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Abacus (aßat, a board or slab), origi- | Liverpool, and so on. The general rule nally any table of rectangular form. The for abbreviating longhand is to omit the term was also applied to a board or table vowels, except initial vowels and such as on which mathematicians drew diagrams. it is obviously necessary to retain to pro The abacus, as at present used to instruct vent confusion. See SHORTHAND. children in the use of numbers, consists of Abbreviations. The abbreviations in a number of parallel wires on which beads scholastic use are chiefly those employed are strung, the upper wire denoting units, to denote academic attainments, as B.A., the next tens, &c.

Bachelor of Arts, M.A., Master of Arts, Abbey or Monastic Schools.—There &c., or to facilitate the working of papers, were two kinds of schools under the direc- &c., in mathematics and other studies. tion of the monasteries : (1) schools almost In university examinations candidates are exclusively devoted to the higher educa- generally permitted to abbreviate extention of novices and those who, having sively in working geometrical papers by completed their probation, had taken the using signs and figures, though many vow; (2) schools distinct from these, in teachers object to the adoption of this which instruction, either gratuitous or on practice by young pupils. payment, was given to children of all A B C Method, by which children learn classes of society living in the neighbour all the letters of the alphabet from an hood of the monastery. The former were A B C book, from the blackboard, from the prototypes of the collegiate schools, or cards, &c. The pupil is instructed to colleges, which developed into the colleges point to the letters singly in turn, and at Oxford, Cambridge, and, later on, those thus associate the form with the name. at Winchester and Eton. From the latter This system has now generally been supersprang many of the endowed grammar seded by the Word Method. schools (q.v.), which, at the dissolution of A B C Shooters (German A B C the monasteries, were placed in the hands Schützen).—Jocular name for German chilof lay trustees by charter or letters patent dren learning the A B C. Schützen'in of the Tudor sovereigns. Cathedral schools the Middle Ages were the younger wanwere similar to this latter kind of mon- dering scholars, who, like fags, were comastic school.

pelled to find food for the elder boys by Abbreviated Longhand.- Schoolmas- begging or shooting,' i.e. purloining, stray ters do not generally encourage the prac- fowls, &c. In German students' slang tice of abbreviated longhand by their schiessen (shoot) still has this sense. pupils, but for their own purposes teachers Abelard, Peter, b. at Palais, near could save much time by adopting the Nantes, 1079, d. 1142.—He is one of abbreviations now in general use by the most famous of the early Scholastics, telegraphists, journalists, and authors. and, as the founder of conceptualism, exerAmongst the commoner of these abbrevia- cised a powerful influence over mediæval tions are l, the ; o, of; w, with ; 4, could ; thought. He was the pupil of Roscelh, have; ha, had; bn, been ; f, for; fm, linus and William of Champeaux. His from , nt, not ; t, that; wh, who, which, attainments and his eloquence combined or what ; 9, ing; t", tion or tian ; mt, to give him an important place as an edument; sh, shall; abt, about ; circs, cir- cationist. His father was wealthy, and cumstances; B’m, Birmingham; L'pool, spared no expense in his son's educa


tion. Having learnt Hebrew, Greek, and children. As a source of inattention it Latin, Abelard went to the University of must be carefully distinguished by the Paris, which enjoyed at that time a wide- teacher from mental sluggishness, as comspread fame. There he became the pupil monly illustrated in idle wandering of the of Guillaume de Champeaux, the most skil. thoughts, or what Locke calls 'saunterful dialectician of the age. Abelard soon ing.' As the history of more than one surpassed his master, and often challenged distinguished man tells us, absent-mindedhim to public disputations. Abelard rn ness in relation to school lessons may be tired to Melun and lectured there, whither a sign of intense mental activity otherwise some of the Parisian students followed absorbed ; and the same fact is still more him. But his health gave way, although strikingly illustrated in the habitual abnot yet twenty-two, owing to his severe straction of the student from his surstudies; and for some time he sought roundings. Absent-mindedness finds its rest. After many changes we find him proper remedy in the habitual awakening again in Paris, as professor of divinity, of the child's interest in his surroundings, surrounded by the most eminent scholars of in the careful training of the observing his age. Here it was that he received faculty and the practical aptitudes, and in Héloise, niece of the rich canon Fulbert, the investing of subjects of instruction as a pupil. Her philosopl.ic studies, how- with all possible attractiveness. See ATever, ended in a romantic attachment that TENTION. has become as celebrated in literature as Abstract and Concrete.-These refer that of Swift and Stella. This disturbed to a fundamental distinction in our know. the rest of Abelard's life, and caused him ledge. We may have a knowledge of some much trouble and many enemies. In particular thing in its completeness, as, for Abelard's time there were two courses example, of water as something at once of scholastic instruction : the 'trivium,' Auid, transparent, &c. This is knowledge containing grammar, rhetoric, and dia- of things in the concrete. On the other lectics or philosophy; the quadrivium,' hand, we may think about the property comprising arithmetic, music, geometry, fluidity apart from water and all other astronomy. Abelard's contemporaries particular substances. This knowledge of agree in regarding him as accom- qualities, as distinct from concrete things plished master in all these. This must be as whɔles, is said to be knowledge of the understood, of course, with regard to the abstract. In Logic all names of things, age in which he lived, for it is certain whether general or singular, are called that no Greek text of the writings of concrete terms, all names of qualities abAristotle existed at that time in France. stract terms. It is evident from this defiSome MS. copies of his works remain, and nition that the region of abstract knowledge they may be seen in the British Museum. is that with which science is specially conIn them and in his printed works all the cerned ; for all science deals with the comquotations from Aristotle are in Latin. mon qualities or properties of things, such Aberdeen University. See UNIVER as form, chemical qualities, &c., and the


