328 Prof. F. L. 0. Wadsworth on the Resolving Power of 



An examination of this result develops the interesting fact 

 that the aperture required to separate the components of a 

 double line is less when the lines have a small finite width than 

 when they are infinitely narrow. For, as may be easily proved, 

 the expression for X becomes a maximum when 



2(1+ y 2) 



g ^ = __^ glX. 



Thus for a line of angular width <r = JX we have 



2 = -91-^=-91«, 



or, what amounts to the same thing, a telescope of given aper- 

 ture has 10 per cent, greater resolving power for lines of 

 width \ol than for lines infinitely narrow. 



To find the width of line for which the resolving power of 

 the instrument is the same as the theoretical resolving power 

 we put 



which gives at once 



syfr=0j or |X, 



or it is just as easy to resolve the components of a double line 

 when these have a width equal to one-half the angular resolu- 

 tion of the telescope as when their width is zero. This in- 

 creased resolving power resulting from increasing the width 

 of the lines from up to J« is due to the same effect as is 

 produced by stopping out the central portion of the telescope 

 objective, i. e., by a strengthening of the centre of the result- 

 ing diffraction-pattern relative to the edges. 



For the spectroscopic resolution we have, as in the first 

 case, 



g(iX) 2 = 2=i(^ + ^X> . . (15) 

 or 



( dX h syJr + ^_ x 



which differs from the expression ordinarily given for the 



purity of a spectrum by the presence of the factor 



as a coefficient of the second term of the denominator. The 



