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certain slight extent talse; and whose influence must be estimated and allowed for before we can obtain a precise knowledge of the place of any object. This cause is what is called the aberration of light; a singular and surprising effect arising from this, that we occupy a station not at rest but in rapid motion; and that the apparent directions of the rays of light are not the same to a spectator in motion as to one at rest. As the estimation of its effect belongs to uranography, we must explain it here, though, in so doing, we must anticipate some of the results to be detailed in subsequent chapters.
(329.) Suppose a shower of rain to fall perpendicularly in a dead calm; a person exposed to the shower, who should stand quite still and upright, would receive the drops on his hat, which would thus shelter him, but if he ran forward in any direction they would strike him in the face. The effect would be the same as if he remained still, and a wind should arise of the same velocity, and drift them against him. Suppose a ball let fall from a point A above a horizontal line EF, and that at B were placed to receive it the open mouth of an inclined hollow tube P Q; if the tube were held im
moveable the ball would strike on its lower side, but if the tube were carried forward in the direction EF, with a velocity properly adjusted at every instant to that of the ball, while preserving its inclination to the horizon, so that when the ball in its natural descent reached C, the tube should have been carried into the position RS, it is evident that the ball would, throughout its whole descent, be found in the axis of the tube; and a spectator referring to the tube the motion of the ball, and carried along with the former, unconscious of its motion, would fancy that the ball had been moving in the inclined direction R S of the tube's axis.
(330.) Our eyes and telescopes are such tubes. In whatever manner we consider light, whether as an advancing wave in a motionless ether, or a shower of atoms traversing space, (provided that in both cases we regard it as absolutely incapable of suffering resistance or corporeal obstruction from the particles of transparent media traversed by it*,) if in the interval between the rays traversing the object glass of the one or the cornea of the other (at which moment they acquire that convergence which directs them to a certain point in fixed space), and their arrival at their focus, the cross wires of the one or the retina of the other be slipped aside, the point of convergence (which remains unchanged) will no longer correspond to the intersection of the wires or the central point of our visual area. The object then will appear displaced; and the amount of this displacement is aberration.
(331.) The earth is moving through space with a velocity of about 19 miles per second, in an elliptic path round the sun, and is therefore changing the direction of its motion at every instant Light travels with a velocity of 192,000 miles per second, which, although much greater than that of the earth, is yet not infinitely so. Time is occupied by it in traversing any space, and in that time the earth describes a space which is to the former as 19 to 192,000, or as the tangent of 20'.5 to radius. Suppose now APS to represent a ray of light from a star at A, and let the tube P Q be that of a telescope so inclined forward that the focus formed by
. This condition is indispensable. Without it we fall into all those difficulties which M. Doppler has so well pointed out in his paper on Aberration (Abhandlungen der k. boemischen Gesellschaft der Wissenschaften. Folge V. vol. iii.). If light itself, or the luminiferous ether, be corporeal, the condition insisted on amounts to a formal surrender of the dogma, either of the extension or of the impenetrability of matter ; at least in the sense in which those terms have been hitherto used by metaphysicians. At the point to which science is arrived, probably few will be found disposed to maintain either the one or the other.
its object glass shall be received upon its cross wire, it is evident from what has been said, that the inclination of the tube must be such as to make PS: SQ:: velocity of light: velocity of the earth :: 1: tan. 20:5; and, therefore, the angle SP Q, or PSR, by which the axis of the telescope must deviate from the true direction of the star, must be 20"5.
(332.) A similar reasoning will hold good when the direction of the earth's motion is not perpendicular to the visual ray. If S B be the true direction of the visual ray, and A C the position in which the telescope requires to be held in the apparent direction, we must still have the proportion BC : BA :: velocity of light: velocity of the earth :: rad. : sine of 20'.5 (for in such small angles D_ it matters not whether we use the sines or tangents). But we have, also, by trigonometry, BC: BA:: sine of B AC: sine of A CB or CB P, which last is the apparent displacement caused by aberration. Thus it appears that the sine of the aberration, or (since the angle is extremely small) the aberration itself, is proportional to the sine of the angle made by the earth's motion in space with the visual ray, and is therefore a maximum when the line of sight is perpendicular to the direction of the earth's motion.
