Abacus

“ The bell often approaches the Classic capital in design, and sometimes even in treatment, as at Canterbury; but this is a rare amount of excellence. More frequently a lotus-like flower rises from the neck, and curls beneath the abacus. The neck is still a mere round bead.
In the next, or Lancet period, the abacus more frequently becomes circular, the top is seldom flat, the mouldings usually consist of two rounds, with a deep undercut, hollow between, the upper one a little overhanging the under, and in the hollow a trail of nail-head or dog-tooth is often found. ”

“ At least that method, and the other one of turning the volutes diagonally, are the only methods that have been practised for giving perfect regularity to the Ionic capital by means of four equal faces; for, though difficult, it is possible to accomplish the same purpose differently, by making the abacus quite square, as in the Doric Order, and letting the volutes grow out of it on each side or face, their curvature commencing not on the upper horizontal edge, but descending from the vertical edges of the abacus. ”

“ It may be imagined that all the foliage above the upper row of leaves in a Corinthian capital has been removed, that a carved Ionic echinus has been put in at the level of the bottom of the Corinthian cauliculi, that on the centre of the echinus there is a calix, from which a flower runs up above the top of the abacus, and from each side of the calix spring curved bands running into the hollow of the abacus and ending in heavy volutes coming down to the tops of the upper row of leaves, the lower parts of the bands and the spaces between the spirals being filled with foliage. ”

“ He was a well-favored man, rather old, and appeared to be much more intelligent than the natives of this valley or those of any of the districts through which the friar had passed in the course of his march. This man reported that the lord of Cibola lived and had his seat of government in one of the seven cities called Abacus, and that he appointed men in the other cities who ruled for him. Abacus is readily identified with Hawikuh, one of the present ruins near K'iapkwainakwin, or Ojo Caliente, about 15 miles southwest of Zuñi. ”

“ In 1778, being attracted to mathematics, he went to live as a resident pupil with John Slee at Mungrisdale, Cumberland. He designed for his own use an elaborate form of abacus, with holes in vertical and horizontal rows, and pegs of various forms to represent the digits and algebraical symbols. ”

“ Apul. Apol. c. 16, p. 426; Sen. Ep. 74, 27; Plut. Cat. min. 70; eruditus pulvis, Cic. N. D. ii. 1. 8, 48.) The name Arenarius applied to the elementary teacher, qui calculare monstrabat (Mart. Cap. vii. init.) , implies that this sort of abacus was used by school-children.
(b) A development of this simple form was the abacus on which ψη̂φοι, calculi, pebbles or counters, were employed to calculate with. It was a board marked off by ridges or grooves (along which balls, counters, or buttons could be moved) into compartments, for the several orders of numbers. ”

“ It is possible that one of the forms of ancient abacus suggested to some Hindu astronomer or mathematician the use of a symbol to stand for the vacant line when the counters were removed. It is well established that in different parts of India the names of the higher powers took different forms, even the order being interchanged. ”

“ While at the sides there is no distinct abacus, in the centre it is always square and moulded. The cusps end in knobs like thistle-heads, and are themselves rather branchlike. In the hollow between the shafts and the framing there are sometimes square or round flowers, sometimes twisting branches. Branches too form the framing of all, they are intertwined up the sides, and form above the arches a straight-topped mass of interlacing twigs, out of which grow three large finials. ”

“ In arithmetic, the name of an instrument employed to teach the elementary principles of the science of numbers. The Chinese abacus is also an instrument for facilitating arithmetical calculations. It consists of several series of beads or counters strung upon brass wires stretched from the top to the bottom of an instrument, and divided in the middle by a cross-piece from side to side. ”

“ Another tenth century treatise is that of Abbo of Fleury (c. 988) , preserved in several manuscripts. Very few treatises on the use of the Abacus can be certainly ascribed to the eleventh century, but from the beginning of the twelfth century their numbers increase rapidly, to judge by those that have been preserved.
The Abacists used a permanent board usually divided into twelve columns; the columns were grouped in threes, each column being called an “arcus,” and the value of a figure in it represented a tenth of what it would have in the column to the left, as in our arithmetic of position. ”