general laws which govern these. It is a Absenteeism. See ATTENDANCE. fundamental maxim of modern education

Absent-mindedness.—This term indi- that concrete knowledge must precede cates that variety of inattention which abstract. Before a child can gain any arises from mental preoccupation. This abstract ideas, as those of number, force, may be due to the action of some external moral courage, some knowledge of constimulus, as when a child fails to listen to crete examples is indispensable. Hence what is said to him because he is watching it follows that subjects which deal largely the movements of a fly on the window. with the concrete, as descriptive geography, In a special manner the term refers to the narrative history, &c., should form the withdrawal of attention from the external first part of the curriculum. A concrete surroundings as a whole, as when a child presentation of the more striking facts of is wholly inattentive to what it sees and physical science by means of object leshears because its thoughts are absorbed in sons, supplemented by description, is the the anticipation of some treat. A bent natural introduction to the more abstract to dreamy imagination and reverie is a consideration of its laws. (On the transicommon cause of absent-mindedness in tion froin concrete to abstract see Herbert





Spencer, Education, chap. ii.; Bain, Edu Abstract Science. - All science, as cation as Science, chap. vii.)

general knowledge of things, i.e. of things Abstraction. In its widest scope this so far as they have common qualities, is term means the withdrawal of the mind abstract knowledge. At the same time a from one object or feature of an object in certain group of the sciences are marked order to fix it on another. It is in this off as Abstract and another group as Consense the necessary accompaniment of all crete. The former deal with a few proconcentration. In a more special sense perties common to a wide variety of things. it refers to the turning away of the Thus mathematics, the best type of an absthoughts from the differences among indi- tract science, deals with the most general vidual things so as to fix them on the aspect of things, viz. quantity ; for all oh points of similarity. It is thus the opera- jects, of whatever nature they may be, tion which immediately leads to a know- exhibit the attribute of quantity. On the ledge of the common qualities of things, other hand, the sciences of description and i.e. to abstract knowledge. Thus, in order classification, as botany, deal with the to gain a clear idea of roundness, the child many common qualities or characters of a has to compare a number of round things, comparatively restricted region of phenoas a ball, a marble, an orange, &c., and inena. Hence they are called Concrete. abstract from the other and distinguishing In many cases we are able to distinguish features of each, as the colour of the an abstract or theoretical and a concrete orange. Abstraction of a greater or less branch of the same subject. Thus in medegree of difficulty is always involved in chanics we have a theoretical department classification or generalisation, i.e. the pro- dealing with the universal laws of equilicess by which the mind forms the notion brium and motion, and concrete applicaof a general class, as animal, toy, &c. It tions of these to particular forms and also enters as the main ingredient into combinations of matter, as hydrostatics. induction, i.e. the operation by which the The distinction between Abstract and Conmind passes from a consideration of par- crete science has an important bearing on ticular facts to that of the general law the order in which the sciences should be which they obey. Since in all cases abs- studied. The Abstract sciences, being traction is a casting aside or putting out of relatively simple and fundamental, should sight of much that is present to the mind, i precede the corresponding Concrete it calls for an effort of will. Hence the sciences. Thus a certain knowledge of difficulty attending the study of all gene- mathematics is necessary to the study of ralities and abstract subjects in the case of physics, chemistry, &c. (See Bain, Logic, young children. The more numerous and Deduction, Introduction, and H. Spencer, striking the points of diversity, and the Education, chap. i.) more subtle and obscure the points of Academy (Gr. 'Akadnuía).- A recreasimilarity, the greater the effort of abstrac- tion ground at Athens, believed to have tion required. The faculty of abstraction, been named after Academus, an Athenian though appearing in a crude form in young hero of the time of the Trojan expedition. children, is the last to reach its full deve- The Academia was the favourite resort of lopment. The higher abstractions, as those Plato. Here he used to lecture to his of mathematics, physical science, gram- pupils and followers; hence his school of mar, &c., should only be introduced in the philosophy was called the Academic School. later stages of education. The natural After the revival of letters the term Acarepugnance of the child to abstraction demy came to be applied to the higher must be met by a careful process of pre- schools of instruction, particularly to such paration. This includes the accumulation as were of a unique and special character, of a sufficient quantity of concrete know- as the academies of music, fine arts, the ledge, a judicious selection of examples naval and military academies, &c. In under each head, and a gradual transition England the application of the word has from exercises of an easy character per- been considerably extended and approformed on sensible qualities, as weight, priated as the appellation of schools of figure, &c., to those of a more difficult various grades. A similar abuse of the order dealing with recondite qualities. term is also common in the United States. (See Sully, The Teacher's Handbook of In France, however, as in Russia, Sweden, Psychology, chaps. xii. and xiii )

