Page:Philosophical Transactions of the Royal Society A - Volume 184.djvu/832

be aimed in front of the object. The shot will go straight along the barrel produced, but the hole in the target will indicate a gun in front of its true position; this error being aberration proper.

Fig. 1.

Diagram of shot fired from a moving cannon; piercing a target, at $\mathrm {Y}$ if stationary, at $\mathrm {Z}$ if moving at same pace as gun. $\mathrm {ABCD}$ is the locus of successive sliots, but is not the line of lire.

If both gun and target are travelling at the same speed everything occurs as if they were at rest, unless a stagnant medium has to be taken into account. Relative motion of the medium causes windage, as is well known.

Since motion of the medium causes a shift of the line of fire, it may be expected to produce a miss, but this is not a true aberration, it only appears to be such because of the fire being limited to one line; suppose instead of a single gun a broadside of guns or a number of guns firing from a turret, then the effect of a cross-wind is, indeed, to displace all the shots, but not to prevent the target being hit by one which would otherwise have missed it, and the hole in the target will indicate the position of the gun really firing the shot.^[1] Hence, even on a corpuscular theory, a wind across the line joining source and receiver, will not cause any effective aberration. Neither can a steady tail wind deliver a stream of bullets from a machine-gun more frequently than they are emitted.

If guns are fired from a revolving turret, the paths of the shot will not be radial, but will be skewed by an amount depending upon the peripheral velocity. Watching the beams of a revolving lighthouse, tracking their way to a distance and brandished rapidly round, it is not at once quite evident whether the shape of those beams is not a spiral of enormous pitch (see below). We see, however, that on the corpuscular view the paths will be straight, though not radiating from the precise centre; for instance, the rays from the Sun, whose peripheral velocity is nearly 5000 miles an hour, would if regarded as projectiles, be inclined to their radius at an angle of ${\tfrac {5}{186\times 3600}}$ radian, or about $1{\tfrac {1}{2}}$ seconds of arc; and the Sun's centre would be, apparently displaced through a fraction of this angle, equal to Sun's radius/Sun's distance; i.e., through, about the ${\tfrac {1}{150}}$th part of a second.

11. But now, proceeding to look at the matter from the point of view of waves, there are many differences; principally depending on the fact that there is no question of initial velocity of projection about a wave : it crawls through the medium,

1. As these projectile examples are only used for illustration, I simplify matters artificially by omitting all curvatures of path. The subject of aberration in general is illustrated more fully in a Royal Institution Lecture, 'Proc. R. I.,' April 1, 1892; also reported in 'Nature,' vol. 46, p. 497.