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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 surfaces of monochromatic or light of single wave length.

(a) Monochromatic Aberration. The elementary theory of optical systems leads to the theorem; Rays of light proceeding from any "object point,' unite in an "image point''; and therefore an "object space'' is reproduced in an "image space.'' The introduction of simple auxiliary terms, due to C. F. Gauss (Dioptrische Untersuchungen, Gottingen, 1841), named the focal lengths and focal planes, permits the determination of the image of any object for any system (see LENS). The Gaussian theory, however, is only true so long as the angles made by all rays with the optical axis (the symmetrical axis of the system) are infinitely small, i.e. with infinitesimal objects, images and lenses; in practice these conditions are not realized, and the images projected by uncorrected systems are, in general, ill defined and often completely blurred, if the aperture or field of view exceeds certain limits. The investigations of James Clerk Maxwell (Phil.Mag., 1856; Quart. Journ. Math., 1858, and Ernst Abbe1) showed that the properties of these reproductions, i.e. the relative position .and magnitude of the images, are not special properties of optical systems, but necessary consequences of the supposition (in Abbe) of the reproduction of all points of a space in image points (Maxwell assumes a less general hypothesis), and are independent of the manner in which the reproduction is effected. These authors proved, however, that no optical system can justify these suppositions, since they are contradictory to the fundamental laws of reflexion and refraction. Consequently the Gaussian theory only supplies a convenient method of approximating to reality; and no constructor would attempt to realize this unattainable ideal. All that at present can be attempted is, to reproduce a single plane in another plane; but even this has not been altogether satisfactorily accomplished, aberrations always occur, and it is improbable that these will ever be entirely corrected.

This, and related general questions, have been treated—besides the above-mentioned authors—by M. Thiesen (Berlin. Akad. Sitzber., 1890, xxxv. 799; Berlin.Phys.Ges. Verb., 1892) and H. Bruns (Leipzig. Math. Phys. Ber., 1895, xxi. 325) by means of Sir W. R. Hamilton's "characteristic function'' (Irish Acad. Trans., "Theory of Systems of Rays,,' 1828, et seq.). Reference may also be made to the treatise of Czapski-Eppenstein, pp. 155-161.

A review of the simplest cases of aberration will now be given. (1) Aberration of axial points (Spherical aberration in the restricted sense). If S (fig.5) be any optical system, rays proceeding from an axis point O under an angle u1 will unite in the axis point O'1; and those under an angle u2 in the axis point O'2. If there be refraction at a collective spherical surface, or through a thin positive lens, O'2 will lie in front of O'1 so long as the angle u2 is greater than u1 ("under correction''); and conversely with a dispersive surface or lenses ("over correction''). The caustic, in the first case, resembles the sign > (greater than); in the second K (less than). If the angle u1 be very small, O'1 is the Gaussian image; and O'1 O'2 is termed the "longitudinal aberration,'' and O'1R the "lateral aberration'' of the pencils with aperture u2. If the pencil with the angle u2 be that of the maximum aberration of all the pencils transmitted, then in a plane perpendicular to the axis at O'1 there is a circular "disk of confusion'' of radius O'1R, and in a parallel plane at O'2 another one of radius O'2R2; between these two is situated the "disk of least confusion.''

The largest opening of the pencils, which take part in the reproduction of O, i.e. the angle u, is generally determined by the margin of one of the lenses or by a hole in a thin plate placed between, before, or behind the lenses of the system. This hole is termed the "stop'' or "diaphragm''; Abbe used the term "aperture stop'' for both the hole and the limiting margin of the lens. The component S1 of the system, situated between the aperture stop and the object O, projects an image of the diaphragm, termed by Abbe the "entrance pupil''; the "exit pupil'' is the image formed by the component S2, which is placed behind the aperture stop. All rays which issue from O and pass through the aperture stop also pass through the entrance and exit pupils, since these are images of the aperture stop. Since the maximum aperture of the pencils issuing from O is the angle u subtended by the entrance pupil at this point, the magnitude of the aberration will be determined by the position and diameter of the entrance pupil. If the system be entirely behind the aperture stop, then this is itself the entrance pupil ("front stop''); if entirely in front, it is the exit pupil ("back stop'').

If the object point be infinitely distant, all rays received by the first member of the system are parallel, and their intersections, after traversing the system, vary according to their "perpendicular height of incidence,'' i.e. their distance from the axis. This distance replaces the angle u in the preceding considerations; and the aperture, i.e. the radius of the entrance pupil, is its maximum value.

(2) Aberration of elements, i.e. smallest objects at right angles to the axis.—If rays issuing from O (fig. 5) be concurrent, it does not follow that points in a portion of a plane perpendicular at O to the axis will be also concurrent, even if the part of the plane be very small. With a considerable aperture, the neighbouring point N will be reproduced, but attended by aberrations comparable in magnitude to ON. These aberrations are avoided if, according to Abbe, the "sine condition,'' sin u'1/sin u1=sin u'2jsin u2, holds for all rays reproducing the point O. If the object point O be infinitely distant, u1 and u2 are to be replaced by pi and h2, the perpendicular heights of incidence; the "sine condition', then becomes sin u,1jh1 sin u'2/h2. A system fulfilling this condition and free from spherical aberration is called "aplanatic'' (Greek a-, privative, plann, a wandering). This word was first used by Robert Blair (d. 1828), professor of practical astronomy at Edinburgh University, to characterize a superior achromatism, and, subsequently, by many writers to denote freedom from spherical aberration. Both the aberration of axis points, and the deviation from the sine condition, rapidly increase in most (uncorrected) systems with the aperture.

(3) Aberration of lateral object points (points beyond the axis) with narrow pencils. Astigmatism.—-A point O (fig. 6) at a finite distance from the, axis (or with an infinitely distant object, a point which subtends a finite angle at the system) is, in general, even then not sharply reproduced, if the pencil of rays issuing from it and traversing the system is made infinitely narrow by reducing the aperture stop; such a pencil consists of the rays which can pass from the object point through the now infinitely small entrance pupil. It is seen (ignoring exceptional cases) that the pencil does not meet he refracting or reflecting surface at right angles; therefore it is astigmatic (Gr. a-, privative, stigmia, a point). Naming the central ray passing through the entrance pupil the "axis of the pencil,' or "principal ray,'' we can say: the rays of the pencil intersect, not in one point, but in two focal lines, which we can assume to be at right angles to the principal ray; of these, one lies in the plane containing the principal ray and the axis of the system, i.e. in the "first principal section'' or "meridional section,', and the other at right angles to it, i.e. in the second principal section or sagittal section. We receive, therefore, in no single intercepting plane behind the system, as, for example, a focussing screen, an image of the object point; on the other hand, in each of two planes lines O' and O" are separately formed (in neighbouring planes ellipses are formed), and in a plane between O' and O" a circle of least confusion. The interval O'O", termed the astigmatic difference, increases, in general, with the angle W made by the principal ray OP with the axis of the system, i.e. with the field of view. Two "astigmatic image surfaces'' correspond to one object plane; and these are in contact at the axis point; on the one lie the focal lines of the first kind, on the other those of the second. Systems in which the two astigmatic surfaces coincide are termed anastigmatic or stigmatic.

Sir Isaac Newron was probably the discoverer of astigmation; the position of the astigmatic image lines was determined by Thomas Young (A Course of Lectures on Natural Philosophy, 1807); and the theory has been recently developed by A. Gullstrand (Skand. Arch. f. physiol., 1890, 2, p. 269; Allgemeine Theorie der monochromat. Aberrationen, etc., Upsala, 1900; Arch. f. Ophth., 1901, 53, pp. 2, 185). A bibliography by P. Culmann is given in M. von Rohr's Die Bilderzeugung in opitschen Instrumenten (Berlin, 1904).

(4) Aberration of lateral object points with broad pencils. Coma. —-By opening the stop wider, similar deviations arise for lateral points as have been already discussed for axial points; but in this case they are much more complicated. The course of the rays in the meridional section is no longer symmetrical to the principal ray of the pencil; and on an intercepting plane there appears, instead of a luminous point, a patch of light, not symmetrical about a point, and often exhibiting a resemblance to a comet having its tail directed towards or away from the axis. From this appearance it takes its name. The unsymmetrical form of the meridional pencil—formerly the only one considered—is coma in the narrower sense only; other errors of coma have been treated by A. Konig and M. von Rohr (op. cit.), and more recently by A. Gullstrand (op. cit.; Ann. d. Phys., 1905, 18, p. 941).

