38 DISPLACEMENT INTERFEROMETRY BY 



the ellipses are small and the spectrum is filled with innumerable lines. More- 

 over, in view of the prism separation (at p, fig. 19) the ellipses are throughout 

 half -ellipses, all terminating in the vertical axis. For the two areas or strips 

 of light (ab, fig. 20) seen on the face of the grating and entering the spectro- 

 telescope are each single, being one-half of the full area of light rays capable 

 of interference obtained at the collimator. This results in the half -ellipses e. 

 If the prism is replaced by a half-silver plate as in the next paragraph, 

 the strips ab 1 and a'b are both double, the full areas being superposed; 

 thus the areas ab and a'b' give rise to the full ellipses ee' . Hence, also, the 

 vertical axis in e, being at the edge of the prism P, is not quite clear. Hori- 

 zontal lines do not occur. These half-ellipses move with displacement of 

 the micrometer at n', or at P, or on rotation of the rail mPn, as a body. It 

 is difficult, however, to use them for measurement, as their vertical terminus 

 is not sharp enough. If AA/" is the micrometer displacement corresponding 

 to the rotation Act, we may write 



aAAT/Aa = o 



I did not succeed, however, in obtaining trustworthy results with the half- 

 ellipses. 



The achromatic phenomenon can not occur when glass columns are used 

 for compensation from the great number of lines in the spectrum. To obtain 

 large ellipses the dispersion effect B/\ 2 must practically vanish. Hence an 

 air-path compensator is to replace the glass column. This is conveniently 

 made (as shown in fig. 21) of two pairs of parallel opaque mirrors ab and cd. 

 The pair ab are clamped between short lengths of square brass tubing and 

 cd similarly and at right angles (nearly) to the pair ab. Both are mounted 

 normally to a horizontal brass table t, provided with three leveling-screws, 

 capable of being raised and lowered and of rotating around a vertical axis. 

 The path-excess introduced is thus equivalent to ab and cd and the ray dm 

 is collinear with ra. This compensator not only introduces path-differ- 

 ence, but since the mirrors are capable of rotating as a whole both around 

 a vertical and a horizontal axis (leveling-screws), the beam dm may be 

 moved right and left or up and down without ceasing to be parallel to ra. 

 If, therefore, the ray entering T (fig. 19), were first made parallel, the ray 

 d may be adjusted by the compensator until the strips of light on P practi- 

 cally coincide at its edge. 



With the use of this air compensator or offset, the fringes were found with- 

 out much difficulty and enlarged as specified. In view of the reflection at 

 P, only half fields are returned; full ellipses or horizontal lines are not ob- 

 tainable, as explained. But on removing the spectroscope and cautiously 

 advancing the micrometer at N, the achromatic fringes eventually appear. 

 In the present experiments these fringes did not take the usual and desirable 

 form, consisting of but few fringes with the middle member in black and white. 

 Probably because of the many reflections at mirrors (fig. 21), none of which 

 was perfect, the fringes were now colored and present in large number 



