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; The ray as perceived, allowing for aberration, θ; The equivalent diffracted ray if all were stationary and the wave-length really shortened, θ₁. As an auxiliary we use the aberration angle ε, such that sin ε = α sin θ, where α = v/V. Among these four angles the following relations hold; so that, given one of them, all are known. { θ = φ - ε { sin θ₁ = (1 - α) sin θ₀ { sin φ = (1 - α vers φ) sin θ₀ Whence θ and θ₁ are very nearly but not absolutely the same. θ₁ is the ray observed by an instrument depending primarily on frequency, like a prism; θ is the ray observed by an instrument depending primarily on wave-length, like a grating. _Prism Theory._ Now let a prism be used to analyse the light; its dispersive power is in most theories held to depend directly upon frequency--i.e. upon a time relation between the period of a light vibration and the period of an atomic or electronic revolution or other harmonic excursion. Let us say, therefore, that prismatic dispersion directly indicates frequency. It cannot depend upon wave-length, for the wave-length inside different substances is different, and though refractive index corresponds to this, dispersive power does not. In the case of a prism, therefore, no distinction can be drawn between motion of source and motion of receiver; for in both cases the frequency with which the waves are received will be altered,--either because they are really shorter, though arriving at normal speed, or because they are swept up faster, although of normal length. _Achromatic Prism._