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



of a slit this resolving power is in general less than the 

 theoretical resolving power for infinitely narrow lines: (1) 

 because of the finite angular width of the slit. ; (2) because 

 of the dispersion of the spectroscope train, which for radiations 

 which are not monochromatic produces the same effect as a 

 widening of the slit. Theoretically we shall distinguish 

 between four cases : — 



1. The resolving power (theoretical) of a spectroscope 

 train for an infinitely narrow slit and monochromatic 

 radiations, i. e., infinitely narrow spectral lines. This is the 

 quantity usually denoted by r. 



2. The resolving power (also theoretical) for a wide slit 

 and monochromatic radiations. Usually denoted by p, the 

 " purity " of the spectrum. 



3. The resolving power (limiting) for an infinitely narrow 

 slit, but for lines of finite width AX. This quantity we will 

 denote by R. 



4. The resolving power (practical) for a wide slit and non- 

 monochromatic radiations ranging for each line over a small 

 value AX as in (3). This quantity, which represents the 

 practical resolving power or purity of the spectrum, will be 

 denoted by P. 



Let D = — be the angular dispersion of the spectroscope 

 ciK 



train. The spectroscopic resolution for any case is defined 



by the ratio — , where d\ is the difference in wave-length of 



two lines of mean wave-length, X, that are just resolved. 

 Therefore for the first case 



r = ™; (1) 



m 



a perfectly general relation which holds good \\ hatever may 



be the nature, form, or arrangement of the spectroscope train. 



Introducing the values of D = -7- = ^-. -r-, we obtain at once 



d\ an oX' 



the usual expressions 

 r=2Nb 



2-20 dX 



nr snr — 



\A- 2 



/ n dn 



(2) 



