carried off, and broken to pieces. A report prevailed, that the first man who touched the goddess, instantly fell down dead. Augustus, supping a long time after this event, with an old soldier, who had shared the plunder, questioned him concerning the truth of the fact; the latter replied, "Caesar, it is the goddess Anaitis's leg you are now eating for supper, and all I have in the world I owe to her.' ANAK; P, Heb. i. e. a collar; the father of the Anakim, was the son of Arba, who gave his name to Kirjath-arba, or Hebron, Josh. xiv. 15. He had three sons, Sheshai, Ahiman, and Talmai, (chap. xv. 14, and Numb. xii. 22,) who, as well as their father, were giants. ANAK SUNGEI, a district in the Island of Sumatra, on the south-west side, extending along the sea-coast, from Manjuta river to that of Urei. The chief bears the title of Sultan; and his capital is Mocomoco, a poor town. The authority of the monarch is very limited, the greater part of the country being inhabited by the native Sumatrans, under their own chiefs, who attend the sultan at certain periods, and pay him a tax or contribution. ANALCIME, in mineralogy, cubic zeolite.This mineral is generally found in granite, gneiss, trap rocks and lavas, at Calton Hill, Edinburgh, at Talisker in Skye, in Dumbartonshire; in the Hartz, Bohemia; and in the Ferroe Islands. From its becoming feebly electrical by heat, it has got the name analcime. Its specific gravity is less than 2.6. It consists of fifty-eight silica, eighteen alumina, two lime, ten soda, eight and a half water, and three and a half loss in 100 parts. ANALECTA, ANALECTES; from ávaλéyw, I gather; in antiquity, a servant whose employment it was to gather up the offals of tables, which were picked up, and not swept away, as the pavements of the Roman floors were too finely inlaid to admit of sweeping. ANALECTA, ANALECTE, in literature, is used to denote a collection of small pieces; as essays, remarks, &c. ANALEMMA, in geometry, a projection of the sphere on the plane of the meridian, orthographically made by straight lines and ellipses, the eye being supposed at an infinite distance, and in the east or west points of the horizon. Analemma denotes likewise an instrument of brass or wood, upon which this kind of projection is drawn, with an horizon and cursor fitted to it, wherein the solstitial coluze, and circles parallel to it, will be concentric circles; all circles oblique to the eye, will be ellipses; and all circles whose planes pass through the eye, will be right lines. This instrument is used in common astronomical problems; but is not very exact unless very large. It is also useful for laying down the signs of the zodiac, with the length of days, and other matters of furniture, upon dials. ANALEPSIS, in medicine, the augmentation or nutrition of an emaciated body. ANALEPSIS, in surgery, the method of suspending a dislocated arm in a string. ANAL FIN, in ichthyology, the fin placed between the vent and tail, which expands persendicularly. VOL. II. ANALIS, in entomology,a specific name occurring in several genera in the Linnæan and Fabrician systems. It is the name: 1. Of a species of scarabeus; 2. Of a species of coccinella; 3. Of a species of chrysomela; 4. Of a species of cerambyx; 5. Of a species of cryptocephalus; 6. Of a species of staphylinus; 7. Of a species of cimex; 8. Of a species of phrygania; 9. Of a species of sphex; 10. Of a species of vespa; 11. Of a species of apis. ANALOGISTA, in civil law, a tutor who is not obliged to give an account of his conduct. ANAL'OGIZE, ̓Αναλογία, from dvd and ANAL'OGY, Aoyog. To institute a comANALOGʻICAL, parison; to ascertain a raANAL'OGOUS, tio,proportion, resemblance. ANALOGAL, The significations may be ANALOGOUSLY. J more particularly collected from the following illustrations. He calleth the Lordes body the congregation redemed with Christes body as he dyd before, and also in the chapter followyng, fetching his analogie and similitude at the naturall body. The Whole Workes of Tyndall, &c. f. 473. c. 1. Besides the express laws of our religion, there is an universal line and limit to our passions and designs, which is called the analogy of christianity; that is, the proportion of its sanctity, and the strictness of its holy precepts. Jeremy Taylor. There is placed the minerals between the inanimate and vegetable province, participating something analogical to either. Hale's Orig. of Mankind. Every one knows that analogy is a Greek word, used by mathematicians to signify a similitude of proportions. For instance, when we observe that two is to six, as three is to nine, this similitude or equality of proportion is termed analogy. Bp. Berkeley's Minute Philo. When a word, which originally signifies any particular idea or object, is attributed to several other objects, not by way of resemblance, but on account of some evident reference to the original idea, this is peculiarly called an analogical word; so a sound or healthy pulse, a sound digestion, a sound sleep, are so called, with reference to a sound and healthy constitution; but if you speak of sound doctrine, or sound speech, this is by way of resemblance to health, and the words