ABERRATION (Lat. ab, from or away, errare,, to wander)

This article appears in Volume V01, Page 55 of the Encyclopedia Britannica.

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ABERRATION (Lat. ab, from or away, errare,, to wander) , a deviation or wandering, especially used in the figurative sense: as in ethics, a deviation from the truth; in

pathology

PATHOLOGY (from Gr. raBos, suffering)

, a mental derangement; in

zoology

ZOOLOGY (from Gr. Nov, a living thing, and ?byos, theory)

and botany, abnormal development or structure. In optics, the word has two special applications: (I) Aberration of Light, and (2) Aberration in Optical Systems. These subjects receive treatment below.
I. ABERRATION OF LIGHT
This astronomical phenomenon may be defined as an apparent motion of the heavenly bodies; the stars describing annually orbits more or less elliptical, according to the

latitude

LATITUDE (Lat. latitudo, latus, broad)

of the star; consequently at any moment the star appears to be displaced from its true position. This apparent motion is due to the finite velocity of light, and the progressive motion of the observer with the earth, as it performs its yearly course about the sun. It may be familiarized by the following illustrations. Alexis Claude Clairaut gave this figure: Imagine rain to be falling vertically, and a person carrying a thin perpendicular tube to be

standing

STANDING

on the ground. If the bearer be stationary, rain-drops will traverse the tube without touching its sides; if, however, the person be walking, the tube must be inclined at an angle varying as his velocity in order that the rain may traverse the tube centrally. J. J. L. de Lalande gave the

illustration

ILLUSTRATION

of a'roofed carriage with an open front: if the carriage be stationary, no rain enters; if, however, it be moving, rain enters at the front. The " umbrella " analogy is possibly the best known figure. When stationary, the most efficient position in which to hold an umbrella is obviously vertical; when walking, the umbrella must be held more and more inclined from the vertical as the walker quickens his pace. Another familiar figure, pointed out by P. L. M. de Maupertuis, is that a sportsman, when aiming at a bird on the wing, sights his gun some distance ahead of the bird, the distance being proportional to the velocity of the bird. The mechanical idea, named the parallelogram of velocities, permits a ready and easy graphical representation of
these facts. Reverting to the analogy of Clairaut, let AB (fig. I) represent the velocity of the rain, and AC the relative velocity of the person bearing the tube. The

diagonal

DIAGONAL (Gr. &a, through, ywvia, a corner)

AD of the parallelogram, of which AB and AC are adjacent sides, will represent, both in direction and magnitude, the motion of the rain as apparent to the observer. Hence for the
rain to centrally traverse the tube, this must be inclined at an angle BAD to the vertical; this angle is conveniently termed the aberration due to these two motions. The umbrella analogy is similarly explained; the most efficient position being when the stick points along the resultant AD.
The discovery of the aberration of light in 1725, due to James Bradley, is one of the most important in the whole domain ofastronomy. That it was unexpected there can be no :doubt; and it was only by extraordinary perseverance and perspicuity that Bradley was able to explain it in 1727. Its origin is seated in attempts shade to free from doubt the prevailing discordances as to whether the stars possessed appreciable parallaxes. The Copernican theory of the solar systemthat the earth revolved annually about the sunhad received confirmation by the observations of Galileo and Tycho Brahe, and the mathematical' investigations of Kepler and Newton. As early as 1573, Thomas Digges had suggested that this theory should necessitate a parallactic shifting of the stars, and, consequently, if such stellar parallaxes existed, then the Copernican theory would receive additional confirmation. Many observers claimed to have determined such parallaxes, but Tycho Brahe and G. B. Riccioli concluded that they existed only in the minds of the observers, and were due to instrumental and personal errors. In 168o Jean Picard, in his Voyage d' Uranibourg, stated, as a result of ten years' observations, that Polaris, or the Pole Star, exhibited variations in its position amounting to 40" annually; some astronomers endeavoured to explain this by

parallax

PARALLAX (Gr. aapa?X6, alternately)

, but these attempts were futile, for the motion was at variance with that which

parallax

PARALLAX (Gr. aapa?X6, alternately)

would occasion. J. Flamsteed, from measurements made in 1689 and succeeding years with his mural quad-rant, similarly concluded that the declination of the Pole Star was 40" less in July than in September. R. Hooke, in 1674, published his observations of y Draconis, a star of the second magnitude which passes practically overhead in the

latitude

LATITUDE (Lat. latitudo, latus, broad)

of London, and whose observations are therefore singularly free from the complex corrections due to astronomical refraction, and concluded that this star was 23" more northerly in July than in October.
When James Bradley and Samuel Molyneux entered this sphere of astronomical research in 1725, there consequently prevailed much uncertainty as to whether stellar parallaxes had been observed or not; and it was with the intention of definitely answering this question that these astronomers erected a large telescope at the

