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



T 



for narrow lines and small resolving powers the ratio ^ is 



very nearly unity, and that formula (16) therefore represents 

 very closely the purity of the spectrum, the same is by no 

 means true for wide lines and large resolving powers. In 

 the extreme case figured in the table the value of this ratio 

 rises as high as 100. In order to show more clearly the 

 influence of this factor on the purity of the spectrum under 

 different conditions, Table V. has been prepared, showing 

 the values of P for different slit apertures, from 005 mm. 

 to 0*3 mm., different widths of lines from 001 to 1*00 tenth- 

 metres, and resolving powers varying from 25000 to 1000000. 

 For comparison the values of p are given for each slit-width 

 and resolving power, and also the value of p calculated from 

 the old formula for purity (6). An inspection of the table 

 shows at once how greatly in error estimates of purity 

 based upon this old formula may be in some very common 

 cases. 



Take for example the case of a spectroscope having a re- 

 solving power of 100000 (5-inch grating, 20000 lines, 2nd 

 order) ; working with angular slit-width such that syfr = *005 

 (s=^L mm., aJr = T L, as i n the concave grating). The value 

 of p (16) is about 158000, while the value of P varies from 

 163000 to 10000. The value of p' (the old formula for 

 purity) for the same case is only 105000. It is therefore 

 in this case from 50 per cent, to 1000 per cent, in error. 

 In case of larger resolving-powers (r= 1000000) it may be 

 as much as 60 times too great. In general, of course, the 

 large values of rA\ that give rise to the smaller values of P 

 will not be used for visual work, as there is, as already indi- 

 cated, but little gain in practical resolving power or purity 

 when the value of r is greater than the value of R ma i. given 

 in Table V. But in photographic work it is, as has already 

 been shown in a previous paper, a great advantage to use (for 

 extended sources) a short camera and very high resolving 

 power, in order to attain a given degree of photographic 

 purity. Another point which is of considerable practical 

 importance in this connexion is that for these large values 



of p the purity of the spectrum may be maintained constant 



or even actually improved over a wide range of those slit- 

 widths actually used in practice. For the maximum value 

 of P (as of p) will be attained when 



* a Ki)" 



