All this is familiar, and was geometrically illustrated in Chapter [III], but there are some minor and rather curious details which are worthy of brief consideration.
Grating Theory.
For suppose a 'grating' is used to analyse the light. Its effect can depend on nothing kinetic; it must be regulated by the merely geometric width of the ruled spaces on it. Consequently it can only directly apprehend wave-lengths, not frequencies.
In the case of a moving source, therefore, when the wave-length is really changed, a grating will appreciate the fact, and will show a true Doppler effect. But in the case of a moving observer, when all the waves received are of normal length, though swept up with abnormal frequency, the grating must still indicate wave-length alone, and accordingly will show no true Doppler effect.
But inasmuch as the telescope or line of vision is inclined at the angle of dispersion to the direction of the incident ray, ordinary aberration must come in, as it always does when an observer moves athwart his line of vision; and so there will be a spurious or apparent Doppler effect due to common aberration. That is to say a spectrum line will not be seen in its true place, but will appear to be shifted by an amount almost exactly imitative of a real Doppler effect—the imitation being correct up to the second order of aberration magnitude. The slight outstanding difference between them is calculated in my Philosophical Transactions paper, 1893, page 787. It is too small to observe.
It is not an important matter, but as it is rather troublesome to work out the diffraction observed by a grating advancing towards the source of light, it may be as well to record the result here.
The following are the diffracted rays which require attention,—with the inclination of each to the grating-normal specified:—
The diffracted ray if all were stationary, θ0;
The real diffracted ray when grating is advancing, φ;