Telescopes and Spectroscopes for Lines of Finite Width. 339 



closely indeed to it by replacing the function yfr n by the 

 function 



sni 2 -- 7 



........ (30) 



DM 



which between the points y = JH and y=fll, or over all 

 that part of the curve which is important in determining the 

 resolution of a double line, coincides, as seen in fig. 5 (dashed 

 curve), almost exactly with the curve t^i(/c, 7, a). 

 The expression for I /y then becomes 



f-^W^(f-7) 

 I„=^ -Ji df, .... (31) 



which is exactly similar in form to (9), the only difference 

 being that a has been replaced by XI. 



We may therefore obtain at once the limit of resolution 

 for this case from (12) and (14) by replacing a by H, 

 giving us 



n 2 



% x — limiting angular resolution = cr -f - — — -^. . (32) 



Replacing a and XI by their values in terms of s,ty, R, r, and 

 X and reducing, we finally obtain for 2^ 



^4l> + -^7]' (33) 



and for purity 



p = ^ =_ ^— r . . . . (34) 



2sf + X^ 



This expression differs from (16) only in the presence of 



f 



the factor B asa coefficient of X in the denominator. When 



this ratio is unity P=p, or the practical purity is equal to 

 the theoretical purity for monochromatic radiations. 



By an inspection of Table IV. it will be seen that while 



