We may now proceed to point out the internal ar- | make this statement on personal observation." It rangement of the machinery. Motion is communi- consists essentially of two parts, a calculating, and a cated by the wheel and axis a b, which is furnished printing part, both of which are necessary to the fulfilwith a contrite wheel c. This actuates the next in ment of the inventor's views, for the whole advantage the series which is placed in the opposite direction. would be lost if the computations made by the maOn the same axis are placed two similar wheels de, chine were copied by human hands and transferred to the last of which gives motion to the wheel and barrel types by the common process. The greater part of fg. There are two apertures in the upper plate A B, the calculating machinery, of which the drawings through which the figures on the barrel may be seen, alone cover upwards of 400 square feet of surface, is so that the person who moves the wheel a may already constructed, and exhibits workmanship of readily register the amount of motion, by observing such extraordinary skill and beauty, that nothing apthe figures as they pass these apertures. proaching to it has hitherto been witnessed. In the printing part, less progress has been made in the actual execution, in consequence of the difficulty of its contrivance, not for transferring the computations from the calculating part to the copper, or other plate destined to receive them, but for giving to the plate itself that number and variety of movements which the forms adopted in printed tables may call for in practice.

The practical object of the calculating engine is to compute and print a great variety and extent of astronomical and navigation tables, which could not otherwise be done without enormous intellectual and ma nual labour, and which, even if executed by such labour, could not be calculated with the requisite accuracy. Mathematicians, astronomers, and navigators In the complete machine there are several of these do not require to be informed of the real value of such trains of wheels, and they communicate with each tables; but it may be proper to state, for the inforother by a small lever h, shewn in the diagram. mation of others, that seventeen large folio volumes of Now, if we suppose the first of these barrels to have logarithmic tables alone were calculated under the made an entire revolution, the two connecting bars superintendance of M. Prony, at an enormous expense i i, will have raised the lever and moved the commu- to the French government; and that the British gonicating wheel of the next train one tooth forward in vernment regarded these tables to be of such national its course. If, for example, it be the barrel which value, that they proposed to the French Board of represents shillings, it will by this means indicate a Longitude, to print an abridgement of them at the single pound on the divided circle of the next train. joint expense of the two nations, and offered to advance Notwithstanding the skill and contrivance bestowed £5000 for that purpose. But, besides logarithmic upon instruments of a nature similar to that we have tables, Mr. Babbage's machine will calculate tables just described, their power is necessarily but very of the powers and products of numbers, and all astrolimited, and they bear no comparison either in inge-nomical tables for determining the positions of the nuity or magnitude to the grand design conceived, and nearly executed, by Mr. Babbage. Their very highest functions were but to perform the operations of common arithmetic; Mr. Babbage's engine, it is true, can perform these operations, it can also extract the roots of numbers, and approximate to the roots of equations, and even to their impossible roots; but this is not its object. Its function in contradistinction to that of all other On the means of accomplishing this, we need make contrivances for calculating, is to embody in machi- no apology for quoting Mr. Babbage's own words. nery the method of differences, which has never before" As the possibility of performing arithmetical calcubeen done; and the effects which it is capable of pro-lations by machinery may appear to non-mathemaducing, and the works which, in the course of a few tical readers too large a postulate, and as it is conyears, we expect to see it execute, will place it at an nected with the subject of the division of labour, I infinite distance from all other efforts of mechanical shall here endeavour, in a few lines, to give some genius. Great as the power of mechanism is known slight perception of the manner in which this can be to be, yet we venture to say, that many of the most done; and thus to remove a small portion of the veil intelligent of our readers will scarcely admit it to be which covers that apparent mystery. That nearly all possible, that astronomical and navigation tables can tables of numbers which follow any law, however be accurately computed by machinery; that the ma- complicated, may be formed, to a greater or less exchine can itself correct the errors which it may com- tent, solely by the proper arrangement of the succesmit; and that the results, when absolutely free from sive addition and subtraction of numbers befitting error, can be printed off without the aid of human each table, is a general principle which can be demonhands, or the operation of human intelligence. "All strated to those only who are well acquainted with this, however," says Sir David Brewster, in his enter-mathematics; but the mind, even of the reader who taining Letters on Natural Magic, "Mr. Babbage's is but very slightly acquainted with that science, will machine can do; and, as I have had the advantage of readily conceive that it is not impossible, by attending seeing it actually culculate, and of studying its con- to the following example. Let us consider the substruction with Mr. Babbage himself, I am able to joined table. This table is the beginning of one in

