298 On Spectroscopic Measurements, 



for the visibility-curve due to a distribution of light, y = cj)(x), 

 is identical with that of the intensity-curve at the focus of a 

 telescope provided with apertures which produce this distri- 

 bution 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 dis- 

 tances any particular visibility-curve may be more or less 

 accurately copied, thus furnishing a means of studying the 

 relations between V and $(ti'), 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 a change of phase in the interference-fringes of one 

 hundredth of a fringe in a total distance of 200 millimetres, 

 or over 300,000 waves. 



Both the green and the blue lines are fairly well adapted 

 for the purpose, and will prove very valuable as checks. Each 

 of these, however, has a small companion, and it is necessary 

 to know the effect of this in altering the phase of the inter- 

 ference-bands. 



If cj) be the fraction of a wave by which the position of a 

 minimum is shifted on account of the presence of the com- 

 panion, a the number of " periods n in the difference of path, 

 and r the ratio of the intensities, then 



, . » . r sin 27ra * 



tan 2770= — — s 



T l+rcos27ra 



Thus, if r = l/4, $ is a maximum when a is about 1/3 ; and 

 for this we have, approximately, </>=— '04. 



This is the largest correction to be applied, and is negative 

 if the brighter line has the greater wave-length. It is theo- 

 retically possible, by this means, to determine, in case of an 

 unequal double, or a line unsymmetrically broadened, whether 

 the brighter side is toward the blue or the red end of the 

 spectrum. 



III. It has been argued that, even if all practical diffi- 

 culties in making large gratings could be removed, nothing 



* See Phil. Mag. April 1891, page 345. (The value of r is the reci- 

 procal of that here used.) 



