ON SPECTROSCOPIC MEASDEEMENTS. 185 



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 pur- 

 pose, 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 interference bands. 



If (j) 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 number of 



' periods ' in the difference of path, and r the ratio of the intensities, 



then 



, ct , '>' sin 27ra , 



tan 27rd)=— ^ - ^ 



1 + r cos ZTTii 



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

 we have, approximately, 



0=--O4. 



This is the largest correction to be applied, 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 line unsym- 

 metrically 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 difficulties in making 

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

 resolution of groups of spectral lines on account of the real width of the 

 lines themselves, caused by the lack of homogeneity in the radiations 

 which produce them. The results of the preceding investigations show 

 that, while this is very far from being true with present gratings, such a 

 limit undoubtedly exists. The accordance between the measured widths 

 of eighteen lines shows further that this broadening of lines in a rare gas 

 can be fully accounted for by the application of Doppler's principle to the 

 motion of the vibrating atoms in the line of sight, and, indeed, furnishes 

 what may be considered one of the most direct proofs of the kinetic 

 theory of gases. 



The form of the ultimate components of all the groups of lines thus 

 far examined is found to agree fairly well with an exponential curve, 

 <j^(a!)=e""°''°, which shows that the distribution of velocities cannot vary 

 widely from that demanded by Maxwell's theory. 



If the limit abovementioned were due solely to the motion of the 

 molecule, and the radiating substance could be rendered luminous while 

 its temperature was very low, it might be possible to observe interference 

 phenomena with a difference of path of many metres. But it must be 

 considered that, since every vibrating molecule is communicating its 

 energy to the ether in the form of light waves, its vibrations must 

 diminish in amplitude ; consequently the train of waves is no longer homo- 

 geneous, even though the vibrations remain absolutely isochronous, and 

 the result is a broadening of the line and limitation of the difference of 

 path at which interference is visible. 



' See PJdl. Mar/., April 1891, p. 345. (The value of r is the reciprocal of that 

 here used.) 