(5) Curvature of the field of the image.—-If the above errors be eliminated, the two astigmatic surfaces united, and a sharp image obtained with a wide aperture—there remains the necessity to correct the curvature of the image surface, especially when the image is to be received upon a plane surface, e.g. in photography. In most cases the surface is concave towards the system.

(6) Distortion of the image.—If now the image be sufficiently sharp, inasmuch as the rays proceeding from every object point meet in an image point of satisfactory exactitude, it may happen that the image is distorted, i.e. not sufficiently like the object. This error consists in the different parts of the object being reproduced with different magnifications; for instance, the inner parts may differ in greater magnification than the outer ("barrel-shaped distortion''), or conversely ("cushion-shaped distortion'') (see fig. 7). Systems free of this aberration are called "orthoscopic'' (orthos , right, skopein to look). This aberration is quite distinct from that of the sharpness of reproduction; in unsharp, reproduction, the question of distortion arises if only parts of the object can be recognized in the figure. If, in an unsharp image, a patch of light corresponds to an object point, the "centre of gravity'' of the patch may be regarded as the image point, this being the point where the plane receiving the image, e.g. a focussing screen, intersects the ray passing through the middle of the stop. This assumption is justified if a poor image on the focussing screen remains stationary when the aperture is diminished; in practice, this generally occurs. This ray, named by Abbe a "principal ray'' (not to be confused with the "principal rays'' of the Gaussian theory), passes through the centre of the enttance pupil before the first refraction, and the centre of the exit pupil after the last refraction. From this it follows that correctness of drawing depends solely upon the principal rays; and is independent of the sharpness or curvature of the image field. Referring to fig. 8, we have O'Q'/OQ = a' tan w'/a tan w = 1/N, where N is the "scale'' or magnification of the image. For N to be constant for all values of w, a' tan w'/a tan w must also be constant. If the ratio a'/a be sufficiently constant, as is often the case, the above relation reduces to the "condition of Airy,'' i.e. tan w'/ tan w= a constant. This simple relation (see Camb. Phil. Trans., 1830, 3, p. 1) is fulfilled in all systems which are symmetrical with respect to their diaphragm (briefly named "symmetrical or holosymmetrical objectives''), or which consist of two like, but different-sized, components, placed from the diaphragm in the ratio of their size, and presenting the same curvature to it (hemisymmetrical objectives); in these systems tan w' / tan w = 1. The constancy of a'/a necessary for this relation to hold was pointed out by R. H. Bow (Brit. Journ. Photog., 1861), and Thomas Sutton (Photographic Notes, 1862); it has been treated by O. Lummer and by M. von Rohr (Zeit. f. Instrumentenk., 1897, 17, and 1898, 18, p. 4). It requires the middle of the aperture stop to be reproduced in the centres of the entrance and exit pupils without spherical aberration. M. von Rohr showed that for systems fulfilling neither the Airy nor the Bow-Sutton condition, the ratio a' tan w'/a tan w will be constant for one distance of the object. This combined condition is exactly fulfilled by holosymmetrical objectives reproducing with the scale 1, and by hemisymmetrical, if the scale of reproduction be equal to the ratio of the sizes of the two components.

Analytic Treatment of Aberrations.—-The preceding review of the several errors of reproduction belongs to the "Abbe theory of aberrations,'' in which definite aberrations are discussed separately; it is well suited to practical needs, for in the construction of an optical instrument certain errors are sought to be eliminated, the selection of which is justified by experience. In the mathematical sense, however, this selection is arbitrary; the reproduction of a finite object with a finite aperture entails, in all probability, an infinite number of aberrations. This number is only finite if the object and aperture are assumed to be "infinitely small of a certain order''; and with each order of infinite smallness, i.e. with each degree of approximation to reality (to finite objects and apertures), a certain number of aberrations is associated. This connexion is only supplied by theories which treat aberrations generally and analytically by means of indefinite series.

A ray proceeding from an object point O (fig. 9) can be defined by the co-ordinates (x, e). Of this point O in an object plane I, at right angles to the axis, and two other co-ordinates (x, y), the point in which the ray intersects the entrance pupil, i.e. the plane II. Similarly the corresponding image ray may be defined by the points (x', e'), and (x', y'), in the planes I' and II'. The origins of these four plane co-ordinate systems may be collinear with the axis of the optical system; and the corresponding axes may be parallel. Each of the four co-ordinates x', e', x', y' are functions of x, e, x, y; and if it be assumed that the field of view and the aperture be infinitely small, then x, e, x, y are of the same order of infinitesimals; consequently by expanding x', e', x', y' in ascending powers of x, e, x, y, series are obtained in which it is only necessary to consider the lowest powers. It is readily seen that if the optical system be symmetrical, the orqins of the co-ordinate systems collinear with the optical axis and the corresponding axes parallel, then by changing the signs of x, e, x, y, the values x', e', x', y' must likewise change their sign, but retain their arithmetical values; this means that the series are restricted to odd powers of the unmarked variables.

The nature of the reproduction consists in the rays proceeding from a point O being united in another point O'; in general, this will not be the case, for x', e' vary if x, e be constant, but x, y variable. It may be assumed that the planes I' and II' are drawn where the images of the planes I and II are formed by rays near the axis by the ordinary Gaussian rules; and by an extension of these rules, not, however, corresponding to reality, the Gauss image point O'0, with co-ordinates x'0, e'0, of the point O at some distance from the axis could be constructed. Writing Dx'=x'-x'0 and De'=e'-e'0, then Dx' and De' are the aberrations belonging to x, e and x, y, and are functions of these magnitudes which, when expanded in series, contain only odd powers, for the same reasons as given above. On account of the aberrations of all rays which pass through O, a patch of light, depending in size on the lowest powers of x, e, x, y which the aberrations contain, will be formed in the plane I'. These degrees, named by (J. Petzval (Bericht uber die Ergebnisse einiger dioptrischer Untersuchnungen, Buda Pesth, 1843; Akad. Sitzber., Wien, 1857, vols. xxiv. xxvi.) "the numerical orders of the image,'' are consequently only odd powers; the condition for the formation of an image of the mth order is that in the series for Dx' and De' the coefficients of the powers of the 3rd, 5th . . . (m-2)th degrees must vanish. The images of the Gauss theory being of the third order, the next problem is to obtain an image of 5th order, or to make the coefficients of the powers of 3rd degree zero. This necessitates the satisfying of five equations; in other words, there are five alterations of the 3rd order, the vanishing of which produces an image of the 5th order.

The expression for these coefficients in terms of the constants of the optical system, i.e. the radii, thicknesses, refractive indices and distances between the lenses, was solved by L. Seidel (Astr. Nach., 1856, p. 289); in 1840, J. Petzval constructed his portrait objective, unexcelled even at the present day, from similar calculations, which have never been published (see M. von Rohr, Theorie und Geschichte des photographischen Objectivs, Berlin, 1899, p. 248). The theory was elaborated by S. Finterswalder (Munchen. Acad. Abhandl., 1891, 17, p. 519), who also published a posthumous paper of Seidel containing a short view of his work (Munchen. Akad. Sitrber., 1898, 28, p. 395); a simpler form was given by A. Kerber (Beitrage zur Dioptrik, Leipzig, 1895-6-7-8-9). A. Konig and M. von Rohr (see M. von Rohr, Die Bilderzeugung in optischen Instrumenten, pp. 317-323) have represented Kerber's method, and have deduced the Seidel formulae from geometrical considerations based on the Abbe method, and have interpreted the analytical results geometrically (pp. 212-316).

The aberrations can also be expressed by means of the "characteristic function'' of the system and its differential coefficients, instead of by the radii, &c., of the lenses; these formulae are not immediately applicable, but give, however, the relation between the number of aberrations and the order. Sir William Rowan Hamilton (British Assoc. Report, 1833, p. 360) thus derived the aberrations of the third order; and in later times the method was pursued by Clerk Maxwell (Proc. London Math. Soc., 1874—1875; (see also the treatises of R. S. Heath and L. A. Herman), M. Thiesen (Berlin. Akad. Sitzber., 1890, 35, p. 804), H. Bruns (Leipzig. Math. Phys. Ber., 1895, 21, p. 410), and particularly successfully by K. Schwartzschild (Gottingen. Akad. Abhandl., 1905, 4, No. 1), who thus discovered the aberrations of the 5th order (of which there are nine), and possibly the shortest proof of the practical (Seidel) formulae. A. Gullstrand (vide supra, and Ann. d. Phys., 1905, 18, p. 941) founded his theory of aberrations on the differential geometry of surfaces.

