured along a given ray, for any position of M or iV, is 
also constant. The equation may be corroborated by drawing the 
diffracted wave front i for instance, which cuts off a length 2e sin d 
from d". 
Since sin 8 = X/Z) if Z) is the grating space, the last equation becomes 
n = 2e/D 
or per fringe 
8e = D/2, 