sun, moon, and planets; and the same mechanical principles have enabled him to integrate innumerable equations of finite differences, that is, when the equation of differences is given, he can, by setting an engine, produce at the end of a given time, any distant term which may be required, or any succession of terms commencing at a distant point.

very extensive use, which has been printed and re- | which will strike three, and at the same time, in conprinted very frequently in many countries, and is sequence of the mechanism we have referred to above. called a table of square numbers.

Any number in the table, column A, may be obtained by multiplying the number which expresses the distance of that term from the commencement of the table by itself; thus 25 is the fifth term from the beginning of the table, and 5 multiplied by itself, or by 5, is equal to 25. Let us now subtract each term of this table from the next succeeding term, and place the results in another column (B), which may be called first-difference column. If we again subtract each term of this first-difference from the succeeding term, we find the result is always the number 2 (column C); and that the same number will always recur in that column, which may be called the second-difference, will appear to any person who takes the trouble to carry on the table a few terms further. Now, when once this is admitted as a known fact, it is quite clear that, provided the first term (1) of the table, the first term (3) of the first-differences, and the first term (2) of the second or constant difference are originally given, we can continue the table to any extent, merely by simple addition: for the series of first-differences may be formed by repeatedly adding the constant difference 2 to (3) the first number in column B, and we then necessarily have the series of odd numbers, 3, 5, 7, &c.; and again, by successively adding each of these to the first number (1) of the table, we produce the square numbers."

will advance the hand of A three divisions. Pull the string of C, which will strike two and advance the hand of B two divisions, or to division V. Let this operation be repeated; A will then strike four; B will strike five, and in so doing will advance the hand of A five divisions; and C will again strike two, at the same time advancing the hand of B two divisions. Again pull A, and it will strike nine; B will strike seven, and C two. If now those divisions struck, or pointed at by the clock A be attended to and written down, it will be found that they produce a series of the squares of the natural numbers; and this wili be the more evident, if the operation be continued further than we have carried it. Such a series could of course be extended by this mechanism only so far as the three first figures; but this may be sufficient to give some idea of the construction, and was in fact, Mr. Babbage states, the point to which the first model of his calculating engine was directed.

In order to convey some idea of the power of this stupendous machine, we may mention the effects produced by a small trial engine constructed by the inventor, and by which he computed the following table from the formula a2+x+41. The figures as they were calculated by the machine, were not exhibited to the eye as in sliding-rules and similar instruments, but were actually presented to it on two opposite sides of the machine, the number 383, for example, appearing in figures before the person employed in copying. The following table was calculated by the engine referred to:

While the machine was occupied in calculating this table, a friend of the inventor undertook to write down the numbers as they appeared. In consequence of the copyist writing quickly, he rather more than kept pace with the engine at first, but as soon as five figures appeared, the machine was at least equal Having thus thrown some light on the theoretical part in speed to the writer. At another trial, thirty-two of the question, Mr. Babbage proceeds to shew that numbers of the same table were calculated in the the mechanical execution of such an engine as would space of two minutes and thirty seconds, and as these produce this series of numbers, is not so far removed contained eighty-two figures, the engine produced from that of ordinary machinery as might be conceived. thirty-three figures every minute, or more than one He imagines three clocks to be placed on a table, figure in every two seconds. On a subsequent oc side by side, each having only one hand, and a thou-casion, it produced 44 figures per minute; and this sand divisions instead of twelve hours marked on the rate of computation could be maintained for any length face; and every time a string is pulled, each strikes of time. on a bell the numbers of the divisions to which the It may be proper to add, that M.. Babbage stated hand points. Let it be supposed that two of the to the editor of this work, that he considered the clocks, for the sake of distinction called B and C, have powers of his machine as scarcely at all developed― some mechanism by which the clock C advances the indeed, that the automaton was yet but in its infancy. hand of the clock B one division for each stroke it If such be the childhood of this gigantic engine, what makes on its own bell; and let the clock B by a simi- may we not expect from its maturity? There is a lar contrivance advance the hand of the clock A one general belief that this gentleman has received a large division for each stroke it makes on its own bell. parliamentary grant as a reward for his invention; Having set the hand of the clock A to the division I, this is, however, a vulgar error. He has superinthat of B to III, and that of C to II, pull the string tended the construction of the instrument at the exof clock A, which will strike one; pull that of clock B, | pense of the Government, but he has not directly or

indirectly received the slightest pecuniary compensa- | surrounding the umbilicus between the epigastrium tion for his services. and a line drawn from the crest of one os ilii to the ABAISSED, abaissé, a term used in Heraldry to other, is the umbilical region. The hypogastric reexpress the situation of the fesse, or any other bear-gion is of course the lowest part of the belly, consisting, when it is depressed below the centre of the ing of the angle between the umbilical region, the spines of the ossa ilii, and the pubis. The two lateral

shield.

ABASSI, OF ALBAAJER, a silver coin current in Persia, equivalent in value to two mamoodis, or four chayés. It took its name from Schah Abbas II., king of Persia, under whom it was struck, and is worth about one shilling of our money.

ABAS, a weight which is used in Persia for weigh-spaces between the false ribs and the spine of the os ing pearls. According to Dr. Kelly's late work on ilii, are the iliac regions, or the loins. Oriental Metrology, it answers to 3.66 diamond The boundaries of the abdomen are everywhere grains English, or 2.25 troy grains.148 deci-lined by a thin and elastic membrane called the perigramme. toneum, which also more or less envelopes the contained viscera. The peritoneum may be compared to a flaccid bladder behind, and on the outside of which the intestines and other supposed contents are placed. This membrane is then folded around them, and the two sides of the bladder, after enfolding the intestines, ABATEMENT, a term used in Heraldry, to denote a are brought together, forming the mesentery. The mark annexed to the paternal coat, in order to express peritoneum is therefore contiguous on its internal or point out some ungentlemanlike behaviour or in-surfaces, or only separated by a vapour called halitus, famy, by which that coat is abated or lowered m which after death condenses into a watery fluid. dignity. The marks of abatement mentioned by The term viscera, though referring more particuheraldic authors are nine in number; but although larly to the fleshy or solid contents of the great cavianciently heralds, or officers of arras, might have ties, is applied generally to all the parts contained in settled these bearings as the proper tessera or abate-them. The economy of the abdominal viscera is very ment of honour to deter men from the commission of such dishonourable acts, scarcely an instance of any one of them having been actually borne, is given by heraldic writers, and the French discard it altogether as an English fancy.

ABATIS, a species of military defence formed of trees cut down and laid with their branches turned towards the enemy, so as to protect troops stationed behind them. They are sometimes placed before redoubts and other works, to render attacks difficult; and along the skirts of a wood, in order to prevent the enemy from getting possession of it. In this case, the trunks serve as a breast-work, behind which the troops are posted, and should therefore be so disposed, that the parts may, if possible, flank one another. In addition to these applications, the abatis may often be of essential service, by retarding the progress of the enemy.

ABB, the yarn of a weaver's warp, whence the wool of which it is made is termed abb-wool.