The aberrations of the third order are: (1) aberration of the axis point; (2) aberration of points whose distance from the axis is very small, less than of the third order—-the deviation from the sine condition and coma here fall together in one class; (3) astigmatism; (4) curvature of the field; (5) distortion.

(1) Aberration of the third order of axis points is dealt with in all text-books on optics. It is important for telescope objectives, since their apertures are so small as to permit higher orders to be neglected. For a single lens of very small thickness and given power, the aberration depends upon the ratio of the radii r:r', and is a minimum (but never zero) for a certain value of this ratio; it varies inversely with the refractive index (the power of the lens remaining constant). The total aberration of two or more very thin lenses in contact, being the sum of the individual aberrations, can be zero. This is also possible if the lenses have the same algebraic sign. Of thin positive lenses with n=1.5, four are necessary to correct spherical aberration of the third order. These systems, however, are not of great practical importance. In most cases, two thin lenses are combined, one of which has just so strong a positive aberration ("under-correction,'' vide supra) as the other a negative; the first must be a positive lens and the second a negative lens; the powers, however: may differ, so that the desired effect of the lens is maintained. It is generally an advantage to secure a great refractive effect by several weaker than by one high-power lens. By one, and likewise by several, and even by an infinite number of thin lenses in contact, no more than two axis points can be reproduced without aberration of the third order. Freedom from aberration for two axis points, one of which is infinitely distant, is known as "Herschel's condition.'' All these rules are valid, inasmuch as the thicknesses and distances of the lenses are not to be taken into account.

(2) The condition for freedom from coma in the third order is also of importance for telescope objectives; it is known as "Fraunhofer's condition.'' (4) After eliminating the aberration On the axis, coma and astigmatism, the relation for the flatness of the field in the third order is expressed by the "Petzval equation,'' S1/r(n'-n) = 0, where r is the radius of a refracting surface, n and n' the refractive indices of the neighbouring media, and S the sign of summation for all refracting surfaces.

Practical Elimination of Aberrations.—-The existence of an optical system, which reproduces absolutely a finite plane on another with pencils of finite aperture, is doubtful; but practical systems solve this problem with an accuracy which mostly suffices for the special purpose of each species of instrument. The problem of finding a system which reproduces a given object upon a given plane with given magnification (in so far as aberrations must be taken into account) could be dealt with by means of the approximation theory; in most cases, however, the analytical difficulties are too groat. Solutions, however, have been obtained in special cases (see A. Konig in M. von Rohr's Die Bilderzeugung, p. 373; K. Schwarzschild, Gottingen. Akad. Abhandl., 1905, 4, Nos. 2 and 3). At the present time constructors almost always employ the inverse method: they compose a system from certain, often quite personal experiences, and test, by the trigonometrical calculation of the paths of several rays, whether the system gives the desired reproduction (examples are given in A. Gleichen, Lehrbuch der geometrischen Optik, Leipzig and Berlin, 1902). The radii, thicknesses and distances are continually altered until the errors of the image become sufficiently small. By this method only certain errors of reproduction are investigated, especially individual members, or all, of those named above. The analytical approximation theory is often employed provisionally, since its accuracy does not generally suffice.

In order to render spherical aberration and the deviation from the sine condition small throughout the whole aperture, there is given to a ray with a finite angle of aperture u* (width infinitely distant objects: with a finite height of incidence h*) the same distance of intersection, and the same sine ratio as to one neighbouring the axis (u* or h* may not be much smaller than the largest aperture U or H to be used in the system). The rays with an angle of aperture smaller than u* would not have the same distance of intersection and the same sine ratio; these deviations are called "zones,'' and the constructor endeavours to reduce these to a minimum. The same holds for the errors depending upon the angle of the field of view, w: astigmatism, curvature of field and distortion are eliminated for a definite value, w*, "zones of astigmatism, curvature of field and distortion,' attend smaller values of w. The practical optician names such systems: "corrected for the angle of aperture u* (the height of incidence h*) or the angle of field of view w*.'' Spherical aberration and changes of the sine ratios are often represented graphically as functions of the aperture, in the same way as the deviations of two astigmatic image surfaces of the image plane of the axis point are represented as functions of the angles of the field of view.

The final form of a practical system consequently rests on compromise; enlargement of the aperture results in a diminution of the available field of view, and vice versa. The following may be regarded as typical:—(1) Largest aperture; necessary corrections are—for the axis point, and sine condition; errors of the field of view are almost disregarded; example— high-power microscope objectives. (2) Largest field of view; necessary corrections are—for astigmatism, curvature of field and distortion; errors of the aperture only slightly regarded; examples—photographic widest angle objectives and oculars. Between these extreme examples stands the ordinary photographic objective: the portrait objective is corrected more with regard to aperture; objectives for groups more with regard to the field of view. (3) Telescope objectives have usually not very large apertures, and small fields of view; they should, however, possess zones as small as possible, and be built in the simplest manner. They are the best for analytical computation.

(b) Chromatic or Colour Aberration. In optical systems composed of lenses, the position, magnitude and errors of the image depend upon the refractive indices of the glass employed (see LENS, and above, "Monochromatic Aberration''). Since the index of refraction varies with the colour or wave length of the light (see DISPERSION), it follows that a system of lenses (uncorrected) projects images of different colours in somewhat different places and sizes and with different aberrations; i.e. there are "chromatic differences'' of the distances of intersection, of magnifications, and of monochromatic aberrations. If mixed light be employed (e.g. white light) all these images are formed; and since they are ail ultimately intercepted by a plane (the retina of the eye, a focussing screen of a camera, &c.), they cause a confusion, named chromatic aberration; for instance, instead of a white margin on a dark background, there is perceived a coloured margin, or narrow spectrum. The absence of this error is termed achromatism, and an optical system so corrected is termed achromatic. A system is said to be "chromatically under-corrected'' when it shows the same kind of chromatic error as a thin positive lens, otherwise it is said to be "over-corrected.''

If, in the first place, monochromatic aberrations be neglected —-in other words, the Gaussian theory be accepted—-then every reproduction is determined by the positions of the focal planes, and the magnitude of the focal lengths, or if the focal lengths, as ordinarily happens, be equal, by three constants of reproduction. These constants are determined by the data of the system (radii, thicknesses, distances, indices, &c., of the lenses); therefore their dependence on the refractive index, and consequently on the colour, are calculable (the formulae are given in Czapski-Eppenstein, Grundzuge der Theorie der optischen Instrumente (1903, p. 166). The refractive indices for different wave lengths must be known for each kind of glass made use of. In this manner the conditions are maintained that any one constant of reproduction is equal for two different colours, i.e. this constant is achromatized. For example, it is possible, with one thick lens in air, to achromatize the position of a focal plane of the magnitude of the focal length. If all three constants of reproduction be achromatized, then the Gaussian image for all distances of objects is the same for the two colours, and the system is said to be in "stable achromatism.''

In practice it is more advantageous (after Abbe) to determine the chromatic aberration (for instance, that of the distance of intersection) for a fixed position of the object, and express it by a sum in which each component conlins the amount due to each refracting surface (see Czapski-Eppenstein, op. cit. p. 170; A. Konig in M. v. Rohr's collection, Die Bilderzeugung, p. 340). In a plane containing the image point of one colour, another colour produces a disk of confusion; this is similar to the confusion caused by two "zones'' in spherical aberration. For infinitely distant objects the radius Of the chromatic disk of confusion is proportional to the linear aperture, and independent of the focal length (vide supra, "Monochromatic Aberration of the Axis Point''); and since this disk becomes the less harmful with au increasing image of a given object, or with increasing focal length, it follows that the deterioration of the image is propor-, tional to the ratio of the aperture to the focal length, i.e. the "relative aperture.'' (This explains the gigantic focal lengths in vogue before the discovery of achromatism.)

Examples.—(a) In a very thin lens, in air, only one constant of reproduction is to be observed, since the focal length and the distance of the focal point are equal. If the refractive index for one colour be n, and for another n+dn, and the powers, or reciprocals of the focal lengths, be f and f + d f, then (1) df/f = dn/(n-1) = 1/n; dn is called the dispersion, and n the dispersive power of the glass.

