1915]
ON THE WIDENING OF SPECTRUM LINES
293
multiple of £X. If bands are visible corresponding to various values of X, the darkest places are absolutely devoid of light, and this remains true however great X may be, that is however high the order of interference.
The above conclusion requires that the light (duplicated by reflexion or otherwise) should have an absolutely definite frequency, i.e. should be absolutely homogeneous. Such light is not at our disposal; and a defect of homogeneity will usually entail a limit to interference, as X increases. We are now to consider the particular defect arising in accordance with Doppler's principle from the motion of the radiating particles in the line of sight. Maxwell showed that for gases in temperature equilibrium, the number of molecules whose velocities resolved in three rectangular directions lie within the range d^dyd^ must be proportional to
If £ be the direction of the line of sight, the component velocities 77, £ are without influence in the present problem. All that we require to know is that the number of molecules for which the component £ lies between f and £ + dj; is proportional to
er&d£ ..................................... (3)
The relation of /3 to the mean (resultant) velocity v is
2
v =
.(4)
It was in terms of v that my (1889) results were expressed, but it was pointed out that v needs to be distinguished from the velocity of mean square with which the pressure is more directly connected. If this be called v',
.(5)
so that
.(6)
Again, the relation between the original wave-length A and the actual wavelength X, as disturbed by the motion, is
c denoting the velocity of light. The intensity of the light in the interference bands, so far as dependent upon the molecules moving with velocity £, is by (2)
(8)e. This theoretical roHtilfc can then be compared with a purely experimental one, and an agreement will confirm the principles on which the calculation was founded. I think ib desirable to include here a sketch of this treatment of the question »u the lines followed in 1889, but with a few slight changes of notation.