are metaphorical. Watts's Logick. The unction of our Lord was the descent of the Holy Ghost upon him at his baptism. This was analogous to the ceremony of anointing. Horsley's Sermons. ANALOGY, in philosophy. A great part of our philosophy has no other foundation than analogy. It is natural to mankind to judge of things less known by some similitude, real or imaginary, between them and things more familiar or better known. And where the things compared have really a great similitude in their nature, when there is reason to think that they are subject to the same laws, there may be a conside rable degree of probability in conclusions drawn from analogy. Thus we may observe a very great similitude between this earth which we inhabit, and the other planets, Saturn, Jupiter, Mars, Venus, and Mercury. They all revolve round the sun, as the earth does, although at different distances, and in different periods. They all borrow their light from the sun, as the earth does. Several of them are known to revolve round their axis like the earth, and by that M means must have a like succession of day and aight. Some of them have moons that serve to give them light in the absence of the sun, as our moon does to us. They are all in their motions subject to the same law of gravitation, as the earth is. From this general similitude, it is not unreasonable to think, that those planets may, like our earth, be the habitation of various orders of living creatures: there is even great probability in this conclusion from analogy, But perhaps no author has made so just and happy a use of this mode of reasoning as bishop Butler in his Analogy of Natural and Revealed Religion. In that excellent work, the author does not ground any of the truths of religion upon analogy, as their proper evidence: he only makes use of analogy to answer objections against them; shewing that when objections are made to religion, which may be made with equal strength against what we know to be true in the course of nature, such objections can have no weight. Analogical reasoning, therefore, may be of excellent use in answering objections against truths which have other evidence. It may likewise give a greater or a less degree of probability in cases where we can find no other evidence. But, as this kind of reasoning can afford only probable evidence at best, unless great caution be used, we are apt to be led into error by it. To give an instance of this: early anatomists seldom dissected human bodies; but very often the bodies of those quadrupeds whose internal structure was thought to approach nearest to that of the human body; and were led into many mistakes by their arguing on a greater similitude between the structure of men and of animals than there is in reality. Arguments drawn from analogy become weak, as the disparity between the things compared increases; and therefore must be weakest of all when we compare body with mind, because there are scarcely two things in nature more unlike. Yet is there no subject on which men have always been so prone o form their notions by analogy, as in what re.ates to the mind. We form an early acquaintance with material things by means of our senses, and are bred up in a constant familiarity with them. Hence we are apt to measure all things by them; and to ascribe to things most remote from matter, qualities that belong only to material things. It is for this reason that inankind have, in all ages, been so prone to conceive the mind itself to be some subtile kind of matter: that they have been disposed to ascribe human figure, and human organs, not only to angels but even to the Deity. Thus contrary motives are compared to the weights in the opposite scales of a balance; and there is not perhaps any instance that can be named of a more striking analogy between body and mind. The phrases of weighing motives, and of deliberating upon actions, are common to all languages. As the balance it is said cannot incline to one side more than the other, when the opposite weights are equal, so a man cannot possibly determine himself if the motives on both hands are equal; and as the balance must necessarily turn to that side which has most weight, so the man must necessarily be determined to that hand where the motive is strongest. And on this foundation some of the schoolmen maintained, that if a hungry ass were placed between two bundles of hay equally inviting, the beast must stand still and starve to death, being unable to turn to either, because there are equal motives to both! The principal uses of analogy in the investigation of physical and moral truth, according to our author, have been reduced to the four following: 1. By means of our senses to improve, first our own judgment, and afterwards that of others, with respect to intellectual subjects. 