18 ON THE All'JLJCATION OF INTERFERENCE METHODS 



If, now, the density of the vapor is veiy low, the second cause may be 

 ionored, and it will be shown that in the case of hydrogen this is the case 

 wlu'u the pressure is one or two millimeters. 



In most of the cases investigated the pressm-e was so low that the dis- 

 charge jiassed with difficulty, 8ui)posing, then, the effect of colhsions to be 

 insigiiiticaut, let it be proposed to find the effect due to the motion of the 

 molecule in the hne of sight. K v be the mean velocity of the molecule and 

 Fthat of hght, then the formula for the resulting visibihty cm■^^e, as given 

 by Lord Rayleigh,* is h = (1 -a" )/(! + «" )• 



If the definition of \nsibility as given above be taken, however, this 



becomes 



V= a" = exj) — " [i v) • 



If A be the difference of path at which the visiljihty is reduced to half 

 its value at X=0, then 



or approximatelv "^r — 0.15 — . 



' * /- V 



If we take for hydrogen v = 2000 meters per second, then 



y- = 22500. 



Again, if we ignore the difference iu the temperatm-e (about which there 

 is considerable imcertainty) at which the other substances were examined, 

 the velocities v would vaiy inversely as the square root of the atomic weight, 

 and the number of waves iu the difference of path at which the ^dsibility is 

 0.5 is therefore 22500 Vm. 



Considering the difficulties and uncertainties of the problem, the follow- 

 ing table shows a remarkable agreement between the values actually found 

 and the calculated results.f 



• '• On the Limit to Interference when Light is Radiated from Moving Molecules." Philosophical 

 Maguzine, April, 1889. 



t It should be stated that the value of A for the yellow sodium line, if taken from the ciu-ve, would 

 be much larger than that given. The latter was the mean of a number of observations taken withm the 

 past month. As has been stated before, this particular curve has not been obtain(>d since last year. A 

 few other substances very ditlieult to examine, either because the lines are too feeble, or becau.sc the 

 spectrum is so unstable, have given results not quite so consistent as the above, though all an- of the 

 same trder of magnitude as that required by theory. 