(333.) The uranographical effect of aberration, then, is to distort the aspect of the heavens, causing all the stars to crowd as it were directly towards that point in the heavens which is the vanishing point of all lines parallel to that in which the earth is for the moment moving. As the earth moves round the sun in the plane of the ecliptic, this point must lie in that plane, 90° in advance of the earth’s longitude, or 90° behind the sun's, and shifts of course continually, describing the circumference of the ecliptic in a year. It is easy to demonstrate that the effect on each particular star will be to make it apparently describe a small ellipse in the heavens, having for its centre the point in which the star would be seen if the earth were at rest.
(334.) Aberration then affects the apparent right ascensions and declinations of all the stars, and that by quantities easily calculable. The formulæ most convenient for that purpose, and which, systematically embracing at the same time the corrections for precession and nutation, enable the observer, with the utmost readiness, to disencumber his observations of right ascension and declination of their influence, have been constructed by Prof. Bessel, and tabulated in the appendix to the first volume of the Transactions of the Astronomical Society, where they will be found accompanied with an extensive catalogue of the places, for 1830, of the principal fixed stars, one of the most useful and best arranged works of the kind which has ever appeared.
(335.) When the body from which the visual ray emanates is itself in motion, an effect arises which is not properly speaking aberration, though it is usually treated under that head in astronomical books, and indeed confounded with it, to the production of some confusion in the mind of the student. The effect in question (which is independent of any theoretical views respecting the nature of light*) may be explained as follows. The ray by which we see any object is not that which it emits at the moment we look at it, but that which it did emit some time before, viz. the time occupied by light in traversing the interval which separates it from us. The aberration of such a body then arising from the earth's velocity must be applied as a correction, not to the line joining the earth’s place at the moment of observation with that occupied by the body at the same moment, but at that antecedent instant when the ray quitted it. Hence it is easy to derive the rule given by astronomical writers for the case
* The results of the undulatory and corpuscular theories of light, in the matter of aberration are, in the main, the same. We say in the main. There is, however, a minute difference even of numerical results. In the undulatory doctrine, the propagation of light takes place with equal velocity in all directions, whether the luminary be at rest or in motion. In the corpuscular, with an excess of velocity in the direction of the motion over that in the contrary equal to twice the velocity of the body's motion. In the cases, then, of a body moving with equal velocity directly to and directly from the earth, the aberrations will be alike on the undulatory, but different on the corpuscular hypothesis, The utmost difference which can arise from this cause in our system cannot amount to above six thousandths of a second.
of a moving object. From the known laws of its motion and the earth's, calculate its apparent or relative angular motion in the time taken by light to traverse its distance from the earth.
This is the total amount of its apparent misplacement. Its effect is to displace the body observed in a direction contrary to its apparent motion in the heavens. And it is a compound or aggregate effect consisting of two parts, one of which is the aberration, properly so called, resulting from the composition of the earth’s motion with that of light, the other being what is not inaptly termed the Equation of light, being the allowance to be made for the time occupied by the light in traversing a variable space.
(336.) The complete Reduction, as it is called, of an astronomical observation consists in applying to the place of the observed heavenly body as read off on the instruments (supposed perfect and in perfect adjustment) five distinct and independent corrections, viz. those for refraction, parallax, aberration, precession, and nutation. Of these the correction for refraction enables us to declare what would have been the observed place, were there no atmosphere to displace it. That for parallax enables us to say from its place observed at the surface of the earth, where it would have been seen if observed from the centre. That for aberration, where it would have been observed from a motionless, instead of a moving station : while the corrections for precession and nutation refer it to fixed and determinate instead of constantly varying celestial circles. The great importance of these corrections, which pervade all astronomy, and have to be applied to every observation before it can be employed for any practical or theoretical purpose, renders this recapitulation far from superfluous.
(337.) Refraction has been already sufficiently explained, Art. 40. and it is only, therefore, necessary here to add that in its use as an astronomical correction its amount must be applied in a contrary sense to that in which it affects the observation ; a remark equally applicable to all other corrections.
(338.) The general nature of parallax or rather of paral