Page:Philosophical Transactions of the Royal Society A - Volume 184.djvu/835

called the aberration angle. The velocity with which light journeys over the radius vector, $r$, is

$\mathrm {V} \cos \epsilon +v\cos \theta$, $=\mathrm {V} _{1}$ say:

the time of the journey being simply $t$, as before.

The angle $\epsilon$ is defined by the equally obvious geometrical relation

$\mathrm {V} \sin \epsilon -v\sin \theta =0$.

Fig. 4.

Successive waves emitted by a fixed source $S$ into a drifting medium. The row of dots $SC$ represent the respective wave-centres. The figure also represents waves in a stationary medium, emitted by a source moving from $C$ to $S$

Here is a picture of the source and successively-emitted and abandoned drifting wave-fronts. $\mathrm {SM}$ is the path of a labelled disturbance, and is to be considered as a ray; it is inclined at angle $\epsilon$ to the corresponding wave-normals.

$\mathrm {SP}$ is what would have been the light journey in the same time if the medium had been stationary; $\mathrm {PM}$ or $\mathrm {SC}$ represents the drift.

The result of the state of things exhibited in the diagram may or may not be appreciated by a spectator—that depends on what his own motion is,—but if he is moving simply with the medium, he perceives the following:—

(1) An aberration, $\epsilon$, in any direction inclined at angle $\theta$ to the motion, such that

$\sin \epsilon ={\tfrac {v}{\mathrm {V} }}\sin \theta =\alpha \sin \theta$,

it being convenient to denote the ratio of velocities, $v/\mathrm {V}$, by a single symbol $\alpha$, and to call it the aberration constant. A telescope moving with the medium and placed with its object glass tangential to the advancing wave-fronts, will focus the image on its