good transmitters, are not so luminous at the same temperature; for instance, melted silver, which reflects well, is not so luminous as carbon at the same temperature, and common salt, which is very transparent for most kinds of radiation, when poured in a fused condition out of a bright red-hot crucible, looks almost like water, showing only a faint red glow for a moment or two. But all such bodies appear to lose their distinctive properties when heated in a vessel which nearly encloses them, for in that case those radiations which they do not emit are either transmitted through them from the walls of the vessel behind, or else reflected from their surface. This fact may be expressed by saying that the radiation within a heated enclosure is the same as that of a perfectly black body.
Coefficient of Absorption, and Law of Absorption.—The law which governs the rate of decay of light intensity in passing through any medium may be readily obtained. If I0 represents the intensity of the light which enters the surface, I1 the intensity after passing through 1 centimetre, I2 the intensity after passing through 2 centimetres, and so on; then we should expect that whatever fraction of I0 is absorbed in the first centimetre, the same fraction of I1 will be absorbed in the second. That is, if an amount j I0 is absorbed in the first centimetre, j I1 is absorbed in the second, and so on. We have then
and so on, so that if I is the intensity after passing through a thickness t in centimetres
| (1). |
We might call j, which is the proportion absorbed in one centimetre, the “coefficient of absorption” of the medium. It would, however, not then apply to the case of a body for which the whole light is absorbed in less than one centimetre. It is better then to define the coefficient of absorption as a quantity k such that k/n of the light is absorbed in 1/n th part of a centimetre, where n may be taken to be a very large number. The formula (1) then becomes
| (2) |
where e is the base of Napierian logarithms, and k is a constant which is practically the same as j for bodies which do not absorb very rapidly.
There is another coefficient of absorption (κ) 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＝4πκ/λ, λ being the wave-length 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 effect 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 δι-, two, and χρῶμα, 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 neighbourhood 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. Wüllner’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
