184 REPOET— 1892. 



tages which may be expected from a study of the variations of clearness 

 of interference fringes Avith increase in difference of path. The funda- 

 mental principle by which the ' structure ' of a line or group of lines is 

 determined by this method is not essentially different from that of spec- 

 trum analysis by the grating, both depending, in fact, on interference 

 phenomena, but in consequence of the almost complete freedom from 

 errors arising from defects in optical or mechanical parts, the method 

 has extraordinary advantages for this special work. A glance at fig. 18, 

 Plate III., will give a fair idea of the 'resolving power ' of the method as 

 compared with that of the grating. In order that the comparison be 

 quite fair, however, it would be necessary to take for a comparison spec- 

 trum that of the substances here used, and under the same conditions. 

 With the best instrumental appliances now in use, it is difficult to ' re- 

 solve ' lines as close together as the components of either of the yellow 

 sodium lines. It is evident, however, that by Li'ght-tvave Analysis, if I 

 may venture so to call the foregoing method, a tenth of this distance is 

 obviously within the limit ; indeed, if the width of the lines themselves be 

 less than their distance apart, there can be no limit. 



Supplement. 



I. It has already been pointed out that in many cases it is difficult or 

 impossible to decide between two or more distributions of lines which 

 give very nearly the same visibility curve ; and when there are many 

 lines in the source, the combinations of intensities and arrangements of 

 these from which a type may be selected are enormously great. Indeed, 

 even when the number of lines is greater than three, excepting perhaps 

 the cases where the lines may be in pairs (as in the case of yellow sodium 

 light), the resulting visibility curve becomes so complex that it is very 

 difficult to analyse. Doubtless in many cases where the components are 

 not too close, the grating will give the information necessary for the in- 

 vestigator to select the proper combination. 



It may readily be shown that the formula 



for the visibility curve due to a distribution of light, y=<f>{x), is identical 

 with that of the intensity curve at the focus of a telescope provided with 

 apertures which produce this distribution in the light passing through. 

 Accordingly, if a telescope be provided with apertures adjustable in 

 width, or length, and distance apart, the diffraction image of a distant 

 illuminated slit will give, at once, a representation of the whole visibility 

 curve, and by adjustment of intensities and distances any particular 

 visibility curve may be more or less accurately copied, thus furnishing a 

 means of studying the relations between V and 9f)(a;), which, while 

 giving, perhaps only a rough approximation to the truth, may prove more 

 convenient than analytical or graphical methods. 



II. One of the purposes which led to these investigations was the search 

 for a radiation of sufficient homogeneity to serve as an ultimate standard 

 of length. It will appear from the curves of cadmium that there are 

 three lines which may be used for this purpose. The red cadmium line 

 is almost ideally homogeneous, and will readily permit the estimation of 



