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

Rh 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

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

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 Rh