to D= 1/2 (f1+f2), known as the ``condition for oculars.''
If a constant of reproduction, for instance the focal length,
be made equal for two colours, then it is not the same for
other colours, if two different glasses are employed. For
example, the condition for achromatism (4) for two thin lenses
in contact is fulfilled in only one part of the spectrum, since
dn2/dn1 varies within the spectrum. This fact was first
ascertained by J. Fraunhofer, who defined the colours by means
of the dark lines in the solar spectrum; and showed that the
ratio of the dispersion of two glasses varied about 20% from the
red to the violet (the variation for glass and water is about
50%). If, therefore, for two colours, a and b, fa =
fb = f, then for a third colour, c, the focal length is
different, viz. if c lie between a and b, then fc<
f, and vice versa; these algebraic results follow from
the fact that towards the red the dispersion of the positive
crown glass preponderates, towards the violet that of the
negative flint. These chromatic errors of systems, which
are achromatic for two colours, are called the ``secondary
spectrum,'' and depend upon the aperture and focal length
in the same manner as the primary chromatid errors do.
In fig. 11, taken from M. von Rohr,s Theoric und Geschichte des
photographischen Objectivs, the abscissae are focal lengths, and the
ordinates wave-lengths; of the latter the Fraunhofer lines used are--
A' C D Green Hg. F G' Violet Hg.
767.7 656.3 589.3 546.1 486.2 454.1 405.1 mm,
and the focal lengths are made equal for the lines C and F.
In the neighbourhood of 550 mm the tangent to the curve
is parallel to the axis of wave-lengths; and the focal
length varies least over a fairly large range of colour,
therefore in this neighbourhood the colour union is at its
best. Moreover, this region of the spectrum is that which
appears brightest to the human eye, and consequently this
curve of the secondary on spectrum, obtained by making
fc = fF, is, according to the experiments of Sir G.
G. Stokes (Proc. Roy. Soc., 1878), the most suitable for
visual instruments (``optical achromatism,'). In a similar
manner, for systems used in photography, the vertex of the
colour curve must be placed in the position of the maximum
sensibility of the plates; this is generally supposed to be at
G'; and to accomplish this the F and violet mercury lines are
united. This artifice is specially adopted in objectives for
astronomical photography (``pure actinic achromatism''). For
ordinary photography, however, there is this disadvantage:
the image on the focussing-screen and the correct adjustment
of the photographic sensitive plate are not in register; in
astronomical photography this difference is constant, but in
other kinds it depends on the distance of the objects. On this
account the lines D and G' are united for ordinary photographic
objectives; the optical as well as the actinic image is
chromatically inferior, but both lie in the same place; and
consequently the best correction lies in F (this is known as
the ``actinic correction'' or ``freedom from chemical focus'').
Should there be in two lenses in contact the same focal lengths
for three colours a, b, and c, i.e. fa = fb =
fc = f, then the relative partial dispersion (nc-
nb) (na-nb) must be equal for the two kinds of glass
employed. This follows by considering equation (4) for the
two pairs of colours ac and bc. Until recently no glasses
were known with a proportionap degree of absorption; but R.
Blair (Trans. Edin. Soc., 1791, 3, p. 3), P. Barlow, and
F. S. Archer overcame the difficulty by constructing fluid
lenses between glass walls. Fraunhofer prepared glasses which
reduced the secondary spectrum; but permanent success was
only assured on the introduction of the Jena glasses by E.
Abbe and O. Schott. In using glasses not having proportional
dispersion, the deviation of a third colour can be eliminated
by two lenses, if an interval be allowed between them; or
by three lenses in contact, which may not all consist of
the old glasses. In uniting three colours an ``achromatism
of a higher order'' is derived; there is yet a residual
``tertiary spectrum,'' but it can always be neglected.
The Gaussian theory is only an approximation; monochromatic
or spherical aberrations still occur, which will be different
for different colours; and should they be compensated for one
colour, the image of another colour would prove disturbing.
The most important is the chromatic difference of aberration
of the axis point, which is still present to disturb the
image, after par-axial rays of different colours are united
by an appropriate combination of glasses. If a collective
system be corrected for the axis point for a definite
wave-length, then, on account of the greater dispersion in
the negative components--the flint glasses,--over-correction
will arise for the shorter wavelengths (this being the
error of the negative components), and under-correction for
the longer wave-lengths (the error of crown glass lenses
preponderating in the red). This error was treated by
Jean le Rond d'Alembert, and, in special detail, by C. F.
Gauss. It increases rapidly with the aperture, and is more
important with medium apertures than the secondary spectrum
of par-axial rays; consequently, spherical aberration must
be elliminated for two colours, and if this be impossible,
then it must be eliminated for those particular wave-lengths
which are most effectual for the instrument in question (a
graphical representation of this error is given in M. von Rohr,
Theorie und Geschichte des photographischen Objectivs).
