14 DISPLACEMENT INTERFEROMETRY BY 



as it should be; i. e., the relation of Ae and AN is practically linear, if the 

 displacement AN is not excessive or goes beyond the field width. 



As the determination of AJV is inconvenient, we thus come back to the 

 practical equation (3) already used, or 



cos* 



or if Ld<p = be and Ae and 8e are the displacement and the fringe breadth 

 measured on the same ocular micrometer, 



Ae 2de cos i 



With this deduction, equations (5), (6), (7) now take on the new form in 

 terms of the fringe breadth de and the fringe displacement Ae, which it 

 is well to record here; 



X 



(12) 



bRde i 



(13) d = ~^~T~ 



X Ae 



2 



(14) S 



oKoe 



If into the last equation we insert such values as are easily obtained and 

 will be used in the sequel, viz, d = kilometer = io 5 cm. ; b = 200 cm. ; R = 10 cm. ; 

 50 = 0.015 cm.; 8(Ae) =0.001 cm. (i/io scale part of ocular micrometer) ; then 



io 10 X6Xio- 5 Xio- 3 

 od = - ~ =20 cm. 



2ooXioXi5Xio~ 3 



that is, an object should be located at a distance of a kilometer to 20 cm. 

 If there is sufficient light, however, fringes may be easily made larger than 

 0.015 cm - m breadth, certainly 3 to 5 times, in which case 8d would be cor- 

 respondingly smaller. With ordinary daylight, however, io 3 8e=io to 20 

 cm. should not be exceeded. 



Results similar to the preceding may be obtained if the glass paths of 

 the interferometer are alone considered. 



If /JL is the index of refraction and e is the effective thickness of the plates, 

 i. e., the difference of effective thickness of M and N and of compensators 

 (fig. i) through which the beams pass, we may write as in the colors of thin 

 plates (since the beam passes the plate but once) 



(8) ri\ = en cos r zN cos * 



if r is the angle of refraction corresponding to the angle of incidence i. If 

 n, i, r alone vary, while e, X, N are fixed (i. e., if the eye travels through the 

 field of the telescope from left to right), A<p = di/dn, and since sin i = n sin r r 



di X 



i \ 

 (9) 



dn 2N sin i e tan r cos i 



