20 DISPLACEMENT INTERFEROMETRY BY 



a whole, where A0 = 2AA r cos i/e. If Ax corresponds to A0 on an ocular 

 micrometer and if the length of the telescope is L, 



A6 = x/L or A,r=2LAA r cos i/e 



so that Ax may be very large as compared with AN. If, therefore, the 

 distance of one object in the field is given, the distance of others might be 

 advantageously found from Ad or Ax. There is a difficulty, however, since 

 Ad and e vary together; i e., d = bR/eAd. From this it follows that 



d-d' = (dd'/bR) (e'Ad'-eA6) 



and only for such small differences of d and d' as may leave e appreciably 

 constant could d d' be regarded as proportional to A0' A6. 



To get rid of the e it is necessary to introduce the fringe-breadth A<p, 

 which is measurable, while e is not. Since e = \/A<p nearly, the equation 

 becomes 



A0\ 



d d = - 1 --- ) 

 bR VAv/ A<p/ 



But this is virtually counting the number of fringes which pass between 

 d and d'. If there are n fringes the equation may be written 



If d' = o , this becomes d = bR/n\ = bR/(A6/A<p)\, where n is zero if d=&> . 

 There are but few fringes visible, however, and hence such an equation has 

 but the specified limited application for distances close together, if fringes 

 only are to be used. An example of the use of the latter equation follows, 

 A0 and A<p being estimated by an ocular micrometer. As before, if 6 = 36.6 

 cm. ; 2R = 9.4 cm. ; X = 6 X io~ 5 cm., it was found that 



A<p = o.oio cm. A0 = o.6cm. 



Hence 



36.6X4-7 

 d= - 1 = 5X10* cm. 



(o.6i/o.oio)X6XicT 5 



This is too large as compared with rf = 4-3X io 4 cm. above, but no more so 

 than the difficulty of measuring A 8 for a group of fringes A<p and the estimated 

 X imply. These 60 odd fringes as they passed by definite points of the ocular 

 could have been counted here. In conclusion, measurement in terms of 

 A0 require a brightening of fringes and a diminution of the visible number. 

 The number here was about 20 or more and they were visible during a dis- 

 placement of A0=iooA<p, about. They were not quite equidistant, moreover, 

 decreasing about 10 per cent in distance apart toward the ends of the group. 

 A narrow strip of white paper illuminated by sunshine and visible in the 

 field was the best background for their illumination. A few experiments 

 were made on the relation of A0, AN, and Atp = o.oi cm. on the ocular microm- 

 eter. The results were 