and other European countries, the use of

the term is now almost confined to the itself indefinitely, spreading out into all learned societies for the advancement of the surrounding air, like the ripples on a literature, science, and art. The Académie smooth lake fronı a stone which is thrown française is the final court of appeal on in. The rate at which this disturbance questions relating to French philology, travels is in air about 1,090 feet a second. grammar, &c. The Académie des inscrip- The distance which a complete wave occutions et belles-lettres is another famous asso- pies varies. The central c of the piano is ciation of French savants. The desirable- a recurrent wave whose length is about ness of establishing an English academy of 4 feet. Hence the number of waves learned men having the authority of the which fall on the ear in a second can be Académie française has been ably advo- calculated. If each takes up 4f feet and cated by Mr. Matthew Arnold and others. there are enough of them in a second to Accidence. See GRAMMAR.

cover 1,090 feet, then we approximately Accidents. See School SURGERY. find the number by dividing 1,090 by 45,

Accomplishments. This terin refers to which gives us 264. The standard numthat part of the education of girls (q.v.) ber of vibrations for the central c has which includes instruction in those arts altered in recent times owing to a change which for the most part are ornamental. in the standard of pitch. It is now exAccomplishments include drawing and actly 264 vibrations in a second. Any painting of a mildly artistic kind, dancing, concussion or rapid disturbance leads to and that kind of music which finds favour the formation of waves in the air or in in drawing-rooms. Locke attached great any medium. These waves are not in importance to dancing as a necessary ac- general musical notes. For the produccomplishment even for a gentleman, but tion of the latter regularly recurrent objected to painting on the ground that disturbances are necessary, and ordinary ‘ill painting is one of the worst things in noises consist of an indefinite number of the world, and to attain a tolerable degree musical notes so mingled together that of skill in it requires too much of a man's their separate existences are undiscernible. cime. See ÆSTHETIC CULTURE.

The chief modes of producing musical Acoustics.—The subject of sound has sounds are by the vibration of a string, two branches—one purely observational of a membrane, and of a thin tongue of and concerned with the vibrations of air metal in a current of air. The power of or of liquids and solids of such a nature the note produced is much intensified by as to stimulate the sense of hearing. a resounding board or a closed mass of These vibrations are different from those air of such dimensions as to vibrate nawhich excite the sense of sight, inasmuch turally in accord with the note produced. as they are longitudinal and not trans- Thus in an organ the sound is produced versal ; that is, they consist of condensa- by an insignificant tongue of metal, which tions and rarefactions in the direction in vibrates with a multitude of notes. The which the sound travels, not, as in the organ-pipe takes up that one which it is case of light of vibrations, at right angles adapted for, and is the cause of the whole to the direction in which the disturb- volume of sound. If vibrations exceed a ance is propagated. The other branch of certain number in a second they pass beacoustics consists in a study of the means yond the limits of audibility. This varies by which it produces sensation in the with different persons. Some can hear brain, and the physical conditions under the cry of a bat; it is too shrill for others which those sensations are estimated as to discern. A whistle has been designed pieasurable or painful. All substances by Mr. Galton in which the rate of vibraare more or less elastic. When a portion tion can be gradually altered, and a note of an elastic medium is compressed it is produced which, gradually becoming tends to expand again, and having ex- shriller, passes beyond the hearing first of panded it passes through the normal con one then of another of a company who dition to a condition of rarefaction, and listen to it. When it is inaudible to any before it comes to its original condition it one it will still influence a sensitive flame. passes through many such phases. Thus Similarly vibrations pass below the limits any violent disturbance of the air pro- of audibility when they become slower duces an alternate condensation and rare- than a certain rate. faction called a wave, and this repeats A most instructive experiment, which


