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ON  THE  WIDENING OP  SPECTRUM LINES                        [391
calculation*, taking into account the variable velocity of the molecules as defined by Maxwell's law, from which it appeared that there was really no disagreement with observation. Michelson compared these theoretical results with those of his important observations upon light from vacuum-tubes and tumid an agreement which was thought sufficient, although there remained Komi- points of uncertainty.
The same ground was traversed by Schonroekf, who made the notable remark that while the agreement was good for the monatomic gases it failed tor diatomic hydrogen, oxygen, and nitrogen; and he put forward the suggestion that in these cases the chemical atom, rather than the usual molecule, was to bo regarded as the carrier of the emission-centres, By this substitution, entailing an increase of velocity in the ratio V2:1, the agreement was much improved.
While I do not doubt that Schdnrock's comparison is substantially correct, I think that his presentation of the theory is confused and unnecessarily complicated by the introduction (in two senses) of the "width of the spectrum lino," a quantity not usually susceptible of direct observation. Unless I misunderstand, what he calls the observed width is a quantity not itself observed at all but deduced from the visibility of interference bands by arguments which already assume Doppler's principle and the theory of gases. I do not HOC what is gained by introducing this quantity. Given the nature of the radiating1 gas and its temperature, we can calculate from known data the cliwtribution of light in the bands corresponding to any given retardation, and from photometric experience we can form a pretty good judgment as to the maximum retardation at which they should still be visible. 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.
The phenomenon of interference in its simplest form occurs when two oqual trains of waves are superposed, both trains having the same frequency and one being retarded relatively to the other by a linear retardation X\. Then if X denote the wave-length, the aggregate may be represented by
cos nt -h cos (nt - 27rX/\) = 2 cos (irX)\). cos (nt - -rrX/X).......(1)
The intensity is given by
I = 4 cos2 (77-Z/X) = 2 {1 + cos (2-jrX/\)\................(2)
If wu regard X as gradually increasing from zero, / is periodic, the maxima (4) occurring when JK is a multiple of X and the minima (0) when X is an odd
* "On the limits to interference when light is radiated from moving molecules," Phil. Mag. Vol. xxvu. p. 298 (1889) ;  Scientific Papers, Vol. HI. p. 258. f Ann. der JPhysik, Vol. xx. p. 995 (1906). $ In the paper of 1889 the retardation was denoted by 2A.