342 Mr. A. A. Michelson on the Application of 



whence 



or, since n = -*, 



£±*+l=0, -1, -2, Ac., 



n=|-.+ l + a, 



a being any positive integer. 



The visibility-curve for this case has, therefore, the remark- 

 able property of vanishing at equal intervals, with the exception 



f) 

 of the first, which is V + 1 times as great. 



Thus, if N 7H be the number of waves in the difference in 

 path at the mth disappearance, then 







N»- 



-*!.-£ 



= M; 







t 



For 



example, 

 P = 



■ (rectangle), 



= £ (approx. circle), 



Ni= 



: M, 

 :1-25M, 





p = 



»1(C0B*J), 



N,= 



:l-5 



M, 





p = 



= 2 ("cos 2 



7T- I, 



N 1= 



:2-0 



M. 



Thus the first interval determines the shape of the intensity- 

 curve, while the succeeding ones measure the width. 



_ x l 



VI. <f>(x)=e *"*• 



This is the distribution resulting from Maxwell's law ; the 

 resulting curve is 



Y=e p , 

 which is not periodic. [If oc = \a for ?/ = £, /> = 4 log 2.] 



VII. Double Source. 



The general equation V 2 = — p^ — may be put in a more 

 useful form in the case of two distinct symmetrical sources. 



