Telescopes and Spectroscopes for Lines of Finite Width. 341 



For r= 200000, A\=l'00^ = 20-75,and the maximum value 



of P is therefore attained when the value of syjr is about 

 4*15 X or about '0023, corresponding for the usual spectro- 

 scope (^r=jy to a slit-width of about g 1 ^ mm, Under the 

 same circumstances the practical purity is still as great 

 when the slit-width is -^ mm. as when it is zero. For still 

 higher resolving powers the maximum allowable widths of 



T 



slit are still greater. Even with such low values of ^ as 



2 or 3 (corresponding to lines as fine as those sometimes 

 found in the solar chromosphere, i. e., 0'2 to 0'25 tenth- 

 metre), and resolving powers of only 100000, the purity 

 remains undiminished up to values of syfr = \ to 1|A, (-0005 

 to *0008), or to slit-widths (with the concave grating) of 

 from ^ mm. to o- 1 ^ mm. 



One further case remains to be considered, viz. that of a 

 wide slit and non-monochromatic radiations in which the 

 slit-image is not uniformly brought across the whole width. 

 The expression for the intensity in the diffraction-pattern 

 then becomes 



I«,-f + 'V(f)M?-7, ",*)<& • ■ (35) 



J -a/2 



where /(£) expresses the intensity at any part of the slit at a 

 distance \ from its centre. The only case of importance of 

 this kind is the case of stars. If the star-image is perfect, 

 L e. unaffected by atmospheric or instrumental aberration, 

 the distribution in intensity for anyone wave-length is repre- 

 sented by the law 



sm * * 



a being the resolving power of the telescope-lens which 

 forms an image of the star. 



As before, the integration could only be effected by me- 

 chanical quadrature or by development into a series {^ not 

 being known in finite terms). It has not been thought 

 worth while to go through the necessary labour of integration 

 for the reason that, practically, such conditions are never 

 realized, at least in stellar spectrographic work. There 

 might be moments at which, if the star were kept perfectly 

 centred on the slit, the full resolving power resulting from 



