I=I0e-kt (2)
where e is the base of Napierian logarithms, and
k is a constant which is practically the same
as for bodies which do not absorb very rapidly.
There is another coefficient of absorption (k) which occurs
in Helmholtz's theory of dispersion (see DISPERSION.)
It is closely related to the coefficient k which we have
just defined, the equation connecting the two being k=4
pk/l, l being the wavelength of the incident light.
The law of absorption expressed by the formula (2) has been
verified by experiments for various solids, liquids and
gases. The method consists in comparing the intensity after
transmission through a layer of known thickness of the absorbent
with the intensity of light from the same source which has
not passed through the medium, k being thus obtained for
various thicknesses and found to be constant. In the case of
solutions, if the absorption of the solvent is negligible, the
eflect of increasing the concentration of the absorbing solute
is the same as that of increasing the thickness in the same
ratio. In a similar way the absorption of light in the
coloured gas chlorine is found to be unaltered if the thickness
is reduced by compression, because the density is increased
in the same ratio that the thickness is reduced. This is
not strictly the case, however, for such gases and vapours
as exhibit well-defined bands of absorption in the spectrum,
as these bands are altered in character by compression.
If white light is allowed to fall on some coloured
solutions, the transmitted light is of one colour when the
thickness of the solution is small, and of quite another
colour if the thickness is great. This curious phenomenon
is known as dichromatism (from di-, two, and chroma,
colour). Thus, when a strong light is viewed through a
solution of chlorophyll, the light seen is a brilliant green
if the thickness is small, but a deep blood-red for thicker
layers. This effect can be explained as follows. The solution
is moderately transparent for a large number of rays in the
neighborhoodood of the green part of the spectrum; it is,
on the whole, much more opaque for red rays, but is readily
penetrated by certain red rays belonging to a narrow region
of the spectrum. The small amount of red transmitted is at
first quite overpowered by the green, but having a smaller
coefficient of absorption, it becomes finally predominant.
The effect is complicated, in the case of chlorophyll and
many other bodies, by selective reflexion and fluorescence.
For the molecular theory of absorption, see SPECTROSCOPY.
REFERENCES.---A. Schuster's Theory of Optics (1904); P. K. L.
Drude's Theory of Optics (Eng. trans., 1902); F. H. Wullner's
Lehrbuch der Experimentalphysik, Bd. iv. (1899). (J. R. C.)
ABSTEMII (a Latin word. from abs. away from. temetum.
intoxicating liquor, from which is derived the English
``abstemious'' or temperate), a name formerly given to such
persons as could not partake of the cup of the Eucharist
on account of their natural aversion to wine. Calvinists
allowed these to communicate in the species of bread only,
touching the cup with their lip; a course which was deemed a
profanation by the Lutherans. Among several Protestant sects,
both in Great Britain and America, abstemii on a somewhat
different principle have appeared in modern times. These are
total abstainers, who maintain that the use of stimulants is
essentially sinful, and allege that the wine used by Christ and
his disciples at the supper was unfermented. They accordingly
communicate in the unfermented ``juice of the grape.''
ABSTINENCE (from Lat. abstinere, to abstain), the fact
or habit of refraining from anything, but usually from the
indulgence of the appetite and especially from strong drink.
``Total abstinence'' and ``total abstainer'' are associated
with taking the pledge to abstain from alcoholic liquor (see
TEMPERANCE.) In the discipline of the Christian Church
abstinence is the term for a less severe form of Fasting (q.v..)
ABSTRACTION (Lat. abs and trahere), the process or
result of drawing away; that which is drawn away, separated or
derived. Thus the noun is used for a summary, compendium
or epitome of a larger work, the gist of which is given in
a concentrated form. Similarly an absent-minded man is said
to be ``abstracted,'' as paying no attention to the matter in
hand. In philosophy the word has several closely related
technical senses. (1) In formal logic it is applied to those
terms which denote qualities, attributes, circumstances,
as opposed to concrete terms, the names of things; thus
``friend'' is concrete, ``friendship'' abstract. The term
which expresses the connotation of a word is therefore an
abstract term, though it is probably not itself connotative;
adjectives are concrete, not abstract, e.g. ``equal'' is
concrete, ``equality'' abstract (cf. Aristotle's aphaeresis
and prosthesis.) (2) The process of abstraction takes
an important place both in psychological and metaphysical
speculation. The psychologist finds among the earliest
of his problems the question as to the process from the
perception of things seen and heard to mental conceptions,
which are ultimately distinct from immediate perception
(see PSYCHOLOGY.) When the mind, beginning with isolated
individuals, groups them together in virtue of perceived
resemblances and arrives at a unity in plurality, the process
by which attention is diverted from individuals and concentrated
on a single inclusive concept (i.e. classification) is one of
abstraction. All orderly thought and all increase of knowledge
depend partly on establishing a clear and accurate connexion
between particular things and general ideas, rules and
principles. The nature of the resultant concepts belongs
to the great controversy between Nominalism, Realism and
Conceptualism. Metaphysics, again, is concerned with the
ultimate problems of matter and spirit; it endeavours to go
behind the phenomena of sense and focus its attention on the
fundamental truths which are the only logical bases of natural
science. This, again, is a process of abstraction, the
attainment of abstract ideas which, apart from the concrete
individuals, are conceived as having a substantive existence.