ABDOMEN, or lower venter, the anatomical term for the belly. This cavity is that division of the human body which is situated betwixt the thorax and the pelvis. It is bounded above by the arch of the diaphragm, behind, by the spine, on the sides and fore part, by the abdominal muscles; and below, the abdominal viscera are supported by what are termed the aloe ilii and the pubis. It contains the viscera more or less immediately connected with digestion, and the kidneys which secrete the urine.

To give greater accuracy to the description of the seat of the viscera, or perhaps rather more strictly, to connect the knowledge of the internal parts with the exterior of the belly, it has been long customary to mark certain arbitrary divisions on its surface, which are called regions.

important in the processes of digestion. The organs destined to receive the food, and to perform the first of those changes upon it, which after a due succession of actions fit it for becoming a component part of the living body-are the stomach and intestines, which may be considered as primary, and the glandular viscera, the liver, the pancreas, and in all probability the spleen, as subservient or secondary organs. These may be divided into the membranous or floating viscera, comprising the whole track of the intestinal canal, and the glandular viscera; or, what is still better, they may be distinguished into those parts which have action and motion, and those which are quiescent, or possessed of no power of contraction. Thus the stomach, intestines, gall-bladder, and bladder of urine (though this belongs to the pelvis), have muscular coats, and possess the power of contracting their cavities; while the liver, spleen, pancreas, and kidneys have no muscularity but in their vessels and excretory ducts.

The intestinal canal may be divided into three parts; the stomach, the great and the small intestines. The small intestines are subdivided into the duodenum, jejunum, and ileon; the great, into the cœcum, colon, and rectum. The stomach, into which the food is conveyed by the œsophagus, or gullet, is the seat of the digestive process; in the duodenum, the food receives the addition of the secretions from the liver and pancreas, and is still further adapted to animalization; in the long tract of the jejunum ard ileon the nutritious part is absorbed ; and in the great intestines the effete matters are carried slowly forward, and at the same time suffer a further absorption of their fluid contents, until as faeces they lodge in the rectum, or last division of the canal. From this view, it is apparent that cach of the divisions of the intestinal canal is marked by some peculiarity in its use or function; and for a more detailed account of their structure individually, we must refer to the several portions of which it is composed.

The epigastric region is the upper part of the belly, under the point of the sternum, and in the angle made by the meeting of the cartilages of the ribs with the sternum. Upon the sides, under the cartilages of the ribs, are the hypochondriac regions, or the right ABDUCTOR, a term applied to those muscles which and left hypochondrium. These three regions com- draw backwards the moveable parts into which they pose the upper division of the abdomen, in which are are inserted, and of which there are many in the seated the stomach, liver, spleen, pancreas, duode-human body.

num, and part of the arch of the colon. The space} ABERRATION of light. We see an object because

R

the rays of light proceeding from it strike our eyes, | a pretty bright image of the sun at F; but as the rays and we see the place of the object in the direction in of the sun, which pass through the outer part of LL which they proceed. Let us now imagine the earth, of the lens, have their foci at points between ƒ and F, in its circuit round the sun, just arrived opposite to the rays will, after arriving at those points, pass on a fixed star, which sends off rays perpendicularly to to the plane G H, and occupy a circle whose diameter the direction of the earth's motion. The eye of the is GH; hence the image of the sun in the focus F spectator meets the ray, and as he perceives not his will be a bright disc, surrounded and rendered indisown motion, he supposes the light to be moving in tinct by a broad halo of light, growing fainter and an opposite direction; as, when we sail in a boat, fainter from F to G and H. In like manner, every the trees on the shore appear to pass along by us. object seen through such a lens, and every image Thus the eye misses the perpendicular ray, but meets formed by it, will be rendered confused and indistinct an oblique one, and thence receives the impression of by spherical aberration. the light in the direction which results from this compound motion, namely, in the diagonal of a parallelogram, the sides of which represent the real motion of the light, and the apparent one (i. e. the motion of the earth), which take place at the same time. The spectator sees the star in its true place only when he is either approaching it, or receding from it, in a straight line. When moving in any other direction, the star appears a little in advance of its true position in the same direction (the maximum is 20′′-25′′); and we call by the name of aberration of light these apparent changes in the situation of the heavenly bodies, occasioned by the motion of the earth. We easily see that these changes are common to all the heavenly bodies, and are only more striking in the case of the fixed stars. They afford an additional proof of the motion of the earth. In consequence of this abberration, the fixed stars appear, during the revolution of the earth about the sun, according as they are situated, either in the plane of the ecliptic, or in its poles, or somewhere between them, in the first case to deviate in a straight line to the right or left of their true place, in the second to describe a circle, in the third an ellipse about that point, which further observation determines to be their real situation. This discovery we owe to Bradley.