The condition for the reproduction of a surface element in the
place of a sharply reproduced point--the constant of the sine
relationship must also be fulfilled with large apertures for
several colours. E. Abbe succeeded in computing microscope
objectives free from error of the axis point and satisfying
the sine condition for several colours, which therefore,
according to his definition, were ``aplanatic for several
colours''; such systems he termed ``apochromatic''. While,
however, the magnification of the individual zones is the
same, it is not the same for red as for blue; and there is a
chromatic difference of magnification. This is produced in the
same amount, but in the opposite sense, by the oculars, which
ate used with these objectives (``compensating oculars''), so
that it is eliminated in the image of the whole microscope.
The best telescope objectives, and photographic objectives
intended for three-colour work, are also apochromatic, even
if they do not possess quite the same quality of correction
as microscope objectives do. The chromatic differences of
other errors of reproduction have seldom practical importances.
1 The investigations of E. Abbe on geometrical optics,
originally published only in his university lectures, were
first compiled by S. Czapski in 1893. See below, AUTHORITIES.
AUTHORITIES.---The standard treatise in English is H. D.
Taylor, A System of Applied Optics (1906); reference may also
be made to R. S. Heath, A Treatise on Geometrical Optics (2nd
ed., 1895); and L A. Herman, A Treatise on Geometrical Optics
(1900). The ideas of Abbe were first dealt with in S. Czapski,
Theorie der optischen Instrumente nach Abbe, published
separately at Breslau in 1893, and as vol. ii. of Winkelmann's
Handbuch der Physik in 1894; a second edition, by Czapski
and O. Eppenstein, was published at Leipzig in 1903 with the
title, Grundzuge der Theorie der optischen Instrumente nach
Abbe, and in vol. ii. of the 2nd ed. of Winkelmann's Handbuch
der Physik. The collection of the scientific staff of Carl
Zeiss at Jena, edited by M. von Rohr, Die bilderzeugung in
optischen Instrumenten vom Standpunkte der geometrischen
Optik (Berlin, 1904), contains articles by A. Konig and
M. von Rohr specially dealing with aberrations. (O. E.)
ABERSYCHAN, an urban district in the northern parliamentary
division of Monmouthshire, England, 11 m. N. by W. of Newport,
on the Great Western, London and North-Western, and Rhymney
railways. Pop. (1901) 17,768. It lies in the narrow upper
valley of the Afon Lwyd on the eastern edge of the great coal
and iron mining district of Glamorganshire and Monmouthshire,
and its large industrial population is occupied in the mines
and ironworks. The neighbourhood is wild and mountainous.
ABERTILLERY, an urban district in the western parliamentary
division of Monmouthshire, England, 16 m. N.W. of Newport, on
the Great Western railway. Pop. (1891) 10,846; (1901) 21,945.
It lies in the mountainous mining district of Monmouthshire
and Glamorganshire, in the valley of the Ebbw Fach, and the
large industrial population is mainly employed in the numerous
coalmines, ironworks and tinplate works. Farther up the
valley are the mining townships of NANTYOLO and BLAINA,
forming an urban district with a population (1901) of 13,489.
ABERYSTWYTH, a municipal borough, market-town and seaport of
Cardiganshire, Wales, near the confluence of the rivers Ystwyth
and Rheidol, about the middle of Cardigan Bay. Pop. (1901)
8013. It is the terminal station of the Cambrian railway,
and also of the Manchester and Milford line. It is the
most popular watering-place on the west coast of Wales, and
possesses a pier, and a fine sea-front which stretches from
Constitution Hill at the north end of the Marine Terrace to the
mouth of the harbour. The town is of modern appearance, and
contains many public buildings, of which the most remarkable
is the imposing but fantastic structure of the University
College of Wales near the Castle Hill. Much of the finest
scenery in mid-Wales hes within easy reach of Aberystwyth.
The history of Aberystwyth may be said to date from the time
of Gilbert Strongbow, who in 1109 erected a fortress on the
present Castle Hill. Edward I. rebuilt Strongbow's castle
in 1277, after its destruction by the Welsh. Between the
years 1404 and 1408 Aberystwyth Castle was in the hands of
Owen Glendower, but finally surrendered to Prince Harry of
Monmouth, and shortly after this the town was incorporated
under the title of Ville de Lampadarn, the ancient name of the
place being Llanbadarn Gaerog, or the fortified Llanbadarn,
to distinguish it from Llanbadarn Fawr, the village one mile
inland. It is thus styled in a charter granted by Henry
VIII., but by Elizabeth's time the town was invariably termed
Aberystwyth in all documents. In 1647 the parliamentarian
troops razed the castle to the ground, so that its remains
are now inconsiderable, though portions of three towers still
exist. Aberystwyth was a contributory parliamentary borough
until 1885, when its representation was merged in that of the
county. In modern times Aberystwyth has become a Welsh
educational centre, owing to the erection here of one of the
three colleges of the university of Wales (1872), and of a
hostel for women in connexion with it. In 1905 it was decided
to fix here the site of the proposed Welsh National Library.
ABETTOR (from ``to abet,'' O. Fr. abeter, a and beter, to
bait, urge dogs upon any one; this word is probably of Scandinavian
origin, meaning to cause to bite), a law term implying one
who instigates, encourages or assists another to commit an
offence. An abettor differs from an accessory (q.v.) in that
he must be present at the commission of the crime; all abettors
(with certain exceptions) are principals, and, in the absence
of specific statutory provision to the contrary, are punishable