(b) Two thin lenses in contact: let f1 and f2 be the powers corresponding to the lenses of refractive indices n1 and n2 and radii r'1, r"1, and r'2, r"2 respectively; let f denote the total power, and d f, dn1, dn2 the changes of f, n1, and n2 with the colour. Then the following relations hold:—

(2) f = f1-f2== (n1 - 1)(1/r'1-1/r''1) +(n2-1)(1/ r'2 - 1/r''2) = (n1 - 1)k1 + (n2 - 1)k2; and

(3) df = k1dn1 + k2dn2. For achromatism df = 0, hence, from (3),

(4) k1/k2 = -dn2 / dn1, or f1/f2 = -n1/ n2. Therefore f1 and f2 must have different algebraic signs, or the system must be composed of a collective and a dispersive lens. Consequently the powers of the two must be different (in order that f be not zero (equation 2)), and the dispersive powers must also be different (according to 4).

Newton failed to perceive the existence of media of different dispersive powers required by achromatism; consequently he constructed large reflectors instead of refractors. James Gregory and Leonhard Euler arrived at the correct view from a false conception of the achromatism of the eye; this was determined by Chester More Hall in 1728, Klingenstierna in 1754 and by Dollond in 1757, who constructed the celebrated achromatic telescopes. (See TELESCOPE.)

Glass with weaker dispersive power (greater v) is named "crown glass''; that with greater dispersive power, "flint glass.'' For the construction of an achromatic collective lens (f positive) it follows, by means of equation (4), that a collective lens I. of crown glass and a dispersive lens II. of flint glass must be chosen; the latter, although the weaker, corrects the other chromatically by its greater dispersive power. For an achromatic dispersive lens the converse must be adopted. This is, at the present day, the ordinary type, e.g., of telescope objective (fig. 10); the values of the four radii must satisfy the equations (2) and (4). Two other conditions may also be postulated: one is always the elimination of the aberration on the axis; the second either the "Herschel'' or "Fraunhofer Condition,'' the latter being the best vide supra, "Monochromatic Aberration''). In practice, however, it is often more useful to avoid the second condition by making the lenses have contact, i.e. equal radii. According to P. Rudolph (Eder's Jahrb. f. Photog., 1891, 5, p. 225; 1893, 7, p. 221), cemented objectives of thin lenses permit the elimination of spherical aberration on the axis, if, as above, the collective lens has a smaller refractive index; on the other hand, they permit the elimination of astigmatism and curvature of the field, if the collective lens has a greater refractive index (this follows from the Petzval equation; see L. Seidel, Astr. Nachr., 1856, p. 289). Should the cemented system be positive, then the more powerful lens must be positive; and, according to (4), to the greater power belongs the weaker dispersive power (greater v), that is to say, clown glass; consequently the crown glass must have the greater refractive index for astigmatic and plane images. In all earlidr kinds of glass, however, the dispersive power increased with the refractive index; that is, v decreased as n increased; but some of the Jena glasses by E. Abbe and O. Schott were crown glasses of high refractive index, and achromatic systems from such crown glasses, with flint glasses of lower refractive index, are called the "new achromats,'' and were employed by P. Rudolph in the first "anastigmats'' (photographic objectives).

Instead of making df vanish, a certain value can be assigned to it which will produce, by the addition of the two lenses, any desired chromatic deviation, e.g. sufficient to eliminate one present in other parts of the system. If the lenses I. and II. be cemented and have the same refractive index for one colour, then its effect for that one colour is that of a lens of one piece; by such decomposition of a lens it can be made chromatic or achromatic at will, without altering its spherical effect. If its chromatic effect (df/f) be greater than that of the same lens, this being made of the more dispersive of the two glasses employed, it is termed "hyper-chromatic.''

For two thin lenses separated by a distance D the condition for achromatism is D = v1f1+v2f2; if v1=v2 (e.g. if the lenses be made of the same glass), this reduces 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 to the same extent as the actual perpetrator of the offence. A person may in certain cases be convicted as an abettor in the commission of an offence in which he or she could not be a principal, e.g. a woman or boy under fourteen years of age in aiding rape, or a solvent person in aiding and abetting a bankrupt to commit offences against the bankruptcy laws.

ABEYANCE (O. Fr. abeance, "gaping''), a state of expectancy in respect of property, titles or office, when the right to them is not vested in any one person, but awaits the appearance or determination of the true owner. In law, the term abeyance can only be applied to such future estates as have not yet vested or possibly may not vest. For example, an estate is granted to A for life, with remainder to the heir of B, the latter being alive; the remainder is then said to be in abeyance, for until the death of B it is uncertain who his heir is. Similarly the freehold of a benefice, on the death of the incumbent, is said to be in abeyance until the next incumbent takes possession. The most common use of the term is in the case of peerage dignities. If a peerage which passes to heirs-general, like the ancient baronies by writ, is held by a man whose heir-at-law is neither a male, nor a woman who is an only child, it goes into abeyance on his death between two or more sisters or their heirs, and is held by no one till the abeyance is terminated; if eventually only one person represents the claims of all the sisters, he or she can claim the termination of the abeyance as a matter of right. The crown can also call the peerage out of abeyance at any moment, on petition, in favour of any one of the sisters or their heirs between whom it is in abeyance. The question whether ancient earldoms created in favour of a man and his "heirs'' go into abeyance like baronies by writ has been raised by the claim to the earldom of Norfolk created in 1312, discussed before the Committee for Privileges in 1906. It is common, but incorrect, to speak of peerage dignities which are dormant (i.e. unclaimed) as being in abeyance. (J. H. R.)

ABGAR, a name or title borne by a line of kings or toparchs, apparently twenty-nine in number, who reigned in Osrhoene and had their capital at Edessa about the time of the Christian era. According to an old tradition, one of these princes, perhaps Abgar V. (Ukkama or Uchomo, "the black''), being afflicted with leprosy, sent a letter to Jesus, acknowledging his divinity, craving his help and offering him an asylum in his own residence, but Jesus wrote a letter declining to go, promising, however, that after his ascension he would send one of his disciples. These letters are given by Eusebius (Eccl. Hist. i. 13), who declares that the Syriac document from which he translates them had been preserved in the archives at Edessa from the time of Abgar. Eusebius also states that in due course Judas, son of Thaddaeus, was sent (in 340 = A.D. 29). In another form of the story, derived from Moses of Chorene, it is said further that Jesus sent his portrait to Abgar, and that this existed in Edessa (Hist. Armen., ed. W. Whiston, ii. 29-32). Yet another version is found in the Syriac Doctrina Addaei (Addaeus=Thaddaeus), edited by G. Phillips (1876). Here it is said that the reply of Jesus was given not in writing, but verbally, and that the event took place in 343 (A.D. 32). Greek forms of the legend are found in the Acta Thaddaei (C. Tischendorf, Acta apostoloruiu apocr. 261 ff.).

These stories have given rise to much discussion. The testi- mony of Augustine and Jerome is to the effect that Jesus wrote nothing. The correspondence was rejected as apocryphal by Pope Gelasius and a Roman Synod (c. 495), though, it is true, this view has not been shared universally by the Roman church (Tillemont, Memoires, i. 3, pp. 990 ff ). Amongst Evangelicals the spuriousness of the letters is almost generally admitted. Lipsius (Die Edessenische Abgarsage, 1880) has pointed out anachronisms which seem to indicate that the story is quite unhistorical. The first king of Edessa of whom we have any trustworthy information is Abgar VIII., bar Ma'nu (A.D. 176-213). It is suggested that the legend arose from a desire to trace the christianizing of his kingdom to an apostolic source. Eusebius gives the legend in its oldest form; it was worked up in the Doctrina Addaei in the second half of the 4th century; and Moses of Chorene was dependent upon both these sources.

BIBLIOGRAPHY—-R, Schmidt in Herzoe-Hauck, Realencyklopadie; Die Edessenische Abgarsage kritisch untersucht (1880); Matthes, Die Edessenische Abgarsage auf ihre Fortbildung untersucht (1882); Les Origines de l'eglise d'Edesse et la legende d'A. (1888); A. Harnack, Geschichte d. altchristlichen Litteratur, i. 2 (1893); L. Duchesne, Bulletin critique, 1889, pp. 41-48; for the Epistles see APOCRYPHAL LITERATURE, sect. "New Testament'' (c.)

