126 THE INTERFEROMETRY OF 



angle corresponding to AS is measured by the motion of the fringes over the 

 relatively large angle 5. Hence this is a sensitive method for measuring angles 

 which will be utilized below. 



Finally, the cause of displacement is to be given. If the fringes were homo- 

 geneous in light, they would fill the whole field and simply wander indistin- 

 guishably to or from the center of homogeneous circles when the micrometer 

 is moved. But when white light is used the phenomenon is narrowed to a few 

 fringes systematically grouped about two sharply distinguishable achromatic 

 vertical fringes in the middle. The displacement of these is thus accurately 

 measurable and they may always be brought back to the field of the telescope. 

 Moreover, the distance apart of two black fringes must correspond to the 

 mean wave-length of light i.e., if AN is the displacement of the micrometer 

 mirror corresponding to a fringe-breadth for the angle of incidence i (here 45) t 



2 AN cos i = X 

 or 



A7V = X/2 cos i = 6oX io~ 6 /2 Xo. 707= 43 Xio~ 6 cm. 



agreeing reasonably closely with the above rough estimate of AJV = 5 X icr 5 cm. 

 If we take the equation for the residual fringes in the Jamin apparatus as 



n\ = e(ju cos R cos i) 



where c = e e' is the differential thickness of the compensators and the residual 

 angle a is neglected (fig. 84), 



di X 



dn GU cos .R cos i) (dc/di+t sin R/fj. cos R) 



so that for large fringes the compensators must be so chosen that both c and 

 de/di may be small, where de/di may be either positive or negative. 

 The last equation may be written 



di i 



dn fde/e sin R \ 

 \ di ft cos R/ 



and accounts for the rapid decrease of size of fringes with the differential 

 thickness of the plate compensators. 



65. Vertical displacement. In conclusion, the rise and fall of spectrum 

 fringes (i.e., the transverse motion observed and utilized when a compen- 

 sator of the form figure 77 rotates on a horizontal axis) must be considered. 

 This method was used above for centering / 



b 86 



the spectrum fringes. Naturally the actual ~- - -, 



centers is obliquely upward or - _^ = r : I3~~I _ - . _i' 



downward, unless the increase of glass- 

 path is compensated by the micrometer at the opaque mirror. The rays 

 leaving the collimator are parallel in a horizontal plane only. They are 

 not collimated in a vertical plane. Hence these rays intersect at the 



