Analysis Sentence Examples

After careful analysis, he decided not to go.

The atomic weight of the element has been determined by analysis.

The analysis must be deeper, if we are to gain any further conclusions.

He needed to brush up on his analysis techniques.

But analysis has failed to find such differences.

These last articles show a keen analysis and interpretation of facts.

Regression analysis was used to predict the outcome.

This prediction is verified by the result of analysis.

He compiled the history and did an analysis of the writings of all the ecclesiastical writers of the first thirteen centuries.

The analysis of the consolidated data was set for a later date.

An analysis of the case has been made elsewhere, and Miss Keller has written her account of it.

Mathematics has influenced the form and the terminology of the science, and has sometimes been useful in analysis; but mathematical methods of reasoning, in their application to economics, while possessing a certain fascination, are of very doubtful utility.

Between them the general theory of the complex variable, and of the various "infinite" processes of mathematical analysis, was established, while other mathematicians, such as Poncelet, Steiner, Lobatschewsky and von Staudt, were founding modern geometry, and Gauss inaugurated the differential geometry of surfaces.

The analysis of the Hong Kong flora indicates that about threefifths of the species are common to the Indian region, and nearly all the remainder are either Chinese or local forms. The number of species common to southern China, Japan and northern Asia is small.

For the subjects of this general heading see the articles ALGEBRA, UNIVERSAL; GROUPS, THEORY OF; INFINITESIMAL CALCULUS; NUMBER; QUATERNIONS; VECTOR ANALYSIS.

Notable service was also rendered by Augustus de Morgan, who applied logical analysis to the laws of mathematics.

In the following year he published a paper on the analysis of one of the London pump-waters (from Rathbone Place, Oxford Street), which is closely connected with the memoirs just mentioned, since it shows that the calcareous matter in that water is held in solution by the "fixed air" present and can be precipitated by lime.

A second great service was the publication in the British Association Reports for 1833 of his "Report on the Recent Progress and Present State of certain branches of Analysis."

It all seems a very hurried and imperfectly studied philosophical analysis.

This section treats of the qualitative detection and separation of the metals, and the commoner methods employed in quantitative analysis.

Martin Heinrich Klaproth showed the necessity for igniting precipitates before weighing them, if they were not decomposed by this process; and he worked largely with Louis Nicolas Vauquelin in perfecting the analysis of minerals.

The evolution of mathematical thought in the invention of the data of analysis has thus been completely traced in outline.

Thus the current applications of mathematics to the analysis of phenomena can be justified by no a priori necessity.

For the subjects of this general heading see the articles Mechanics; Dynamics, Analytical; Gyroscope; Harmonic Analysis; Wave; HYDROMechanics; Elasticity; Motion, Laws Of; Energy; Energetics; Astronomy (Celestial Mechanics); Tide.

The 18th century witnessed a rapid development of analysis, and the period culminated with the genius of Lagrange and Laplace.

All these views have, however, been cast in the shade by more recent investigations based on minute literary analysis of the Pentateuch, begun by Graf, continued by Kuenen, and culminating in the work of Wellhausen and Robertson Smith.

The argument is supported by an analysis of the phenomena of dreams, which are ascribed to direct spiritual influences.

So also any exhaustive survey of the temperature and salinity of the sea at a great number of points on and below the surface reveals a complexity of conditions that may defy mathematical analysis and could not easily be predicted.

At present, however, the methods of analysis usually employed are not sufficiently delicate to afford all the necessary information as to the intrinsic value of the higher grades of rubber, and do not go much beyond the exclusion of inferior rubber.

It was also a distributory tax (impot de repartition); every year the king in his council fixed the total sum which the taille was to produce in the following year; he drew up and signed the brevet de la taille (warrant), and the contribution of the individual taxpayer was arrived at in the last analysis by a series of subdivisions.

Arithmetical groups, connected with the theory of quadratic forms and other branches of the theory of numbers, which are termed "discontinuous," and infinite groups connected with differential forms and equations, came into existence, and also particular linear and higher transformations connected with analysis and geometry.

Under Abel's guidance, the prevailing obscurities of analysis began to be cleared, new fields were entered upon and the study of functions so advanced as to provide mathematicians with numerous ramifications along which progress could be made.