ABHIDHAMMA, the name of one of the three Pitakas, or baskets of tradition, into which the Buddhist scriptures (see BUDDHISM) are divided. It consists of seven works: 1. Dhamma Sangani (enumeration of qualities). 2. Vibhanga (exposition). 3. Katha Vatthu (bases of opinion). 4. Puggala Pannatti (on individuals). 5. Dhatu Katha (on relations of moral dispositions). 6. Yamaka (the pairs, that is, of ethical states). 7. Patthana (evolution of ethical states). These have now been published by the Pah Text Society. The first has been translated into English, and an abstract of the third has been published. The approximate date of these works is probably from about 400 B.C. to about 250 B.C., the first being the oldest and the third the latest of the seven. Before the publication of the texts, when they were known only by hearsay, the term Abhidhamma was usually rendered "Metaphysics.'' This is now seen to be quite erroneous. Dhamma means the doctrine, and Abhidhamma has a relation to Dhamma similar to that of by-law to law. It expands, classifies, tabulates, draws corollaries from the ethical doctrines laid down in the more popular treatises. There is no metaphysics in it atnall, only psychological ethics of a peculiarly dry and scholastic kind. And there is no originality in it; only endless permutations and combinations of doctrines already known and accepted. As in the course of centuries the doctrine itself, in certain schools, varied, it was felt necessary to rewrite these secondary works. This was first done, so far as is at present known, by the Sarvastivadins (Realists), who in the century before and after Christ produced a fresh set of seven Abhidhamma books. These are lost in India, but still exist in Chinese translations. The translations have been analysed in a masterly way by Professor Takakusu in the article mentioned below, They deal only with psychological ethics. In the course of further centuries these hooks in turn were superseded by new treatises; and in one school at least, that of the Maha-yana (great Vehicle) there was eventually developed a system of metaphysics. But the word Abhidhamma then fell out of use in that school, though it is still used in the schools that continue to follow the original seven books.

See Buddhist Psychology by Caroline Rhys Davids (London, 1900), translation of the Dhamma Sangani, with valuable introduction; or the Royal Asiatic Society, 1892, contains an abstract of the Katha "On the Abhidhamma books of the Sarvastivadins,'' by Prof. Takakusu, in Journal of the Pali Text Society, 1905.

(l'. W. R. D.)

ABHORRERS, the name given in 1679 to the persons who expressed their abhorrence at the action of those who had signed petitions urging King Charles II. to assemble parliament. Feel ing against Roman Catholics, and especially against James, duke of York, was running strongly; the Exclusion Bill had been passed by the House of Commons, and the popularity of James, duke of Monmouth, was very great. To prevent this bill from passing into law, Charles had dissolved parliament in July 1679, and in the following October had prorogued its successor without allowing it to meet. He was then deluged with petitions urging him to call it together, and this agitation was opposed by Sir George Jeffreys (q.v.) and Francis Wythens, who presented addresses expressing "abhorrence'' of the "Petitioners,'' and thus initiated the movement of the abhorrers, who supported the action of the king. "The frolic went all over England,'' says Roger North; and the addresses of the Abhorrers which reached the king from all parts of the country formed a counterblast to those of the Petitioners. It is said that the terms Whig and Tory were first applied to English political parties in consequence of this dispute.

ABIATHAR (Heb. Ebyathar, "the [divine] father is pre-eminent''), in the Bible, son of Ahimelech or Ahijah, priest at Nob. The only one of the priests to escape from Saul's massacre, he fled to David at Keilah, taking with him the ephod (1 Sam. xxii. 20 f., xxiii. 6, 9). He was of great service to David, especially at the time of the rebellion of Absalom (2 Sam. xv. 24, 29, 35, xx. 25). In 1 Kings iv. 4 Zadok and Abiathar are found acting together as priests under Solomon. In 1 Kings i. 7, 19, 25, however, Abiathar appears as a supporter of Adonijah, and in ii. 22 and 26 it is said that he was deposed by Solomon and banished to Anathoth. In 2 Sam. viii. 17 "Abiathar, the son of Ahimelech'' should be read, with the Syriac, for "Ahimelech, the son of Abiathar.'' For a similar confusion see Mark ii. 26.

ABICH, OTTO WILHELM HERMANN VON (1806-1886), German mineralogist and geologist, was born at Berlin on the 11th of December 1806, and educated at the university in that city. His earliest scientific work related to spinels and other minerals, and later he made special studies of fumaroles, of the mineral deposits around volcanic vents and of the structure of volcanoes. In 1842 he was appointed professor of mineralogy in the university of Dorpat, and henceforth gave attention to the geology and mineralogy of Russia. Residing for some time at Tiflis he investigated the geology of the Caucasus. Ultimately' he retired to Vienna, where he died on the 1st of July 1886. The mineral Abichite was named after him.

PUBLICATIONS.—-Vues illustratives de quelques phenomenes geologiques, prises sur le Vesuve et l'Etna, pendant les annees 1833 et 1834 (Berlin, 1836); Ueber die Natur und den Zusammenhang der vulcanischen Bildungen (Brunswick, 1841); Geologische Forschungen in den Kaukasischen Landern (3 vols., Vienna, 1878, 1882, and 1887).

ABIGAIL (Heb. Abigayil, perhaps "father is joy''), or ABIGAL (2 Sam. iii. 3), in the Bible, the wife of Nabal the Carmelite, on whose death she became the wife of David (1 Sam. xxv.). By her David had a son, whose name appears in the Hebrew of 2 Sam. iii. 3 as Chileab, in the Septuagint as Daluyah, and in 1 Chron. iii. 1 as Daniel. The name Abigail was also borne by a sister of David (2 Sam. xvii. 25; 1 Chron. ii. 16 f.). From the former (self-styled "handmaid'' 1 Sam. xxv. 25 f.) is derived the colloquial use of the term for a waiting-woman (cf. Abigail, the "waiting gentlewoman,'' in Beaumont and Fletcher's Scornful Lady.)

ABIJAH (Heb. Abiyyah and Abiyyahu, "Yah is father''), a name borne by nine different persons mentioned in the Old Testament, of whom the most noteworthy are the following. (i) The son and successor of Rehoboam, king of Judah (2 Chron. xii. 16—xiii.), reigned about two years (918-915 B.C..) The accounts of him in the books of Kings and Chronicles are very conflicting (compare 1 Kings xv. 2 and 2 Chron. xi.20 with 2 Chron. xiii.2). The Chronicler tells us that he has drawn his facts from the Midrash (commentary) of the prophet Iddo This is perhaps sufficient to explain the character of the narrative. (2) The second son of Samuel (1 Sam. viii. 2; 1 Chron. vi. 28 [13j). He and his brother Joel judged at Beersheba. Their misconduct was made by the elders of Israel a pretext for demanding a king (1 Sam. viii. 4). (3) A son of Jeroboam I., king of Israel; he died young (1 Kings xiv. 1 ff., 17). (4) Head of the eighth order of priests (1 Chron. xxiv. 10), the order to which Zacharias, the father of John the Baptist, belonged (Luke i. 5).

The alternative form Abijam is probably a mistake, though it is upheld by M. Jastrow.

ABILA, (1) a city of ancient Syria, the capital of the tetrarchy of Abilene, a territory whose extent it is impossible to define. It is generally called Abila of Lysanias, to distinguish it from (2) below. Abila was an important town on the imperial highway from Damascus to Heliopolis (Baalbek). The site is indicated by ruins of a temple, aqueducts, &c., and inscriptions on the banks of the river Barada at Suk Wadi Barada, a village called by early Arab geographers Abil-es-Suk, between Baalbek and Damascus. Though the names Abel and Abila differ in derivation and in meaning, their similarity has given rise to the tradition that this was the place of Abel's burial. According to Josephus, Abilene was a separate Iturean kingdom till A.D. 37, when it was granted by C to Agrippa I.; in 52 Claudius granted it to Agrippa II. (See also LYSANIAS.) (2) A city in Perea, now Abil-ez-Zeit.

ABILDGAARD, NIKOLAJ ABRAHAM (1744-1809), called "the Father of Danish Painting,'' was born at Copenhagen, the son of Soren Abildgaard, an antiquarian draughtsman of repute. He formed his style on that of Claude and of Nicolas Poussin, and was a cold theorist, inspired not by nature but by art. As a technical painter he attained remarkable success, his tone being very harmonious and even, but the effect, to a foreigner's eye, is rarely interesting. His works are scarcely known out of Copenhagen, where he won an immense fame in his own generation. He was the founder of the Danish school of painting, and the master of Thorwaldsen and Eckersherg.