illustrates many facts of optics as well as Although in the air the multitudinous of acoustics, is the following : We take vibrations of a piece of music are comtwo tuning-forks of different periods of pounded into a single complex agitation, vibration. Two small beads are hung by still the ear has the power of picking out a thread so that one just touches the prong each note, and even the particular kind of of each fork. A third tuning-fork is now note of every instrument—that is to say, sounded which is of the same period of there is the power in the ear of disvibration as one of the forks. The bead tinguishing the several vibrations, howin proximity to that fork will be thrown ever compounded. The state of the air to and fro, while the bead touching the through which a number of musical notes other tuning-fork will remain at rest. This is passing is very complicated. We will shows that the tuning-fork will take up consider two instances. Take the note o from the air the vibration which it itself and the c above it. When the note o will give out, and the solid mass of steel sounds, the air has its point of greatest will be set in motion by the extremely compression and greatest rarefaction at minute influences of the waves of air. distances of 4 feet from each other. Due The same effect is produced with strings to the higher c there are compressions when stretched to various degrees of ten- and rarefactions at distances of 2 feet sion. Let us imagine a room to be com- from each other. These will combine into pletely filled with strings of one length a series at a distance of 2 feet, but these and one degree of tension, such that they compressions and rarefactions will not be would all give out the same note. Let identical ; where the phases of the two then a set of musical notes traverse the notes coincide there will be a more marked room, consisting of the note to which the effect than where they differ. Still the strings are attuned and others as well. total series will be regular, and its phases That note will set all the strings in vibra- will recur, complicated as they are, within tion, and as a consequence it will itself be a short interval. If two notes, however, absorbed—it will not pass through the be sounded together, the periods of which room, while the other notes will pass on, differ but slightly, they will, if started in not being taken up in producing an effect corresponding phases at one time, augment in the room. Here the room full of each other considerably, but after a cerstrings is of the nature of a substance tain time, when the faster wave has gained which absorbs that kind of vibration sufficiently on the slower wave, they will which it, when itself set in vibration, almost neutralise each other. Hence, the would give out. There are many instances sound will rise and fall in intensity at of an action of this kind in heat and light, appreciable intervals, giving rise to an and the whole study of spectrum analysis effect similar to that of the flickering of rests upon a similar phenomenon in the a candle. This is productive of an uncase of light.

pleasant sensation to the ear, and it is The vibrations of the air are conveyed found that what are called disharmonies to the brain by a delicate apparatus, con- in music are notes related in the above sisting of the following parts : A mem- fashion to each other. For the experibrane which is agitated by the waves mental and general knowledge of acoustics passing down the passage of the ear. To Tyndall's book on Sound may be consulted. this membrane are attached two bones Airy's and Donkin's books give the more forming a lever and conveying the vibra- mathematical treatment. Helmholtz's tions to another membrane. This latter book on the Sensations of Tone has been membrane encloses a space filled with translated, and is the authority on the fluid, the vestibule, and from this space phenomena of sound in relation to the open out two spiral-formed canals and a sense of hearing space shaped like a snail-shell, the cochlea. Acquisition of Knowledge, or learn. Into the fluid of the cochlea project a ing in its widest signification, includes number of small fibres or rods of varying every operation by which the mind comes lengths, and it is supposed that vibrations into possession of a new fact or truth. of varying rates are picked out by these This may take place either by means of a fibres, each fibre being set in vibration new personal observation, through the inby its corresponding vibration, and con- struction of others, or finally as the result veyed by them to the auditory nerve. I of reflection and reasoning upon what is

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