“ Above this the tr ache lion or necking curves over, constructing what is known as the apophyge up to the fillets, round the base of the echinus, which forms the transition to the square abacus. The varying curve of the echinus, from the earliest times down to the later examples, is shown in the article on mouldings. The relative proportions of the lower diameter and the height of the columns vary according to the date of the example, in the early examples the column being just on 4 diameters high, in the Parthenon nearly 51/2 diameters, and in the Temple of Jupiter Nemaeus 61/2 diameters high. ”

“ At last he came right up on the beach, and a great shout of victory welcomed him. Aboko was ready for him, and with a powerful axe he gave him a tremendous blow that cut off his tail. Then we smashed his head, and cut his body into several pieces, which quivered to and fro for some time. In his stomach we found a great number of fish. If I remember correctly, he had six or seven rows of teeth, and such ugly teeth! I pity the poor man whose leg should unfortunately get caught between them. ”

“ The ass is a well-known phallical symbol, and Bacchus being also a phallical [Pg 340] god, we read in Pliny, "Asellorum duo genera, Callariæ minores, et Bacchi, qui non nisi in alto (in the deep) capiuntur." The Italian name baccalà, given to the cod-fish, seems to me to be derived from the union of the two names Bacchus and Callaria. In the Piedmontese dialect, a stupid man is also called by the name of baccalà. There is also a fish called merula, of which the ancients describe the extraordinary salacity, by indulging which it literally consumes itself away and perishes. ”

“ Abaco Island is roughly crescent-shaped (as shown by the accompanying map) , its two horns pointing about northwest and south. With Little Abaco, which properly belongs to it, it is nearly one hundred miles long, and has an average width of twelve miles. There are six hundred and eighty square miles in the larger island alone. The greater part of its outer side, facing the ocean, is bordered by an inner reef of small keys and rocks, which trend northwest by southeast,
Fig 1.—Map of Abaco Island and its adjoining Reef. ”

“ Among these, as well as the herbaceous plants, the Compositæ prevail over every other natural order. Two common species belong to the tribe of Mutisiaceæ, unknown in Europe, and almost confined to South America. The bushy species of Baccharis, a genus very widely spread in the New World, but not known elsewhere, were also very common. An acacia (A. Cavenia) approached more nearly to the dimensions of a tree. It has stiff, spreading, and very spiny branches, and is widely spread throughout the drier parts of temperate South America. ”

“ The Apache boy, who appeared to be fourteen or fifteen years old, was not more than five yards from him—standing there beside a giant cactus, naked except for a red cloth band about his forehead, and a whitish cotton girdle about his middle, with the broad ends hanging down before and behind, and regular Apache moccasins reaching like leggins half way up his thighs for protection against the brush: standing there, grinning, in his left hand a bow, in his right the wether’s bell! ”

“ Abaches, or Apaches, an erratic tribe of Indians, who infest the prairies of western Texas and New Mexico. They are supposed by some, to consist of not less than 15,000 souls. They are divided into petty bands, known under various names. They are the most vagrant of all the wild hunter tribes of the general area denoted. They do not live in fixed abodes, but shift about in search of game or plunder, and are deemed a pest by the Santa Fe traders. They raise nothing and manufacture nothing. ”

“ The sea-floor between Abaco and the reefs is elsewhere covered with the white coral-sand which causes a marvelously brilliant color-effect in strong lights, the tints ranging from the richest emerald to a transparent greenish-white.
Numerous sea-fowl show themselves as we sail past their haunts: brown pelican, standing immovable like statues on the rocks, but suddenly expanding into birds of astonishing size; men-of-war or frigate birds, whose dark, cleanly-cut forms are strongly silhouetted against the sky ”