The form assumed by the sun's disc is shown by the radial circles at the opposite extremity of the wood-cut.

These results may be illustrated experimentally by taking a ring of black paper and covering up the outer parts of the face LL of the lens. This will diminish the halo G H, and the indistinctness of the image; and if we cover up all the lens excepting a small part in the centre, the image will become perfectly distinct, though less bright, than before, and the focus will be at F. If, on the contrary, we cover up all the central part, and leave only a narrow ring at the circumference of the lens, we shall have a very distinct image of the sun formed about ƒ.

For the aberration of light, see the elementary works on astronomy, the dictionaries of natural phílosophy by Gehler, Fischer, &c. There is a very good account of it in Biot's Traité Elémentaire d'Astronomie Physique, Paris, 1811, 2d Treatise, vol.

The spherical aberration of lenses must be under-3, page 120, et seq. Tables of aberration, accomstood before the student can at all comprehend the principles of optics. It is generally supposed that the rays refracted from lenses or magnifying glasses meet exactly in a focus; but this is by no means strictly true, as those which pass through the centre or axis of the lense go beyond those which are incident at a greater distance.

In order to understand the cause of spherical aberration, let LL be a plano-convex lens, one of whose surfaces is spherical, and let its plane surface, Lm L, be turned towards parallel rays RL, RL. Let R'L', R'L', be rays very near the axis A F of the lens, and let F be their focus after refraction. Let RL, RL be parallel rays incident at the very margin of the lens, and it will be found by the method of projection, that the corresponding refracted rays Lf, Lf will meet at a point much nearer the lens than F. In like manner intermediate rays between R L and R'L' will have the foci intermediate between ƒ and F. Continue the rays Lf, Lƒ, till they meet at G and H, a plane passing through F. The distance f F is called the longitudinal spherical aberration, and G H the literal spherical aberration of the lens. In a plano-convex lens placed like that in the figure, the longitudinal spherical aberration ƒ F is no less than 4 times m a, the thickness of the lens. It is obvious that such a lens cannot form a distinct picture of any object in its focus F. If it is exposed to the sun, the central part of the lens L' m L', whose focus is at F, will form

panied with explanations, are to be found in the baron von Zach's works, Tabula speciales Aberrationis et Nutationis, etc., Gotha, 1806, and in the same author's Nouvelles Tables d'Abérration et de Nutation pour 1404 Etoiles, avec une Table générale d'Aberration pour les Planètes et les Comètes, Marseilles, 1812, and Supplément, 1813.

ABLUENTS, medicines applied to wash off from the external or internal surfaces of the body any matters adhering improperly to them.

ABOMASUM, the fourth stomach of ruminating animals, or that in which the process of digestion is completed.

ABSCESS, a term applied in Surgery to a cavity containing pus or a collection of puriform matter.

ABSCISSA. See Conic Sections.

ABSORBENT SYSTEM, the organs which are employed in the performance of the process of absorption, or that by which the substances that serve for the growth and support of the body are carried into the blood and are assimilated to that fluid. It appears to be a general principle in the animal economy, that all the particles of which the body is composed, after a certain period, lose the power of performing their appropriate functions; and that it consequently becomes necessary to have them replaced by new matter. It is by means of absorption that this exchange of particles take place, the former constituents being taken up by the vessels and returned into the general circulation, to be either discharged, or em