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



For convenience the values of R, R max . and r/R, have been 

 computed for various values of A\, ranging from 0*01 to 1*0 

 tenth-metre, and for values of r from 25000 to 1000000. 

 They are given in Table IV. 



The vertical columns show the decrease in the value of R 

 with an increase in A\ for a given value of r ; the horizontal 

 lines show the increase in R with r for a given width of line. 

 The last column gives the maximum resolving power R max . 

 that can be attained when the lines have the width AX given 

 in the first column. 



We see that in general we shall very nearly reach this limit 

 when the theoretical resolving power r is about twice R max . 

 The additional gain in R, obtained by a further increase in r, 

 would not be worth the expense of the larger instruments 

 required and the sacrifice in brightness necessary. Indeed, 

 in most cases it would hardly be advisable to use a value of 

 r greater than one to one and one-half times R max . as with this 

 we shall have already attained from f to -J of the limiting 

 resolving power. The finest lines so far found (see Table IV.) 

 have a width AX of not less than 0'01 tenth-metre. For 

 this width the value of R max . is 950000, and the maximum 

 theoretical power which it would be advisable to use would 

 therefore be about 1400000, corresponding in the case of 

 a grating to an aperture of from 18 to 20 inches. On the 

 other hand, for some of the wider lines, such as those of 

 hydrogen in the vacuum tube, and of many bright metallic 

 lines in arc spectra, there would be no advantage whatever 

 for visual work in using a resolving power greater than 20000 

 to 25000, for which a grating of J-inch aperture, or 5 

 60-prisms of 1J inches aperture would suffice. For solar 

 spectrum work, in which the lines are not likely to be 

 narrower than ^ tenth-metre*, our present 5 and 6 inch 

 gratings will do nearly all that we could hope to attain with 

 larger apertures f, unless indeed there should be some marked 

 advantage in particular cases in the use of the first and second 

 orders of spectra, rather than the higher orders. 



The preceding conclusions are all based on the assump- 



* In the case of faint lines the apparent width may sometimes be 

 much less than this, because of the rapid falling off in intensity towards 

 the edge of the line. Indeed, for faint lines, it is not likely that the 

 apparent width of the line is greater than 28, and in some cases even les3. 

 Hence estimates of pressure based upon direct visual observations of the 

 widening o lines may be considerably in error. 



t The latter would, however, be advantageous in photographic work 

 in giving increased accuracy and increased photographic resolution by 

 reason of the greater linear dispersion. See ' Astrophysical Journal,' vol. j, 

 p. 233, and vol. ii. p. 264, 