ABIMELECH (Hebrew for "father of [or is] the king''). (1) A king of Gerar in South Palestine with whom Isaac, in the Bible, had relations. The patriarch, during his sojourn there, alleged that his wife Rebekah was his sister, but the king doubting this remonstrated with him and pointed out how easily adultery might have been unintentionally committed (Gen. xxvi.). Abimelech is called "king of the Philistines,'' but the title is clearly an anachronism. A very similar story is told of Abraham and Sarah (ch. xx.), but here Abimelech takes Sarah to wife, although he is warned by a divine vision before the crime is actually committed. The incident is fuller and shows a great advance in bdeas of morality. Of a more primitive character, however, is another parallel story of Abraham at the court of Pharaoh, king of Egypt (xii. 10-20), where Sarah his wife is taken into the royal household, and the plagues sent by Yahweh lead to the discovery of the truth. Further incidents in Isaac's life at Gerar are narrated in Gen. xxvi. (cp. xxi. 22-34, time of Abraham), notably a covenant with Abimelech at Beer-sheba (whence the name is explained "well of the oath''); (see ABRAHAM.) By a pure error, or perhaps through a confusion in the traditions, Achish the Philistine (of Gath, 1 Sam. xxi., xxvii.), to whom David fled, is called Abimelech in the superscription to Psalm xxxiv.

(2) A son of Jerubbaal or Gideon (q.v.), by his Shechemite concubine (Judges viii. 31, ix.). On the death of Gideon, Abimelech set himself to assert the authority which his father had earned, and through the influence of his mother's clan won over the citizens of Shechem. Furnished with money from the treasury of the temple of Baal-berith, he hired a band of followers and slew seventy (cp. 2 Kings x. 7) of his brethren at Ophrah, his father's home. This is one of the earliest recorded instances of a practice common enough on the accession of Oriental despots. Abimelech thus became king, and extended his authority Over central Palestine. But his success was short-lived, and the subsequent discord between Abimelech and the Shechemites was regarded as a just reward for his atrocious massacre. Jotham, the only one who is said to have escaped, boldly appeared on Mount Gerizim and denounced the ingratitude of the townsmen towards the legitimate sons of the man who had saved them from Midian. "Jotham's fable'' of the trees who desired a king may be foreign to the context; it is a piece of popular lore, and cannot be pressed too far: the nobler trees have no wish to rule over others, only the bramble is self-confident. The "fable'' appears to be antagonistic to ideas of monarchy. The origin of the conflicts which subsequently arose is not clear. Gaal, a new-comer, took the opportunity at the time of the vintage, when there was a festival in tho temple, to head a revolt and seized Shechem. Abimelech, warned by his deputy Zebul, left his residence at Arumah and approached the city. In a fine bit of realism we are told how Gaal observed the approaching foe and was told by Zebul, "You see the shadow of the hills as men,'' and as they drew nearer Zebul's ironical remark became a taunt, "Where is now thy mouth? is not this the people thou didst despise? go now and fight them!'' This revolt, which Abimelech successfully quelled, appears to be only an isolated episode. Another account tells of marauding bands of Shechemites which disturbed the district. The king disposed his men (the whole chapter is specially interesting for the full details it gives of the nature of ancient military operations), and after totally destroying Shechem, proceeded against Thebez, which had also revolted. Here, while storming the citadel, he was struck on the head by a fragment of a millstone thrown from the wall by a woman. To avoid the disgrace of perishing by a woman's hand, he begged his armour-bearer to run him through the body, but his memory was not saved from the ignominy he dreaded (2 Sam. xi. 21). It is usual to regard Abimelech's reign as the first attempt to establish a monarchy in Israel, but the story is mainly that of the rivalries of a half-developed petty state, and of the ingratitude of a community towards the descendants of its deliverer. (See, further, JEWS, JUDGES.) (S. A. C.)

ABINGDON, a market town and municipal borough in the Abingdon parliamentary division of Berkshire, England, 6 m. S. of Oxford, the terminus of a branch of the Great Western railway from Radley. Pop. (1901) 6480. It lies in the fiat valley of the Thames, on the west (right) bank, where the small river Ock flows in from the Vale of White Horse. The church of St Helen stands near the river, and its fine Early English tower with Perpendicular spire is the principal object in the pleasant views of the town from the river. The body of the church, which has five aisles, is principally Perpendicular. The smaller church of St Nicholas is Perpendicular in appearance, though parts of the fabric are older. Of a Benedictine abbey there remain a beautiful Perpendicular gateway, and ruins of buildings called the prior's house, mainly Early English, and the guest house, with other fragments. The picturesque narrow-arched bridge over the Thames near St Helen's church dates originally from 1416. There may be mentioned further the old buildings of the grammar school, founded in 1563, and of the charity called Christ's Hospital (1583); while the town-hall in the marketplace, dating from 1677, is attributed to Inigo Jones. The grammar school now occupies modern buildings, and ranks among the lesser public schools of England, having scholarships at Pembroke College, Oxford. St Peter's College, Radley, 2 m. from Abingdon, is one of the principal modern public schools. It was opened in 1847. The buildings he close to the Thames, and the school is famous for rowing, sending an eight to the regatta at Henley each year. Abingdon has manufactures of clothing and carpets and a large agricultural trade. The borough is under a mayor, four aldermen and twelve councillors. Area, 730 acres.

Abingdon (Abbedun, Abendun) was famous for its abbey, which was of great wealth and importance, and is believed to have been founded in A.D. 675 by Cissa, one of the subreguli of Centwin. Abundant charters from early Saxon monarchs are extant confirming laws and privileges to the abbey, and the earliest of these, from King Ceadwalla, was granted before A.D. 688. in the reign of Alfred the abbey was destroyed by the Danes, but it was restored by Edred, and an imposing list of possessions in the Domesday survey evidences recovered prosperity. William the Conqueror in 1084 celebrated Easter at Abingdon, and left his son, afterwards Henry I., to be educated at the abbey. After the dissolution in 1538 the town sank into decay, and in 1555, on a representation of its pitiable condition, Queen Mary granted a charter establishing a mayor, two bailiffs, twelve chief burgesses, and sixteen secondary burgesses, the mayor to be clerk of the market, coroner and a Justice of the peace. The council was empowered to elect one burgess to parliament, and this right continued until the Redistribution of Seats Act of 1885. A town clerk and other officers were also appointed, and the town boundaries described in great detail. Later charters from Elizabeth, James I., James II., George Il. and George III. made no considerable change. James II. changed the style of the corporation to that of a mayor, twelve aldermen and twelve burgesses. The abbot seems to have held a market from very early times, and charters for the holding of markets and fairs mere granted by various sovereigns from Edward I. to George II. In the 13th and 14th centuries Abingdon was a flourishing agricultural centre with an extensive trade in wool, and a famous weaving and clothing manufacture. The latter industry declined before the reign of Queen Mary, but has since been revived.

The present Christ's Hospital originally belonged to the Gild of the Holy Cross, on the dissolution of which Edward VI. founded the hospital under its present name.

See Victoria County History, Berkshire; Joseph Stevenson, Chronicon Monasterii de Abingdon, A.D. 201—1189 (Rolls Series, 2 vols., London, 1858).

