REVERSED AND NON-REVERSED SPECTRA. 75 



The observations for medium and fine fringes were made together, so that 

 a single micrometer reading suffices. Beginning with very small distances 

 apart, called zero, this was rapidly increased to nearly i cm. The fine fringes 

 soon vanished, later the medium fringes vanished, finally (when e is several 

 centimeters) the coarse fringes also vanish. The three together, therefore, 

 cover with accuracy a relatively enormous range of displacement for measure- 

 ments of this kind. 



The curves b and c show that the observations are not completely repro- 

 duced by the line. Mean lines drawn through the observations indicate that 

 the zeros do not correspond sufficiently for the two lines b and c to locate the 

 common zero. This is inevitable, since the micrometer begins to count at a 

 small distance as specified, which is otherwise arbitrary. In fact, it should 

 be noticed, as an accessory property of this interferometry, that the two lines 

 for finding the zero determine the absolute reading of the micrometer, mutu- 

 ally, and these readings are here 0.22 mm. too large. But even if the zeros 

 were horizontally to coincide, the observations would not adequately conform 

 to the computed lines. All that can be affirmed is that the angle between 

 the observed and computed loci is about the same. 



The main reason for the divergence is referable to the fact that the air-space 

 is not quite plane parallel, but slightly wedge-shaped, so that the effect of the 

 angle of the wedge is superposed on the interferences. Any slight unsteadi- 

 ness of the micrometer slide, for instance, would already introduce the wedge 

 discrepancy, without necessarily interfering with the sharpness of visibility , 

 while any attempt to readjust would destroy the continuity of measurement. 

 There will also be many secondary reasons for divergence, as, for instance, the 

 three separate focal planes in which the fringes lie and the fact that the glass 

 plates which limit the air-space are themselves wedge-shaped; other, but 

 fainter, fringes are marching through 

 the spectrum, such cases as coincidence 

 and opposition, for instance, as were 

 pointed out above, etc. But the ade- 

 quate reason for the discrepancies in 

 this paper is the incidental change of 

 the angle of incidence, i. 



If the film is wedge-shaped, very 

 little disturbance results; but the cor- 

 rection to the second order of small 

 quantities is unfortunately somewhat 

 cumbersome. Let the edge of the wedge of air be vertical and subtend a small 

 angle, <p, figure 55, between the two faces A and B. Let I and /' be the two 

 corresponding rays incident at the angle i at the first face and at the angle 

 i-\-<p at the second face, n and n' being the normals. Let e and e' be the con- 

 secutive thicknesses of the air-plate, taken normal to B for convenience. Then 

 the I rays R' will issue at the A face, after reflection, at an angle i-\-z<p, and 

 will interfere with the I' rays R, if the objective of the telescope is sufficiently 