house

of the latter at Kew. They determined to reinvestigate the motion of y Draconis; the telescope, constructed by George Graham (1675-1751), a celebrated instrument-maker, was affixed to a vertical chimney stack, in such manner as to permit a small oscillation of the eyepiece, the amount of which, i.e. the deviation from the vertical, was regulated and measured by the introduction of a screw and a plumb-line. The instrument was set up in November 1725, and observations on y Draconis were made on the 3rd, 5th, 11th, and 12th of December. There was apparently no shifting of the star, which was therefore thought to be at its most southerly point. On the 17th of December, however, Bradley observed that the star was moving southwards, a motion further shown by observations on the loth. These results were unexpected, and, in fact, inexplicable by existing theories; and an examination of the telescope showed that the observed anomalies were not due to instrumental errors. The observations were continued, and the star was seen to continue its southerly course until March, when it took up a position some co" more southerly than its December position. After March it began to pass north-wards, a motion quite apparent by the middle of April; in June it passed at the same distance from the zenith as it did in December; and in September it passed through its most northerly position, the extreme range from north to south, i.e. the angle between the March and September positions, being 40".
This motion is evidently not due to parallax, for, in this case, the maximum range should be between the June and December positions; neither was it due to observational errors. Bradley and Molyneux discussed several hypotheses in the hope of fixing the solution. One hypothesis was: while y Draconis was stationary, the plumb-line, from which the angular measurements were made, varied; this would follow if the axis of the earth varied. The oscillation of the earth's axis may arise in two distinct ways; distinguished as " nutation of the axis " and " variation of latitude. " Nutation, the only form of oscillation imagined by Bradley, postulates that while' the earth's
c A
axis is fixed with respect to the earth, i.e. the north and south poles occupy permanent geographical positions, yet the axis is not directed towards a fixed point in the heavens; variation of latitude, however, is associated with the shifting of the axis within the earth, i.e. the geographical position of the north pole varies.
Nutation of the axis would determine a similar apparent motion for all stars: thus, all stars having the same polar distance as y Draconis should exhibit the same apparent motion after or before this star by a constant interval. Many stars satisfy the condition of equality of polar distance with that of y Draconis, but few were

bright

BRIGHT, JOHN (1811-188g)
BRIGHT, SIR CHARLES TILSTON

enough to be observed in Molyneux's telescope. One such star, however, with a right ascension' nearly equal to that of y Draconis, but in the opposite sense, was selected and kept under observation. This star was seen to possess an apparent motion similar to that which would be a consequence of the nutation of the earth's axis; but since its declination varied only one half as much as in the case of y Draconis, it was obvious that nutation did not supply the requisite solution. The question as to whether the motion was due to an irregular distribution of the earth's atmosphere, thus involving abnormal variations in the refractive index, was also investigated; here, again, negative results were obtained.
Bradley had already perceived, in the case of the two stars previously scrutinized, that the apparent difference of declination from the ihaximum positions was nearly proportional to the sun's distance from the equinoctial points; and he realized the necessity for more observations before any generalization could be attempted. For this purpose he repaired to the Rectory,

Wanstead

WANSTEAD

, then the residence of Mrs Pound, the widow of his uncle James Pound, with whom he had made many observations of the heavenly bodies. Here he had set up, on the rgth of August 1727, a more convenient telescope than that at Kew, its range extending over 6',- on each side of the zenith, thus covering a far larger area of the sky. Two hundred stars in the British Catalogue of Flamsteed traversed its field of view; and, of these, about fifty were kept under close observation. His conclusions may be thus summarized: (I) only stars near the solstitial colure had their maximum north and south positions when the sun was near the equinoxes, (2) each star was'at its maximum positions when it passed the zenith at six o'clock morning and evening (this he afterwards showed to be inaccurate, and found the greatest change in declination to be proportional to the latitude of the star), (3) the apparent motions of all stars at about the same time was in the same direction.
A re-examination of his previously considered hypotheses as
to the cause of these phenomena was fruitless; the true theory
was ultimately discovered by a pure accident, comparable in
simplicity and importance with the association of a falling apple
with the discovery of the principle of universal gravitation.
Sailing on the river Thames, Bradley repeatedly observed the
shifting of a vane on the mast as the boat altered its course;
and, having been assured that the motion of the vane meant
that the boat, and not the wind, had altered its direction, he
realized that the position taken up by the vane was determined
by the motion of the boat and the direction of the wind. The
application of this observation to the phenomenon which had so
long perplexed him was not difficult, and, in 1727, he published
his theory of the aberration of lighta corner-stone of the
edifice of astronomical science. Let S (fig. 2) be a star and the
s observer be carried along the line AB; let SB be
perpendicular to AB. If the observer be stationary
at B, the star will appear in the direction BS; if,
however, he traverses the distance BA in the same
time as light passes from the star to his eye, the star will
appear in the direction AS. Since, however, the ob-
server is not conscious of his own translatory motion
a displacement which is at all times parallel to the motion
of the observer. To generalize this, let S (fig. 3) be the sun,

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