2. To deduce a general from a particular truth. Having discovered and proved the truth of a proposition with respect to any particular object, examine whether this truth flows from a quality peculiar to this single object, or common to several objects. In the latter case all these objects may be comprehended under one general idea, founded on their common quality. Substitute this general idea instead of the particular object, and the proposition will become general without ceasing to be true; because whatever evidently and solely results from the identity, on which an analogy is founded, must necessarily be true with respect to all those objects in which the analogy is the same. prove the truth or falsehood of propositions which cannot be otherwise demonstrated. 4. To discover new truths in both natural and moral philosophy. 3. To ̓Ανὰ and λύω, το loosen. To resolve a compound substance into its elements or first principles. ANʼALYZE, v. As Stellus, late dictator of the feast, There is an account of dew falling, in some places, in the form of butter, or grease, which grows extremely fetid; so that the analysis of the dew of any place may, perhaps, be the best method of finding such contents of the soil as are within the reach of the sun. Arbuthnot. We cannot know any thing of nature, but by an analysis of its true initial causes; till we know the first springs of natural motions, we are still but igno rants. Glanville. To investigate truth with success, in mathematics, in natural philosophy, and, indeed, on every occasion where it is difficult to be found, the analytic method must be employed. Bolingbroke's Essay on Hum, Know. last principles; if it be enquired, Why such an action To analyze the immorality of any action into is to be avoided; the immediate answer is, Because it is sin. Norris's Miscell. Analytic method takes the whole compound as it finds it, whether it be a species or an individual, and leads us into the knowledge of it, by resolving into its first principles, or parts, its generic nature, and its special properties; and therefore it is called the method of resolution. Watts's Logic Analysis consists in making experiments and observations, and in drawing general conclusions from them by induction, and admitting of no objections but such as are taken from experiments, or other certain truths. Newton's Optics. The great work of which Justinian has the credit, consists of texts collected from law books of approved authority; and those texts are digested according to a scientifical analysis; the names of the original authors and the titles of their books being constantly cited. Sir William Jones. ANALYSIS, in chemistry, is a term applied to the process by which a separation is effected of the constituent principles of any substance: it has been divided into proximate and ultimate. When we have a compound of two or more ingredients, these ingredients themselves being also compounded, the separation of the compounds from each other has been named the proximate analysis of the body; while ultimate analysis is an expression by which is understood the separation of these compounds into their components. A further division has likewise obtained among chemists of analysis into simple or true, and complicated or false. When a body is exposed to a certain degree of heat, the principles of which it is compounded may be so far interfered with that they shall separate; and their volatility being different in degree, the one which is most volatile shall be the first to pass off or be expelled. In other cases, however, a body will resist this endeavour at separating its constituent principles by the most intense heat; but if treated with some other chemical agent, this last agent may, by combining with one of its component parts, effect the desired separation. Such, then, are instances of simple or true analysis, for in these cases the re-union of the constituent principles may be brought about by withdrawing the interfering agency, or the body may be again formed by bringing its component parts under circumstances favourable to combination: but in complicated or false analysis the composition of the compound is, as it has been expressed, not only subverted, and its individual existence destroyed, but, from the combination of its principles in new modes and proportions, it is impossible to re-produce it by the union of the products of the analysis. It must ever be recollected that when the analysis or separation of any substance has been carried so far as possible, we arrive not properly at its absolute essence, we only detect its elements; and even this term must be carefully taken as not implying any thing more than that we are at present incapable of decomposing further. Many bodies are daily crumbling into component principles under the powerful grasp of modern science, which had long been considered as simple or elementary; and, in the expectation of still greater discoveries, there is no point at which we may stop. It may here, by the way, be incidentally remarked, that one of the great errors of ancient philosophy consisted in its unwarrantable assumption of simple elementary existence, as of air, earth, fire, and water. See CHEMISTRY. Analysis of course is made to apply both to organic and inorganic matter; but in the former case we cannot uninterruptedly proceed beyond the proximate principles of the substance upon which our experiments are instituted; for when we attempt the ultimate separation of organic compounds, we are liable to obtain the results