TO SPECTROSCOPIC MEASUREMENTS. 23 



or less accm-ately copied ; thus furnishing a means of studying the relations 

 between Fand (p(x) which, while giving perhaps only a rough approxima- 

 tion 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 wall appear from the curves of cadmium that there are three 

 hnes which may be used for this pm-pose. 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 dis- 

 tance of 200 millimeters or over 300,000 waves. 



Both the green and the blue lines ai"e fairly well adapted for the pur- 

 pose, and -^dU 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 interference bands. 



If 'f be the fraction of a wave by which the position of a minimum is 

 shifted on account of the presence of the companion, a the nmnber of 

 "periods" in the difference of path, and r the ratio of the intensities, then 



r sin 2x7. 



tan 2xcp = — :.-- ^ — . 



^ 1 + r cos 2xa 



Thus, if r = 14, cp is a maximum when a is about 1 3 ; and for this we 

 have, approximately, 9 = — 0.04. 



This is the largest correction to be apphed, and is negative if the brighter 

 line has the greater wave-length. It is theoretically possible, by this means, 

 to determine, in case of an unequal double, or a Hne unsymmetricaUy broad- 

 ened, 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 difficulties in making 

 large gratings could be removed, nothing further could be gained in resolu- 

 tion of groups of spectral hnes, on account of the real width of the hnes 

 themselves, caused by the lack of homogeneity in the radiations which pro- 

 duce them. The results of the preceding investigations show that, while 



* See Philosophical Magazine, April, 1891, page 345. (The value of /• is the reciprocal of that here used.) 



