16 DISPLACEMENT INTERFEROMETRY BY 



without ocular micrometer, to remove the slit altogether (fig. 4) and install 

 a glass scale, S, about 2.5 cm. long and divided into 100 parts, in its place. 

 A millimeter scale is usually too coarse. The scale 5 must be so inclined 

 to the horizontal that its image is normal to the fringes in the telescope. 

 No difficulty was found either as to clearness or precision with this adjustment. 

 Measurements were made, from which (A7V is the normal displacement at 

 the mirror M, fig. 4) and Ae the displacement of fringes along the imaged 

 micrometer in the ocular) 



AN 



=0.00101 

 Ac 



was found for the tenth-millimeter fringes considered in the preceding para- 

 graph. Here Ae is therefore nearly 1,000 times larger than AAT. We may 

 thus write 0.00202 Ae cos i = X, so that 



6Xio~ 5 



Ae = = 0.042 cm. 



2X10 3 Xo.;i 



or nearly half a millimeter, corresponds to the wave-length of light in the 

 interferometer measurements. With larger fringes the precision may be 

 enhanced and sharp achromatic lines are available as before. 



If we denote by 5e and Ae the fringe breadth and the displacement of fringes 

 in case of the collimator micrometer (imaged in the ocular) and by 5e and 

 Ae the corresponding quantities in case of the plate ocular micrometer, and 

 if F and / be the principal focal distances of the objectives of the collimator 

 and of the telescope (fig. 4), the relations are obviously 



de &e f 

 6e~Ae ~ F 



so that equations (10) to (14) are equally true when e is replaced by e; but 



FAAT 

 =- 

 / Ae 



Hence AAf/Ae is larger than AN"/Ae in the ratio of F// as actually found; 

 but the data of the collimator micrometer at the slit are at once admissible 

 in computing. 



6. Half=silvered films. The case of regular repetition of the achromatic 

 phenomenon in case of white light, with the ghosts successively fainter, have 

 frequently been mentioned. To possibly interpret this phenomenon a pair of 

 half-silver plates were pressed together on the half-silver sides, so as to in- 

 close a thin film of air between them. This double plate was then put into 

 the beam from the collimater normally, whereupon a succession of ghosts 

 was seen in the telescope, whereas none appeared without the air film. 

 Hence they must be produced by reflection. In one case three repetitions 

 were seen on the left and two (much enlarged) on the right of the main inter- 

 ference fringes, usually at an angle to them and more or less curved. The 