of an entirely new arrangement of principles, or an arrangement different from that presented to us by the hand of nature. In this case, then, we cannot always, as in bodies of the mineral kingdom, proceed from a knowledge of their components to the actual formation of the substances themselves. It is not probable, indeed, that we shall ever attain the power of imitating nature in these operations. For in the functions of a living plant a directing principle appears to be concerned, peculiar to animated bodies, and superior to, and differing from, the cause which has been termed chemical affinity. So it is, and with somewhat still of more force and complication, in the animal world; for chemical agency applied to animal substances gives origin to a set of bodies which had no existence in the subject of experiment, the ultimate elements of which are thus disunited, and are recombined in a new manner. Bones, for example, though they contain no volatile alkali, are yet composed in part of its elements (nitrogen and hydrogen) which at a high temperature unite and generate ammonia. See AMMONIA. On especial analysis we shall have to treat in the article CHEMISTRY, and the composition of the several materials that come under the cognizance of chemical science will be incidentally stated as these substances fall before us for consideration in alphabetical order: we shall in this place confine ourselves to remarking that very considerable improvements, and apparently much nearer approximations to truth, have lately taken place in reference to the analysis even of those materials which in their aggregate are the result of organic agency. The object of these improved methods to which we now refer, and which are equally applicable to vegetable and animal substances, is to convert the whole of the carbon which enters into their composition into carbonic acid, and the whole of their hydrogen into water, by means of some compound containing oxygen in so loose a state of union, as to give it up to those bases at the temperature of ignition. The oxygen too, contained in these bodies, may be detected by examining what quantity of oxygen has been lost by the oxide employed to effect decomposition; and if this fall short of the oxygen contained ir the carbonic acid, and in the water, then the quantity required to make up the amount must have previously existed in the subject of analysis. In a few vegetable substances, moreover, and in all animal ones, azote or nitrogen exists as a component, and its quantity requires to be determined. With a proper attention to the details of the process, this fourth element may be obtained in the condition of gas, which remains after absorbing the carbonic acid by solution of potass, and the oxygen, if any, by a fit agent. Gay Lussac and Thenard, to whom we are principally indebted for the processes now adverted to, first employed as their agent the chlorate of potass, but the former chemist subse quently substituted the peroxide of copper, especially in the analysis of animal compounds. The mode of applying this substance to effect the objects intended we shall describe in another place; see CHEMISTRY: it may be here sufficient to state, that all the analyses which have been performed by these improved methods, conspire to make us believe that the elements of organized, like those of inorganic matter are united in definite proportions; and further, that the laws of simple multiples hold strictly with respect to the elements of organic bodies. See ATTRACTION and ATOMIC THEORY. Under the term mineral, it is usual to comprehend all those substances which are not the results of organization; and for the purposes of analysis a division has been proposed of these substances into earths, salts, inflammable fossils, and metals with their ores; difficulty of solution being the characteristic of the first, comparatively easy solubility of the second, inflammability of the third, and the fourth are characterized by a high degree of specific gravity, metallic lustre, malleability, fusibility, &c. But the line of distinction between these substances is not capable of being drawn out with accuracy or precision; indeed, the recently detected metallic base of the earths and some of the saline class would be sufficient to prove that the above division, however convenient for the purposes of analytical examination, can lay no claim to absolute rectitude. Increase of temperature, minute division of different materials, admixture, and more recently voltaic electricity, are the principal agents employed for resolving minerals into their constituent elements; and we shall have occasion in the article CHEMISTRY to dwell upon the very important improvements lately introduced into the science, in reference to these particulars. Under the word MINERAL also, this subject will be resumed and enlarged upon. The mode of analyzing mineral waters will be treated of particularly in the article WATERS; and the means of detecting and analyzing those materials that are regarded as poisonous (an enquiry which has lately much occupied the attention of physicians and chemists) will be discussed separately and at large