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



The measurement of the angular magnitude of sources of 

 light too small to be resolved by the telescope may also be 

 effected with a considerable degree of accuracy by providing 

 the telescope objective with a slit or diaphragm which can be 

 varied in width or size, and measuring the distance between 

 the centres of the diffraction-fringes by means of a micro- 

 meter eyepiece. In case the slit is used (as found most 

 convenient in practice), the expression for the intensity of 

 illumination at a distance y from the centre of the central 

 bright band will be 



=j>(*) 



IT 



a 



(7-*) 



e (-*)]■ 



# 5 



(18) 



where/ (0) =y is the ordinate of source of light (of uniform 

 intensity) at the distance <£ from the axis. If the source 



has a width «, the limits of the integral are -x and — -. 



1st. In case the source is a uniformly illuminated slit, 

 /((£) = const., and the expression for I becomes 





E <*-♦>! 



re 



or, substituting — (7 — <j>) = #, 

 a 



pr/«o(y + «/ 2 ) gi n 2 t( 

 «/ w/My-a/a) 



C&P. 



(19) 



This integral cannot be found directly, but we may obtain 

 the values of 7 for which I is a maximum or a minimum by 

 differentiating (19) with respect to y. 

 This gives 



— - =(Jonst. 

 ay 



sin' 



=(' + i) 



Sill' 



a 



( 7+ Di 



sin 



Hence 



-E( 7+ !)] E(^9] 



7T / a\ . 7T/ a\ 



00(^2) . Sm aX y ~2) 



= 0. 



= + 



7T/ a\ — 7T/ a\ 



«„( 7 + V «o( 7 -2J 



(20) 