ABINGER, JAMES SCARLETT, 1ST BARON (1769-1844), English judge, was born on the 13th of December 1760 in Jamaica, where his father, Robert Scarlett, had property. In the summer of 1785 he was sent to England to complete his education, and went to Trinity College, Cambridge, taking his B.A. degree in 1789. Having entered the Inner Temple he was called to the bar in 1791, and joined the northern circuit and the Lancashire sessions. Though he had no professional connexions, by steady application he gradually obtained a large practice, ultimately confining himself to the Court of King's Bench and the northern circuit. He took silk in 1816, and from this time till the close of 1834 he was the most successful lawyer at the bar; he was particularly effective before a jury, and his income reached the high-water mark of L. 18,500, a large sum for that period. He began life as a Whig, and first entered parliament in 1819 as member for Peterborough, representing that constituency with a short break (1822-1823) till 1830, when he was elected for the borough of Malton. He became attorney-general, and was knighted when Canning formed his ministry in 1827; and though he resigned when the duke of Wellington came into power in 1828, he resumed office in 1829 and went out with the duke of Wellington in 1830. His opposition to the Reform Bill caused his severance from the Whig leaders, and having joined the Tories he was elected, first for Colchester and then in 1832 for Norwich, for which borough he sat until the dissolution of parliament. He was appointed lord chief baron of the exchequer in 1834, and presided in that court for more than nine years. While attending the Norfolk circuit on the 2nd of April he was suddenly seized with apoplexy, and died in his lodgings at Bury on the 7th of April 1844. He had been raised to the peerage as Baron Abinger in 1835, taking his title from the Surrey estate he had bought in 1813. The qualities which brought him success at the bar were not equally in place on the bench; he was partial, dictatorial and vain; and complaint was made of his domineering attitude towards juries. But his acuteness of mind and clearness of expression remained to the end. Lord Abinger was twice married (the second time only six months before his death), and by his first wife (d. 1829) had three sons and two daughters, the title passing to his eldest son Robert (1794-1861). His second son, General Sir James Yorke Scarlett (1799-1871), leader of the heavy cavalry charge at Balaclava, is dealt with in a separate article; and his elder daughter, Mary, married John, Baron Campbell, and was herself created Baroness Stratheden (Lady Stratheden and Campbell) (d. 1860). Sir Philip Anglin Scarlett (d. 1831), Lord Abinger's younger brother, was chief justice of Jamaica.

See P. C. Scarlett, Memoir of Jaimes, 1st Lord Abinger (1877); Foss's Lives of the Judges; E. Manson, Builders of our Law (1904).

ABINGTON, FRANCES (1737-1815), English actress, was the daughter of a private soldier named Barton, and was, at first, a flower girl and a street singer. She then became servant to a French milliner, obtaining a taste in dress and a knowledge of French which afterwards stood her in good stead. Her first appearance on the stage was at the Haymarket in 1755 as Miranda in Mrs Centlivre's Busybody. In 1756, on the recommendation of Samuel Foote, she became a member of the Drury Lane company, where she was overshadowed by Mrs Pritchard and Kitty Clive. In 1759, after an unhappy marriage with her music-master, one of the royal trumpeters, she is mentioned in the bills as Mrs Abington. Her first success was in Ireland as Lady Townley, and it was only after five years, on the pressing invitation of Garrick, that she returned to Drury Lane. There she remained for eighteen years, being the original of more than thirty important characters, notably Lady Teazle (1777). Her Beatrice, Portia, Desdemona and Ophelia were no less liked than her Miss Hoyden, Biddy Tipkin, Lucy Lockit and Miss Prue. It was in the last character in Love for Love that Reynolds painted his best portrait of her. In 1782 she left Drury Lane for Covent Garden. After an absence from the stage from 1790 until 1797, she reappeared, quitting it finally in 1799. Her ambition, personal wit and cleverness won her a distinguished position in society, in spite of her humble origin. Women of fashion copied her frocks, and a head-dress she wore was widely adopted and known as the "Abington cap.'' She died on the 4th of March 1815.

ABIOGENESIS, in biology, the term, equivalent to the older terms "spontaneous generation,'' Generatio acquivoca, Generatio primaria, and of more recent terms such as archegenesis and archebiosis, for the theory according to which fully formed living organisms sometimes arise from not-living matter. Aristotle explicitly taught abiogenesis, and laid it down as an observed fact that some animals spring from putrid matter, that plant lice arise from the dew which falls on plants, that fleas are developed from putrid matter, and so forth. T. J. Parker (Elementary Biology) cites a passage from Alexander Ross, who, commenting on Sir Thomas Browne's doubt as to "whether mice may be bred by putrefaction,'' gives a clear statement of the common opinion on abiogenesis held until about two centuries ago. Ross wrote: "So may he (Sir Thomas Browne) doubt whether in cheese and timber worms are generated; or if beetles and wasps in cows' dung; or if butterflies, locusts, grasshoppers, shell-fish, snails, eels, and such like, be procreated of putrefied matter, which is apt to receive the form of that creature to which it is by formative power disposed. To question this is to question reason, sense and experience. If he doubts of this let him go to Egypt, and there he will find the fields swarming with mice, begot of the mud of Nylus, to the great calamity of the inhabitants.''

The first step in the scientific refutation of the theory of abiogenesis was taken by the Italian Redi, who, in 1668, proved that no maggots were "bred'' in meat on which flies were prevented by wire screens from laying their eggs. From the 17th century onwards it was gradually shown that, at least in the case of all the higher and readily visible organisms, abiogenesis did not occur, but that omne vivum e vivo, every living thing came from a pre-existing living thing.

The discovery of the microscope carried the refutation further. In 1683 A. van Leeuwenhoek discovered bacteria, and it was soon found that however carefully organic matter might be protected by screens, or by being placed in stoppered receptacles, putrefaction set in, and was invariably accompanied by the appearance of myriads of bacteria and other low organisms. As knowledge of microscopic forms of life increased, so the apparent possibilities of abiogenesis increased, and it became a tempting hypothesis that whilst the higher forms of life arose only by generation from their kind, there was a perpetual abiogenetic fount by which the first steps in the evolution of living organisms continued to arise, under suitable conditions, from inorganic matter. It was due chiefly to L. Pasteur that the occurrence of abiogenesis in the microscopic world was disproved as much as its occurrence in the macroscopic world. If organic matter were first sterilized and then prevented from contamination from without, putrefaction did not occur, and the matter remained free from microbes. The nature of sterilization, and the difficulties in securing it, as well as the extreme delicacy of the manipulations necessary, made it possible for a very long time to be doubtful as to the application of the phrase omne vivum e vivo to the microscopic world, and there still remain a few belated supporters of abiogenesis. Subjection to the temperature of boiling water for, say, half an hour seemed an efficient mode of sterilization, until it was discovered that the spores of bacteria are so involved in heat-resisting membranes, that only prolonged exposure to dry, baking heat can be recognized as an efficient process of sterilization. Moreover, the presence of bacteria, or their spores, is so universal that only extreme precautions guard against a re-infection of the sterilized material. It may now be stated definitely that all known living organisms arise only from pre-existing living organisms.

So far the theory of abiogenesis may be taken as disproved. It must be noted, however, that this disproof relates only to known existing organisms. All these are composed of a definite substance, known as protoplasm (q.v.), and the modern refutation of abiogenesis applies only to the organic forms in which protoplasm now exists. It may be that in the progress of science it may yet become possible to construct living protoplasm from non-living material. The refutation of abiogenesis has no further bearing on this possibility than to make it probable that if protoplasm ultimately be formed in the laboratory, it will be by a series of stages, the earlier steps being the formation of some substance, or substances, now unknown, which are not protoplasm. Such intermediate stages may have existed in the past, and the modern refutation of abiogenesis has no application to the possibility of these having been formed from inorganic matter at some past time. Perhaps the words archebiosis, or archegenesis, should be reserved for the theory that protoplasm in the remote past has been developed from not-living matter by a series of steps, and many of those, notably T. H. Huxley, who took a large share in the process of refuting contemporary abiogenesis, have stated their belief in a primordial archebiosis. (See BIOGENESIS and LIFE.) (P. C. M.)

ABIPONES, a tribe of South American Indians of Guaycuran stock recently inhabiting the territory lying between Santa Fe and St Iago. They originally occupied the Chaco district of Paraguay, but were driven thence by the hostility of the Spaniards. According to Martin Dobrizhoffer, a Jesuit missionary, who, towards the end of the 18th century, lived among them for a period of seven years, they then numbered not more than 5000. They were a well-formed, handsome people, with black eyes and aquiline noses, thick black hair, but no beards. The hair from the forehead to the crown of the head was pulled out, this constituting a tribal mark. The faces, breasts and arms of the women were covered with black figures of various designs made with thorns, the tattooing paint being a mixture of ashes and blood. The lips and ears of both sexes were pierced. The men were brave fighters, their chief weapons being the bow and spear. No child was without bow and arrows; the bow-strings were made of foxes' entrails. In battle the Abipones wore an armour of tapir's hide over which a jaguar's skin was sewn. They were excellent swimmers and good horsemen. For five months in the year when the floods were out they lived on islands or even in shelters built in the trees. They seldom married before the age of thirty, and were singularly chaste. "With the Abipones,'' says Darwin, "when a man chooses a wife, he bargains with the parents about the price. But it frequently happens that the girl rescinds what has been agreed upon between the parents and bridegroom, obstinately rejecting the very mention of marriage. She often runs away and hides herself, and thus eludes the bridegroom.'' Infanticide was systematic, never more than two children being reared in one family, a custom doubtless originating in the difficulty of subsistence. The young were suckled for two years. The Abipones are now believed to be extinct as a tribe.