under the head of POISONS. ANALYSIS, in literature, is also used for a kind of syllabus, or table of the principal heads or articles of a continued discourse, disposed in their natural order and dependency. Analyses are more scientifical than alphabetical indexes; but they are less used, as being more intricate. Analysis is likewise used for a brief, but methodical, illustration of the principles of a science; in which sense it is nearly synonymous with what we otherwise call a synopsis. ANALYSIS, in mathematics, is properly the method of resolving problems by means of algebraical equations; hence we sometimes find that the two words analysis and algebra are used as synonymous. Or, Analysis may be distinguished into the ancient and the modern. The ancient analysis is the method of proceeding from the thing sought as taken for granted, through ' consequences, to something that is really canted or known. The principal authors on the ancient analysis, as recounted by Pappus, in the seventh book of his Mathematical Collections, are Euclid in his Data, Porismata, & de Locis ad Superficiem; Apollonius de Sectione Rationis, de Sectione Spatii, de Tactionibus, de Inclinationibus, de Locis Planis, & de Sectionibus Conicis; Aristæus de Locis Solidis; and Eratosthenes de Mediis Proportionalibus: from which Pappus gives many examples in the same book. To these we may add Pappus himself. This kind of analysis has also been successfully cultivated by many moderns; as Fermat, Viviani, Getaldus, Snellius, Huygens, Simpson, Stewart, Lawson, &c. and more especially Hugo d'Omerique, in his Analysis Geometrica, in which he has endeavoured to restore the analysis of the ancients. Dr. Pemberton says, that 'Sir Isaac Newton used to censure himself for not following the ancients more closely than he did; and spoke with regret of his mistake, at the beginning of his mathematical studies, in applying himself to the works of Des Cartes, and other algebraical writers, before he had considered the Elements of Euclid with that attention so excellent a writer deserves: that he highly approved the laudable attempt of Hugo d'Omerique to restore the ancient analysis.' In the application of the ancient analysis to geometrical problems, every thing cannot be brought within strict rule; nor any directions given, by which we may succeed in all cases; but some previous preparation is necessary, a kind of mental contrivance and construction, to form a connection between the data and quæsita, which must be left to every one's fancy to find out; being various, according to the various nature of the problems proposed: right lines must be drawn in particular directions, or of particular magnitudes; bisecting perhaps a given angle, or perpendicular to a given line; or perhaps tangents must be drawn to a given curve, from a given point; or circles described from a given centre, with given radius, or touching given lines, or other given circles; or suchlike other operations. Whoever is conversant with the works of Archimedes, Apollonius, or Pappus, well knows that they founded their analysis upon some such previous operations; and the great skill of the analyst consists in discovering the most proper affections on which to found his analysis: for the same problems may often be effected in many different ways; and that which leads to the conclusion by the most obvious and satisfactory steps, is the one which ought to be adopted Modern analysis consists chiefly of algebra, arithmetic of infinities, infini'e series, increments, fluxions, &c.; which form a kind of arithmetical and symbolical analysis, depending partly on modes of arithmetical computation, partly on rules peculiar to the symbols made use of, and partly on rules drawn from the nature and species of the quantities they represent, or from the modes of their existence or generation! The modern analysis is a general instrument by which the finest inventions and the greatest improvements have been made in mathematics and philosophy, for near two centuries past. It furnishes the most perfect examples of the manner in which the art of reasoning should be employed; it gives to the mind a remarkable skill in discovering things unknown, by means of a small number that are given; and by emploving short and easy symbols for expressing ideas, it presents to the understanding things which otherwise would seem to lie above its sphere. By this means geometrical demonstratons are greatly abridged: a long train of arguments, in which the mind cannot without the greatest effort of attention discover the connection of ideas, is converted into visible symbols; and the various operations which they require, are simply effected by the combination of those symbols. And, what is still more extraordinary, by this artifice a great number of truths are often expressed in one line only; instead of which, by following the ordinary way of explanation and demonstration, the same truths would occupy whole pages or volumes. And thus, by the bare contemplation of one line of calculation, we may understand in a short time whole sciences, which otherwise could hardly be comprehended in several years. From a comparison of