Dr. Stone returned to the UK in January 2001 to begin data analysis.

It should know what the food on my fork weighs, run a chemical analysis of every bite I take, and log it in my Digital Echo file for my future reference.

The importance of ascertaining the proximate composition of bodies was clearly realized by Otto Tachenius; but the first systematic investigator was Robert Boyle, to whom we owe the introduction of the term analysis.

Having completed the dry analysis we may now pass on to the wet and more accurate investigation.

In the above account we have indicated the procedure adopted in the analysis of a complex mixture of salts.

We see however the similarity of the metal-working of both countries at approximately the same time; both are in the same style of artistic development, the Egyptian perhaps the more advanced of the two, and (if the published analysis by Mosso is to be relied upon) with the additional technique of the alloy with tin, making the metal bronze, and so easier for the heads to be cast.

But his great strength lay in metaphysical analysis, as was shown in his answer to the objections raised against the appointment of Sir John Leslie to the mathematical professorship (1805).

Often this felsitic devitrified glass is so fine-grained that its constituents cannot be directly determined even with the aid of the microscope, but chemical analysis leaves little doubt as to the real nature cf the minerals which have been formed.

In addition to many other researches besides those here mentioned, he wrote or edited various books on chemistry and chemical technology, including Select Methods of Chemical Analysis, which went through a number of editions; and he also gave a certain amount of time to the investigation of psychic phenomena, endeavouring to effect some measure of correlation between them and ordinary physical laws.

There is much keen analysis and original investigation in his two essays Der jiidische Stamm (1869) and Der jiidische Stamm in nicht jiidischen Spriich-wortern (1881-1882).

It is shown in the article on Combinatorial Analysis that (w; 0,n) is the coefficient of a e z w in the ascending expansion of the fraction 1-a.

These are effects of pedantry, and seem rather to be founded on a cold-blooded analysis of celebrated sermons than on any instinctive sense of the duty of the preacher.

The results, together with the chemical analysis of each sample, are given in a table contained in this paper, some of them being also represented graphically.

The second and third implements of analysis above cited are of the nature of cautions or checks.

Laplace was, moreover, the first to offer a complete analysis of capillary action based upon a definite hypothesis - that of forces "sensible only at insensible distances"; and he made strenuous but unsuccessful efforts to explain the phenomena of light on an identical principle.

In this neighbourhood fragments and lumps of glass are still constantly being dug up, and analysis proves that the glass contains a considerable proportion of magnesia.

An analysis of the glass of a Cairene mosque lamp shows that it is a soda-lime glass and contains as much as 4% of magnesia.

In regard to methods and apparatus, mention should be made of his improvements in the technique of organic analysis, his plan for determining the natural alkaloids and for ascertaining the molecular weights of organic bases b y means of their chloroplatinates, his process for determining the quantity of urea in a solution - the first step towards the introduction of precise chemical methods into practical medicine - and his invention of the simple form of condenser known in every laboratory.

His contributions to inorganic chemistry were numerous, including investigations on the compounds of antimony, aluminium, silicon, &c., on the separation of nickel and cobalt, and on the analysis of mineral waters, but they are outweighed in importance by his work on organic substances.

Of the carbon dioxide and ammonia no exhaustion can take place, but of the mineral constitutents the supply is limited because the soil cannot afford an indefinite amount of them; hence the chief care of the farmer, and the function of manures, is to restore to the soil those minerals which each crop is found, by the analysis of its ashes, to take up in its growth.

It is not provided with a glossary, but contains an elaborate and most valuable analysis of the diction, synonymy and syntactical features of the poem.

By reference to the analysis given above, it will be seen that there are four sections in Zech.

A great analysis was to precede a great synthesis, but it was the synthesis on which Comte's vision was centred from the first.

Let us first sketch the nature of the analysis.

They are thus the double key of The double Comte's systematization of the philosophy of all the key of sciences from mathematics to physiology, and his positive analysis of social evolution, which is the base of philo= sociology.

Gold is supposed to have found a place in ancient bronzes, but its presence has never been detected by analysis, and of silver not more than 2% seems to have been admitted at any time.