Martin Dobrizhoffer's Latin Historia de Abiponibus (Vienna, 1784) was translated into English by Sara Coleridge, at the suggestion of Southey, in 1822, under the title of An Account of the Abipones (3 vols.).

ABITIBBI, a lake and river of Ontario, Canada. The lake, in 49 deg. N., 80 deg. W., is 60 m. long and studded with islands. It is shallow, and the shores in its vicinity are covered with small timber. It was formerly employed by the Hudson's Bay Company as part of a canoe route to the fur lands of the north. The construction of the Grand Trunk Pacific railway through this district has made it of some importance. Its outlet is Abitibbi river, a rapid stream, which after a course of 200 m. joins the Moose river, flowing into James Bay.

ABJURATION (from Lat. abjurare, to forswear), a solemn repudiation or renunciation on oath. At common law, it signified the oath of a person who had taken sanctuary to leave the realm for ever; this was abolished in the reign of James I. The Oath at Abjuration, in English history, was a solemn disclaimer, taken by members of parliament, clergy and laymen against the right of the Stuarts to the crown, imposed by laws of William III., George I. and George III.; but its place has since been taken by the oath of allegiance.

ABKHASIA, or ABHASIA, a tract of Russian Caucasia, government of Kutais. The Caucasus mountains on the N. and N.E. divides it from Circassia; on the S.E. it is bounded by Mingrelia; and on the S.W. by the Black Sea. Though the country is generally mountainous, with dense forests of oak and walnut, there are some deep, well-watered valleys, and the climate is mild. The soil is fertile, producing wheat, maize, grapes, figs, pomegranates and wine. Cattle and horses are bred. Honey is produced; and excellent arms are made. This country was subdued (c. 550) by the Emperor Justinian, who introduced Christianity. Native dynasties ruled from 735 to the 15th century, when the region was conquered by the Turks and became Mahommedan. The Russians acquired possession of it piecemeal between 1829 and 1842, but their power was not firmly established until after 1864. Area, 2800 sq. m. The principal town is Sukhum-kaleh. Pop. 43,000, of whom two-thirds are Mingrelians and one-third Abkhasians, a Cherkess or Circassian race. The total number of Abkhasians in the two governments of Kutais and Kuban was 72,103 in 1897; large numbers emigrated to the Turkish empire in 1864 and 1878.

ABLATION (from Lat. ablatus, carried away), the process of removing anything; a term used technically in geology of the wearing away of a rock or glacier, and in surgery for operative removal.

ABLATITIOUS (from Lat. ablatus, taken away). reducina or withdrawing; in astronomy a force which interferes between the moon and the earth to lessen the strength of gravitation is called "ablatitious,'' just as it is called "addititious'' when it increases that strength.

ABLATIVE (Lat. ablativus, sc. casus, from ablatum, taken away), in grammar, a case of the noun, the fundamental sense of which is direction from; in Latin, the principal language in which the case exists, this has been extended, with or without a preposition, to the instrument or agent of an act, and the place or time at, and manner in, which a thing is done. The case is also found in Sanskrit, Zend, Oscan and Umbrian, and traces remain in other languages. The "Ablative Absolute,'' a grammatical construction in Latin, consists of a noun in the ablative case, with a participle, attribute or qualifying word agreeing with it, not depending on any other part of the sentence, to express the time, occasion or circumstance of a fact.

ABLUTION (Lat. ablutio, from ablucre, "to wash off''), a washing, in its religious use, destined to secure that ceremonial or ritualistic purity which must not be confused with the physical or hygienic cleanliness of persons and things obtained by the use of soap and water.1 Indeed the two states may contradict each other, as in the case of the 4th-century Christian pilgrim to Jerusalem who boasted that she had not washed ner face for eighteen years for fear of removing therefrom the holy chrism of baptism. The purport, then, of ablutions is to remove, not dust and dirt, but the—-to us imaginary—stains contracted by contact with the dead, with childbirth, with menstruous women, with murder whether wilful or involuntary, with almost any form of bloodshed, with persons of inferior caste, with dead animal refuse, e.g. leather or excrement, with leprosy, madness and any form of disease. Among all races in a certain grade of development such associations are vaguely felt to be dangerous and to impair vitality. In a later stage the taint is regarded as alive, as a demon or evil spirit alighting on and passing into the things and persons exposed to contamination. In general, water, cows' urine and blood of swine are the materials used in ablutions. Of these water is the commonest, and its efficacy is enhanced if it be running, and still more if a magical or sacramental virtue has been imparted to it by ritual blessing or consecration. Some concrete examples will best illustrate the nature of such ablutions. In the Atharva-Veda, vii. 116, we have this allopathic remedy for fever. The patient's skin burns, that of a frog is cold to the touch; therefore tie to the foot of the bed a frog, bound with red and black thread, and wash down the sick man so that the water of ablution falls

1 in its technical ecclesiastical sense the ablution is the ritual washing of the chalice and of the priest's fingers after the celebration of Holy Communion in the Catholic Church. The wine and water used for this purpose are themselves sometimes called "the ablution.'' on the frog. Let the medicine man or magician pray that the fever may pass into the frog, and the frog be forthwith re-leased, and the cure will be effected. In the old Athenian Anthesteria the blood of victims was poured over the unclean. A bath of bulls' blood was much in vogue as a baptism in the mysteries of Attis. The water must in ritual washings run off in order to carry away the miasma or unseen demon of disease; and accordingly in baptism the early Christians used living or running water. Nor was it enough that the person baptized should himself enter the water; the baptizer must pour it over his head, so that it run down his person. Similarly the Brahman takes care, after ablution of a person, to wipe the cathartic water off from head to feet downwards, that the malign influence may pass out through the feet. The same care is shown in ritual ablutions in the Bukovina and elsewhere.

Water and fire, spices and sulphur, are used in ritual cleansings, says Iamblichus in his book on mysteries (v. 23), as being specially full of the divine nature. Nevertheless in all religions, and especially in the Brahmanic and Christian, the cathartic virtue of water is enhanced by the introduction into it by means of suitable prayers and incantations of a divine or magical power. Ablutions both of persons and things are usually cathartic, that is, intended to purge away evil influences (kathairein, to make katharos, pure). But, as Robertson Smith observes, "holiness is contagious, just as uncleanness is''; and common things and persons may become taboo, that is, so holy as to be dangerous and useless for daily life through the mere infection of holiness. Thus in Syria one who touched a dove became taboo for one whole day, and if a drop of blood of the Hebrew sin-offering fell on a garment it had to be ritually washed off. It was as necessary in the Hebrew religion for the priest to wash his hands ofter handling the sacred volume as before. Christians might not enter a church to say their prayers without first washing their hands. So Chrysostom says: "Although our hands may be already pure, yet unless we have washed them thoroughly, we do not spread them upwards in prayer.'' Tertullian (c. 200) had long before condemned this as a heathen custom; none the less, it was insisted on in later ages, and is a survival of the pagan lustrations or perirranteria. Sozomen (vi. 6) tells how a priest sprinkled Julian and Valentinian with water according to the heathen custom as they entered his temple. The same custom prevails among Mahommedans. Porphyry (de Abst. ii. 44) relates that one who touched a sacrifice meant to avert divine anger must bathe and wash his clothes in running water before returning to his city and home, and similar scruples in regard to holy objects and persons have been observed among the natives of Polynesia, New Zealand and ancient Egypt. The rites, met within all lands, of pouring out water or bathing in order to produce rain from heaven, differ in their significance from ablutions with water and belong to the realm of sympathetic magic.

There are certain forms of purification which one does not know whether to describe as ablutions or anointings. Thus Demosthenes in his speech "On the crown', accused Aeschines of having "purified the initiated and wiped them clean with (not from) mud and pitch.'' Smearing with gypsum (titanos. titanos) had a similar purifying effect, and it has been suggested i that the Titans were no more than old-world votaries who had so disguised themselves. Perhaps the use of ashes in mourning had the same origin. In the rite of death-bed penance given in the old Mozarabic Christian ritual of Spain, ashes were poured over the sick man.

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