144 THE INTERFEROMETRY OF 



Here Aa is computed from equation (i), where 2 = 45 and 2R=io cm., 

 about. The fringes of width 100" and 300" were both brilliant and capable 

 of high magnification. 



Thus it appears that the fringes travel faster in proportion to their width, 

 or if A<p increases n times, AJV (for the same telescopic excursion A0) will 

 decrease n times. Again, the fringes travel as a body over hundreds of times 

 the angle described by the auxiliary mirror (A a), when both are observed in 

 the telescope. In the table A0/Aa is 170 to 500 and could be increased 

 indefinitely for larger fringes. The rotation Act seen in the telescope would 

 be but 2Aa. This is the gist of the present method of measuring small angles 

 i.e., the fringe index moves through the telescopic field many hundred times faster 

 than the image of the slit which measures the change of Aa directly. 



Finally, for the same Ad or displacement of the fringe group, AaA<p is a 

 constant, say C, or 



A6 = CA<p Aa = C'A<p - AN 

 where 



9000 9000 



C = - r~ = 340,000 C =~ - = 24,500 

 0.0265 0.370 



It is not necessary to obtain sharper data, because these constants can be 

 found theoretically. It will presently be shown that 



where R is the radius of rotation measuring a. Thus 



Ad AnA<p 2A<pcosi 

 ~~ 



AN X 



If the A<p in the table be used, and X = 6oXio~ 6 cm., 2 = 45, the results are 



A6/AN=ii'S 35-3 (computed) 



Ad /AN = 12 36 (observed) 



results which agree with the values of the table as closely as these subtle 

 measurements permit. 



A few words may be added relative to the size of fringes so far as the glass- 

 paths are concerned, the air-path conditions having been stated. For this 

 purpose the equation of the phenomenon may be written 



n\ = 2e/j, cos R2N cos i 



where N is the coordinate of the mirror at the micrometer. When the center 

 of ellipses (or of achromatic fringes) is at wave-length X, N = N e , the value 

 given for centers above. If n, i, R above vary, while e, n, X, N are fixed, since 



di 





dn 2N sin ize tan R cos i 



