CHAPTER II. 



THE INTERFEROMETRY OF SMALL ANGLES, ETC. METHODS BY DIRECT 

 AND REVERSED SUPERPOSED SPECTRA. 



14. Introductory. It occurred to me that a number of the methods treated 

 in my papers on direct and reversed spectrum interferometry might be used 

 directly for the measurement of small angles and possibly of the distance 

 of the source of light. Such a procedure would have an apparent advantage, 

 at least theoretically, of not calling for the preliminary superposition of two 

 images of distant objects, as the superposition is inherent in the method 

 itself. But there are large constants involved, which make the result very 

 problematical unless these constants can be removed by a compensator. In- 

 deed, it is also very questionable whether such interference can at all occur. 

 A further difficulty which hampers the method is the decrease of size of 

 objects as their distance increases. Nevertheless a progressive investigation 

 with the object of ascertaining to what degree the experiment is feasible is 

 worth while, and as it will be convenient to develop the methods without 

 reference to the ulterior conditions which limit the interferences, this method 

 has been pursued. 



15. Method with prism. Figure 13 is a sketch of one of the methods in 

 which 5 is the distant source of light, from which rays d and d' strike the 

 mirrors m and n, and are thence reflected to 



the silvered sides of the right-angled prism P. 

 After leaving it the rays enter the spectroscope 

 at T in parallel. If the proper angles are se- 

 lected the prism P may be replaced by one of 

 any angle or by a reflecting grating. 



Suppose now the system mPn is securely at- 

 tached to a rigid metallic beam or rail capable 

 of rotating around a vertical axis at its center 

 (P). This is indicated in figure 14, where the 

 direction of rays and the normals of mirrors 

 have been drawn and where the angle of rota- 

 tion a has placed mPn into the position m'Pn' . 

 The result is that a part y of the ray d is cut 

 off on the left side and a part x added to the 

 ray d' on the right side, so that the path-difference, which may be assumed 

 to have been zero originally, is now appreciably incremented, but not sym- 

 metrically for both sides. 



It may be shown, however, that the rays n'P 2 T z and m'P\T\ still enter 

 the telescope in parallel and that therefore the conditions of interference have 



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