the peculiar natures of the ancient and modern analysis, it results that the ancient method may, in some respects, be regarded as more perspicuous than that of the moderns; though the latter be far superior to it in point of despatch and facility of Invention: that the former is the most proper for one who is entering upon mathematical pursuits, as it will accustom him to a pure, clear, and accurate mode of investigation, and demonstration; but that the modern analysis should be recommended to his attention, as soon as proper habits of reasoning are established, because he may thereby be enabled to extend his views, and to strike out new improvements and discoveries. Or, adopting the conclusion of a late judicious writer on this subject, we may say, that, if mental discipline and recreation are sought for, they may be found in both methods; neither is essentially inaccurate; and, although in simple enquiries the geometrical has greater evidence, in abstruse and intricate investigations the analytical is most luminous; but, if the expeditious deduction of truth is the object, then the analytical calculus ought to be preferred. To arrive at a certain end, we should surely use the simplest means; and there is httle to praise or emulate in the labours of those who resolutely seek truth through the most difficult paths, who love what is arduous, because it is arduous; and, in subjects naturally difficult, toil with instruments the most incommodious.' Phil. Trans. 1822, part I. ANALYSIS RESIDUAL is a branch of the algebraic art, invented by the late Mr. John Landen, and applied to the solution of those problems which have, of late, been more generally solved by the doctrine of fluxions. This method was called the residual analysis, because, in all cases where it is made use of, the conclusions are obtained by means of residual quantities. In this analysis a geometrical or physical problem is reduced to another purely algebraical; and the solution is then obtained without any supposition of motion, and without considering quantities as composed of infinitely small particles. The residual analysis proceeds by taking the dif ference of the same function of a variable quautity in two different states of that quantity, and expressing the relation of this difference to the difference between the two states of the said variable quantity itself. This relation being first expressed generally, is then considered in the case when the difference of the two states of the variable quantity is =0. Mr. Landen published the first book of his Residual Analysis in 1764, and therein exemplified its usefulness in several algebraic enquiries, and in determining the tangents, evolution, ordinates, points of contrary flexure, double and triple, &c. points, asymptotes, centres, &c. of curve lines. In the second book it was intended to show the application of this analysis in a variety of mechanical and physico-geometrical enquiries: but that book was never published. Analysis of powers is the same as resolving them into their roots, and is otherwise called evolution. Analysis of curve lines shows their constitution, nature, and properties. ANALYTIC METHOD. The analytic method in logic stands opposed to the synthetic. In natural philosophy, as in mathematics, the investigation of difficult things by the analytic method ought to precede the method of composition. It consists in making experiments and observations, and in drawing general conclusions therefrom by induction; and admitting of no objections against the conclusions, but such as are drawn from experiments and other certain truths: and though the reasoning from experiments and observations by induction be no demonstration of general conclusions, yet it is the best method of reasoning of which the nature of things admits, and may be esteemed so much the stronger as the induction is more general; and, if no exception occur from phenomena, the conclusion may be pronounced general. this way of analysis, we may proceed from compounds to their ingredients; from motions to the forces producing them; and in general from effects to their causes, and from particular causes to more general ones, until we arrive at those which are the most general. This is the analytic method according to the illustrious Newton. The synthetic method consists in assuming the causes discovered and received as principles, and by them explaining the phenomena proceeding from them, and proving the explanations. See SYNTHESIS. By ANAM, a town of Hindostan, in the province of Oude, district of Lucknow, from the capital of which it is distant thirty-five miles W. S.W. N. lat. 25° 32′, E. lon. 80° 29′. ANAMABOA. See ANNAMABOA. ANAMANI, ANAMANES, or AMANES, in ancient geography, were friends and allies of the Romans, who inhabited Cisalpine Gaul, at the foot of the Apennines to the south of the Po, having Trebia to the west, and Tarus for their principal rivers. In the extent of their country were found Placentia, Veleia, Florentia, and Julia Fidentia. ANAMBAS, a cluster of islands in the China Sea, the largest of which is only twenty miles in circumference. They are situated about lat. 3° N., long. 106° 50' E. |