THE AID OF THE ACHROMATIC FRINGES. 27 



For the case, however, in which the body whose small angles of rotation are 

 to be measured is part of another apparatus which does not admit of manipu- 

 lation, the method may be modified as in figure n. Here all the plate 

 mirrors M,M',N,N' are half-silvers and the rays from the collimator L form 

 the interfering pencils LemeagdT and Lbfm'fct. The mirror m and m' 

 meet their rays normally and m' is in the micrometer screw at n' parallel 

 to /. The mirror m", on the axis A normal to the paper, rotates, and its 

 small angles of displacement are to be measured. Considerable light is lost 

 in the three penetrations of half-silver films by each ray; but in case of the 

 achromatic fringes the light is usually in excess, so that the diminution 

 of light is an advantage. It is more difficult, however, to find the spectrum 

 fringes, as these require a slit. 



The plan of figure n is carried out more simply in figure 12, where both 

 reflections take place at the same mirrors M and M', respectively, the compo- 

 nent rays being Lbm"bach T and Ldem"efgi T. It is necessary to incline the 

 parallel mirrors m' and m" on a vertical axis, in order to avoid the entrance 

 ray L' into the telescope at T. But this separates the component rays h and i 

 locally, so that means must be employed (compensators, rotation of the other 

 mirrors m", N, or M') to obviate this as far as necessary. In both cases of 

 figures ii and 12 it is therefore not easy to find the fringes, and I did not 

 persevere in the quest because of an eye affliction contracted at the time. 



Similarly the system M, M',m" of figure 12 might be used if a half -silver 

 is placed at r and the telescope at T' to the right of it. In this case the mirror 

 m" must be in two parts, with adequate air-space inserted into the shorter 

 ray Lb. 



13. Types of achromatic fringes. The difficulty of obtaining fringes of 

 the strictly achromatic type (i. e., two strong fringes with a black line be- 

 tween and the remaining fringes green-reddish and faint) in the rectangular 

 or other interferometer, has been frequently referred to in the text above. 

 As a rule the fringes found are more or less diffuse, non-symmetric, with 

 large numbers (10 or more) about equally strong. Such fringes are, of course, 

 useless in displacement interferometry. When the sharp fringes needed are 

 obtained, their definition is independent of the particular part of any of the 

 glass plates used, and any plate may be rotated 180 in its own plane without 

 spoiling the sharpness of the fringes. Hence such slight curvatures or wedge- 

 shapes as the plates may possess are without influence on the phenomenon. 

 To further test this I devised a screw-press adapted to push the vertical 

 edges of a plate to the rear and the middle forward, so as to give the plate 

 marked cylindricity. Quarter and eighth inch plates were operated on, in 

 the latter case sufficiently to give the two superposed slit-images quite 

 unequal width; but no essential or useful improvement of the fringes was 

 observed. The type of the fringe was not altered. Again, the symmetrical 

 fringes may be obtained from plates thickly or thinly silvered, without essen- 

 tial difference. 



