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



: Since the spectrum lines must always have a certain 

 u width/' the expression for R last, deduced, which for 

 convenience we will call the limiting resolving power, is more 

 generally useful in determining the greatest resolving power 

 of a spectroscope under practical conditions than the usual 

 expression for r (the theoretical resolution of the instrument). 

 For very small values of ? J AX, i. e. for very small resolving 

 powers or very narrow lines, the value of R will, as in the 

 case of jo, slightly exceed r. But for large values of either r 

 or AX the limiting resolving power will be very much less 

 than the theoretical power of the instrument, particularly for 

 large values of r. No matter how narrow the line may be 

 there is a limit beyond which an increase in the theoretical 

 resolving power is without effect in increasing R. This 

 maximum value of R will evidently be 



-AX 



or the maximum resolving power that can be attained with 

 any instrument with infinitely narrow slit is not more than 

 one and three-quarter times the ratio between the mean 

 wave-length and " width ,J of the spectral lines under exami- 

 nation *. 



Our knowledge of the width of spectral lines under 

 different conditions is at present very limited. Various 

 hypotheses, of which the most noted are those of Lommel, 

 Jauman, Galitzin, and Michelson, have been advanced to 

 account for the broadening of the lines under varying con- 

 ditions of temperature and pressure, and to give us a numerical 

 measure of the amount, but they are all more or less unsatis- 

 factory. Michelson's recent experimental work with the 

 interferometer has given us our most definite knowledge of 

 the widths of some few bright lines in the spark-spectra of 

 some of the metals under different pressures. In each 

 case the exponential law of distribution is assumed, and the 

 quantity given is 8, the " half-width " which has already been 

 denned. It has been assumed as before that the effective 

 range of wave-length AX is about 4S. 



Table III. contains a brief summary of some of the results 

 obtained. 



* As will be presently seen, however, we may attain a somewhat 

 greater practical purity P than this. 



