6 



Mr. A. A. Michelson on the Application of 



It may be noted that under the observations marked R no 

 less than eight successive disk disappearances were noted, the 

 average error being less than 2 per cent. 



Case II. — Uniformly Illuminated Disk. 



If the source be a uniformly illuminated disk of radius r, 

 the expression to be integrated is 



I=4f V7^[l+co S ^-75)]^. . (6) 



Putting a = angular diameter. 

 Then 



/3 



Write 



X a r 



— = w. and 7T— =n. 



r a 



Then omitting the phase constant yb this reduces to the 

 form 



1= j 1±— 1 \/l— ypcosnwdiou . . (7) 



in which the integral is positive for the maxima and negative 

 for the minima. 

 Putting 



i 



\/l— ic 2 cos nw dw = A, we have for V, 



V = A (8) 



Fig. 3. 



Tables for A are given in Airy's " Undulatory Theory," 

 and give the results expressed in the curve shown in fig. 3. 



