CHAPTER I. 



THE DISPLACEMENT INTERFEROMETRY OF LONG DISTANCES. 



1. Introduction. Methods for the measurement of small angles and of 

 long distances were broached at the end of the last report. It is the purpose 

 of the present chapter to continue the work experimentally, with a view to 

 further development. It will therefore be desirable to collect the useful 

 equations in this place in relation to the form of apparatus to be adopted, 

 as well as to deduce the consequences of these equations in relation to their 

 bearing on displacement interferometry in general. Throughout the chapter 

 the work is done chiefly with the aid of the achromatic fringe groups, as I 

 have called them; but these, as a rule, can be found only by means of the 

 spectrum fringes, wherefore the latter become of coordinate importance. 



2. Apparatus. This is an interferometer of the Jamin-Mach type (fig. i) 

 with four vertical plate mirrors, M,M r , N,N', in parallel and at 45 to the 

 horizontal beam of impinging white daylight L, from the country beyond. 

 Three of these mirrors are half -silvered, 



viz, M,N,N', while M' is or may be 

 opaque. The equal distances ab = cd = b 

 constitute the base-line (6) of the appa- $ . 



ratus and the rectangle abed will be called / ;/ K ^p ;/ r ^ 



the ray parallelogram. Its area is 2Kb, /, vicl/:/' : dl/' 



where ad = bc = 2R. Each of the mir- 

 rors must be provided with thfe adjust- 

 ment screws for fine motion, so that 

 the mirrors are each slightly revolvable 

 about a vertical and a horizontal axis. 



In case of the mirrors N, M', these screws must be convenient to manipulate 

 (thumb-screws), for adjustment here will frequently be necessary. The 

 opaque mirror M' is on a Fraunhofer micrometer slide with its screw in the 

 direction of the normal n' to M' and adapted to readings of at least icr 4 cm. 



In the figure S, S' may be regarded as slides of a lathe-bed on which the 

 carriages P and Q carrying the mirrors may move longitudinally. Any 

 distance ab = cd is thus available for a base-line. 



The telescope is at T and receives both the light from L after two reflec- 

 tions from the paired mirrors and the direct light from K through the half- 

 silvers. It is desirable that the two beams from K and L be of about equal 

 intensity. 



The pair of mirrors N and N f is on a vertical axis A, so that it may be 

 rotated as a whole. The amount of rotation may be read off either directly on 

 a divided circle corresponding to the axis A or indirectly by the displacement of 

 M' on the screw at n f in relation to the observed sweep of interference fringes. 



7 



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