“ It is a favourite subject with you Florentines—the triumph of Bacchus and Ariadne; but I want it treated in a new way. A story in Ovid will give you the necessary hints. The young Bacchus must be seated in a ship, his head bound with clusters of grapes, and a spear entwined with vine-leaves in his hand: dark-berried ivy must wind about the masts and sails, the oars must be thyrsi, and flowers must wreathe themselves about the poop; leopards and tigers must be crouching before him, and dolphins must be sporting round. ”

“ All through the work, we have endeavoured to adopt the golden rule of "submission to nature," by reference to which all the fancied difficulties of bee-keeping may be easily overcome. In none of the attempts of men to hold sway over natural objects, is the truth of Bacon's leading doctrine more beautifully illustrated than in the power that the apiarian exercises in the little world of bees. ”

“ Abies is widely distributed in the New World from Labrador and the valley of the Athabasca River to the mountains of North Carolina, and from Alaska through the Pacific and Rocky Mountain regions to the highlands of Guatemala, and in the Old World from Siberia and the mountains of central Europe to southern Japan, central China, Formosa, the Himalayas, Asia Minor, and the highlands of northern Africa. Thirty-three species are now recognized. Several exotic species are cultivated in the northern and eastern states ”

“ The acacias, which are very abundant, and appear in three hundred species, are many of them, as well as some other leguminous plants, distinctly marked from similar plants in Asia, Africa, and America, by having not veined leaves but phyllods, or leaf -like structures, in which the petiole becomes so much developed as to assume the appearance and perform the functions of a leaf. ”

“ The sun was intensely oppressive, and glared like a shield of red-hot brass. A friendly bush, surrounded with fine grass, and standing about one hundred yards to the left of the hard and splendid natural road which runs through four-fifths of the Jornada, invited me to partake of its modest shade, and I turned my horse in that direction, but was surprised at noticing a column of dust to my left, in the direction of the Sierra Blanca, which had the appearance of being in violent motion, and coming my way. Instinctively I felt that it was caused by Apaches ”

“ Young avocets are very precocial and leave the nest soon after hatching. They are expert at hiding, even on the open flats and beaches; and they take to the water at an early age, where they can swim and dive like young ducks. I have seen a brood of four young, that could not have been hatched more than a few hours, swimming out in a lake, as if very much at ease. They soon learn to tip up in shallow water and probe on the bottom, like their parents, for their insect food.
Plumages.—The downy young avocet is well colored for concealment on an open beach or alkaline flat. ”

“ The burnt acacia ash, which is added to the powdered leaf of the pitjuri plant, has a somewhat important function to perform; and one marvels at Nature having given the unsophisticated aboriginal the hint to add it. One of the favourite species, which is burnt for the purpose, is Acacia salicina. ”

“ The Abipones go naked in Summer, and in the Winter Clothe themselves with Furrs; they Paint their whole Bodies with Spots like the Tygers, Carve their Bodies all over, making Cut-work of their Skins, into which they stick Ostriches Feathers, as also through their Nostrils, Lips, and Ears, and account Baldness the greatest Beauty. They honor those for their Gods, who patiently endure unsufferable Tortures. The Women hang their Faces and Breasts full of Pearls: They never bring up above two Children, for they kill all above that number. ”

“ Asia, in its warmer southern territory, and in southwestern China, has many native acacias. Tropical and temperate South America, the West Indies, Central America, Mexico, the southwestern region of the United States, and the islands of the South Pacific, all have representatives of this wonderful and far-scattered genus. There is no country interested in horticulture that does not grow acacias as ornamental shrubs and trees, even if they must be grown under glass the year round. ”

“ The uranoscopus, and also the fish called agnus, which is also called the callionymus, are heavy fish. The boax, when boiled, is very digestible, giving out a very wholesome juice, and is good for the stomach; and that which is broiled on the coals is sweeter and more tender. The bacchus is full of abundant and agreeable and wholesome juice, and is very nutritious. The sea-goat is not very agreeable as to its juice, not very digestible, and has a disagreeable smell. The sea-sparrow and the buglossus are both nutritious and palatable, and the turbot is like them. ”