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



The dotted curve represents 



V = 2- X2/192 cos -7/30*. 



It follows that the visibility-curve is practically the same 

 as that due to a double source, whose components have the 

 intensity ratio 7 : 10, and in each of which the light is distri- 

 buted according to the exponential law, expressed by the first 

 term. 



The formula for a double source, where the components are 

 similar, is 



Y 2 — V 2 



l + ^ + 2r 



in which D, the period of the curve, is inversely proportional 

 to the distance between the components. 

 But D = NX 1 = (N-fl)X 2 , whence 



a — A x — A 2 — jy 



Hence, in the present instance we have for the distance 

 between the components of the red hydrogen-line 



1/30 x (6-56 x 10- 4 ) 2 = l-4 x 10" 8 millim. 



or 0'14 division of Rowland's scale. 



Again, if 8 be the " half-width " of the spectral line (the 

 value of x when <$>{x) = ^) , then 



<£(#) = 2 52 9 and Y=e v . 



12 1 

 If A be the value of X for V = -L then 8= — — , or, with 



•22 7T A' ' 



sufficient accuracy, B— —-. 



Substituting the value of B in the equation for V, we have 



V = 2 a» . The value of A in the hydrogen curve is 19. 

 Accordingly, after reducing to the same units as above, we have 

 8=0*049. 



* As frequent use is to be made of the function 



1+r 2 +2rcog2 X 



l4-r 2 -f2r 



it will "be abbreviated to the form cos r/D. 