The final step in the process is the conception of the Absolute
(q.v.), which is abstract in the most complete sense.
Abstraction differs from Analysis, inasmuch as its object is to
select a particular quality for consideration in itself as it is
found in all the ob)ects to which it belongs, whereas analysis
considers all the qualities which belong to a single object.
ABSTRACT OF TITLE, in English law, an epitome of the
various instruments and events under and in consequence
of which the vendor of an estate derives his title
thereto. Such an abstract is, upon the sale or mortgage
of an estate, prepared by some competent person for the
purchaser or mortgagee, and verified by his solicitor by a
comparison with the original deeds. (See CONVEYANCING.)
ABT, FRANZ (1819-1885), German composer, was born on the
22nd of December 1819 at Eilenburg, Saxony, and died at
Wiesbaden on the 31st of March 1885. The best of his popular
songs have become part of the recognized art-folk-music of
Germany; his vocal works, solos, part-songs, &c., enjoyed
an extraordinary vogue all over Europe in the middle of the
19th century, but in spite of their facile tunefulness have
few qualities of lasting beauty. Abt was kapellmeister
at Bernburg in 1841, at Zurich in the same year and at
Brunswick from 1852 to 1882, when he retired to Wiesbaden.
ABU, a mountain of Central India, situated in 24 deg. 36' N.
lat. and 72 deg. 43' E. long., within the Rajputana state of
Sirohi. It is an isolated spur of the Aravalli range, being
completely detached from that chain by a narrow valley 7
miles across, in which flows the western Banas. It rises
from the surrounding plains of Marwar like a precipitous
granite island, its various peaks ranging from 4000 to 5653
feet. The elevations and platforms of the mountain are
covered with elaborately sculptured shrines, temples and
tombs. On the top of the hill is a small round platform
containing a cavern, with a block of granite, bearing the
impression of the feet of Data-Bhrigu, an incarnation of
Vishnu. This is the chief place of pilgrimage for the
Jains, Shrawaks and Banians. The two principal temples are
situated at Deulwara, about the middle of the mountain, and
five miles south-west of Guru Sikra, the highest summit.
They are built of white marble, and are pre-eminent alike for
their beauty and as typical specimens of Jain architecture in
India. The more modern of the two was built by two brothers,
rich merchants, between the years 1197 and 1247, and for
delicacy of carving and minute beauty of detail stands
almost unrivalled, even in this land of patient and lavish
labour. The other was built by another merchant prince, Vimala
Shah, apparently about A.D. 1032, and, although simpler and
bolder in style, is as elaborate as good taste would allow
in a purely architectural object. It is one of the oldest as
well as one of the most complete examples of Jain architecture
known. The principal object within the temple is a cell
lighted only from the door, containing a cross-legged seated
figure of the god Parswanath. The portico is composed of
forty-eight pillars, the whole enclosed in an oblong courtyard
about 140 feet by 90 feet, surrounded by a double colonnade
of smaller pillars, forming porticos to a range of fifty-five
cells, which enclose it on all sides, exactly as they do in
a Buddhist monastery (vihara.) In this temple, however,
each cell, instead of being the residence of R monk, is
occupied by an image of Parswanath, and over the door, or on
the jambs of each, are sculptured scenes from the life. of the
deity. The whole interior is magnificently ornamented.
Abu is now the summer residence of the governor-general's agent
for Rajputana, and a place of resort for Europeans in the hot
weather. It is 16 miles from the Abu road station of the Rajputana
railway. The annual mean temperature is about 70 deg. , rising to
90 deg. in April; but the heat is never oppressive. The annual
rainfall is about 68 inches. The hills are laid out with
driving-roads and bridle-paths, and there is a beautiful little
lake. The chief buildings are a church, club, hospital and a
Lawrence asylum school for the children of British soldiers.
ABU-BEKR (573-634), the name (``Father of the virgin'') of
the first of the Mahommedan caliphs (see CALIPH.) He was
originally called Abd-el-Ka'ba (``servant of the temple''),
and received the name by which he is known historically in
consequence of the marriage of his virgin daughter Ayesha to
Mahomet. He was born at Mecca in the year A.D. 573, a
Koreishite of the tribe of Beni-Taim. Possessed of immense
wealth, which he had himself acquired in commerce, and
held in high esteem as a judge, an interpreter of dreams
and a depositary of the traditions of his race, his early
accession to Islamism was a fact of great importance. On
his conversion he assumed the name of Abd-Alla (servant of
God). His own belief in Mahomet and his doctrines was
so thorough as to procure for him the title El Siddik
(the faithful), and his success in gaining converts was
correspondingly great. In his personal relationship to the
prophet he showed the deepest veneration and most unswerving
devotion. When Mahomet fled from Mecca, Abu-Bekr was
his sole companion, and shared both his hardships and his
