were due to instrumental and personal errors. In 1680 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, but these attempts were futile, for the motion
was at variance with that which parallax would occasion. J.
Flamsteed, from measurements made in 1689 and succeeding
years with his mural quadrant, similarly concluded that the
declination of the Pole Star was 40" less in July than in
September. R. Hooke, in 1674, pubilshed his observations of
g Draconis, a star of the second magnitude which passes
practically overhead in the latitude 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 Moineux 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 g Draconis; the telescope,
constructed by George Graham (1675-1751), a celebrated
instrument-maker, was affixed to a vertical chimneystack,
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 g 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
20th. 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 20" more southerly than its December
position. After March it began to pass northwards, a motion
quite apuarent 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 observatiooal
errors. Bradley and Molyneux discussed several hypotheses in
the hope of fixing the solution. One hypothesis was: while
g 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 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 g 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 g Draconis, but few were bright enough to
be observed in Molyneux's telescope. One such star, however,
with a right ascension nearly equal to that of g Draconis,
but in thc 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 g 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 maximum positions was nearly proportional
to the sun's distance from the equinoctial points; and he
reallzed the necessity for more observations before any
generalization could be attempted. For this purpose he
repaired to the Rectory, 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 19th of August 1727, a more convenient telescope
than that at Kew, its range extending over 6 1/4 deg. 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 summatized: (1) 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 courser 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 light--a
corner-stone of the edifice of astronomical science. Let
S (fig. 2) be a star and the 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 E
appear in the direction AS. Since, however, the observer is
not conscious of his own translatory motion with the earth
in its orbit, the star appears to have a displacement which
is at all times parallel to the motion of the observer. To
generalize this, let S (fig. 3) be the sun, ABCD the earth's
orbit, and s the true position of a star. When the earth
is at A, in consequence of aberration, the star is displaced
to a point a, its displacement sa being parallel to the
earth's motion at A; when the earth is at B, the star appears
at b; and so on throughout an orbital revolution of the
earth. Every star, therefore, describes an apparent orbit,
which, if the line joining the sun and the star be perpendicular
to the plane ABCD, will be exactly similar to that of the
earth, i.e. almost a circle. As the star decreases in
latitude, this circle will be viewed more and more obliquely,
becoming a flatter and flatter ellipse until, with zero
latitude, it degenerates into a straight line (fig. 4).
The major axis of any such aberrational ellipse is always parallel
to AC, i.e. the ecliptic, and since it is equal to the ratio
of the velocity of light to the velocity of the earth, it is
necessarily constant. This constant length subtends an angle
of about 40" at the earth; the ``constant of aberration'' is
half this angle. The generally accepted value is 20.445", due
to Struve; the last two figures are uncertain, and all that can
be definitely affirmed is that the value lies between 20.43" and
20.48". The minor axis, on the other hand, is not constant,
but, as we have already seen, depends on the latitude, being
the product of the major axis into the sine of the latitude.
Assured that his explanation was true, Bradley corrected his
observations for aberration, but he found that there still
remained a residuum which was evidently not a parallax, for
it did not exhibit an annual cycle. He reverted to his early
idea of a nutation of the earth's axis, and was rewarded by the
discovery that the earth did possess such an osculation (see
ASTRONOMY). Bradley recognized the fact that the experimental
determination of the aberration constant gave the ratio of the
velocities of light and of the earth; hence, if the velocity
of the earth be known, the velocity of light is determined.
In recent years much attention has been given to the nature
of the propagation of light from the heavenly bodies to the
earth, the argument generally being centred about the relative
effect of the motion of the aether on the velocity of light.
This subject is discussed in the articles AETHER and LIGHT.
REFERENCES.--A detailed account of Bradley's work is
given in S. Rigaud, Memoirs of Bradley (1832), and in
Charles Hutton, Mathematical and Philosophical Dictionary
(1795); a particularly clear and lucid account is given
in H. H. Turner, Astronomical Discovery (1904). The
subject receives treatment in all astronomical works.
II. ABERRIATION IN OPTICAL SYSTEMS Aberration in optical
systems, i.e. in lenses or mirrors or a series of them,
may be defined as the non-concurrence of rays from the
points of an object after transmission through the system;
it happens generally that an image formed by such a system
is irregular, and consequently the correction of optical
systems for aberration is of fundamental importance to the
instruunent-maker. Reference should he made to the articles
REFLEXION, REFRACTION and CAUSTIC for the general characters
of reflected and refracted rays (the article LENS considers
in detail the properties of this instrument, and should also
be consulted); in this article will be discussed the nature,
varieties and modes of aberrations mainly from the practical
point of view, i.e. that of the optical-instrument maker.
Aberrations may be divided in two classes: chromatic (Gr.
oroma, colour) aberrations, caused by the composite
nature of the light generally applied (e.g. white light),
which is dispersed by refraction, and monochromatic (Gr.
monos, one) aberrations produced without dispersion.
Consequently the monochromatic class includes the aberrations
at reflecting surfaces of any coloured light, and at refracting