Fortunately it chanced that another people, the Persians, had adopted the Assyrian wedge-shaped stroke as the foundation of a written character, but making that analysis of which the Assyrians had fallen short, had borrowed only so many characters as were necessary to represent the alphabetical sounds.

Every belief of mankind is in the last analysis amenable to reason, and finds its origin in evidence that can appeal to the arbitrament of common sense.

These traditions, finding their clearest delineation in the lines of Homer, had been subjected to the analysis of the critical historians of the early decades of the 19th century, and their authenticity had come to be more than doubted.

Dittmar's analysis of the " Challenger " samples indicated an excess of oxygen in the surface water of high southern latitudes and a deficiency at depths below 50 fathoms.

But his account of the first is imperfect, because in ancient analysis the more general propositions, with which it concludes, are not mere consequences, but the real grounds of the given proposition; while his addition of the second reduces the nature of analysis to the utmost confusion, because hypothetical deduction is progressive from hypothesis to consequent facts whereas analysis is regressive from consequent facts to real ground.

Along this line of speculation we have a logic which claims that whatsoever is in one plane or at one stage in the development of thought a residuum that apparently defies analysis must at another stage and on a higher plane be shown so to be absorbed as to fall altogether within thought.

But it is evident that in these letters she was making a clear analysis of what she was doing.

It combines with many metals to form sulphides, and also decomposes many metallic salts with consequent production of sulphides, a property which renders it extremely useful in chemical analysis.

The complete analysis involves an examination of the fatty matter, of the various forms in which the alkalis are present - free and combined glycerin, &c.

The analysis of organic compounds is also noticed.

The beginning of the 19th century witnessed the discovery of certain powerful methods for the analysis of compounds and the isolation of elements.

Berzelius's investigation of the action of the electric current on salts clearly demonstrated the invaluable assistance that electrolysis could render to the isolator of elements; and the adoption of this method by Sir Humphry Davy for the analysis of the hydrates of the metals of the alkalis and alkaline earths, and the results which he thus achieved, established its potency.

The extraordinary patience requisite to a successful termination of such an analysis can only be adequately realized by actual research; an idea may be obtained from Crookes's Select Methods in Analysis.

Berzelius, in 1813 and 1814, by improved methods of analysis, established that the Daltonian laws of combination held in both the inorganic and organic kingdoms; and he adopted the view of Lavoisier that organic compounds were oxides of compound radicals, and therefore necessarily contained at least three elements - carbon, hydrogen and oxygen.

Unfortunately, the term normal is sometimes given to solutions which are strictly decinormal; for example, iodine, sodium thiosulphate, &c. In technical analysis, where a solution is used for one process only, it may be prepared so that I cc. is equal to.

Another son, James (1786-1869), was a physician, and author of various books, such as Philosophy of the Human Voice (1827) and Analysis of the Human Intellect (1865).

Great advances were made in the study of indeterminate equations, a branch of analysis in which Diophantus excelled.

The Arabians more closely resembled the Hindus than the Greeks in the choice of studies; their philosophers blended speculative dissertations with the more progressive study of medicine; their mathematicians neglected the subtleties of the conic sections and Diophantine analysis, and applied themselves more particularly to perfect the system of numerals, arithmetic and astronomy.

Satire, debarred from comment on political action, turned to social and individual life, and combined with the newly-developed taste for ethical analysis and reflection introduced by Cicero.

As Marcet had foreshadowed from the analysis of 14 samples in 1819, the larger series of exact analyses proved that the variations in the proportion of individual salts to the total salts are very small, and all analyses since Dittmar's have confirmed this result.

Various schemes of analysis have been proposed to account for this and other passages of the same nature in the epistle, e.g.

This resolution or analysis into simple, because clear and distinct, elements may be brought to a standstill again and again by obscurity and indistinctness, but patient and repeated revision of all that is included in the problem should bring the analytic process to fruition.

Syllogism is not the synthesis which together with analysis goes to constitute the new instrument of science.

Hobbes developed the nominalism which had been the hallmark of revolt against scholastic orthodoxy, and, when he brings this into relation with the analysis and synthesis of scientific A notable formula of Bacon's Novum Organum ii.

Analysis is the sole way of invention or discovery.

Nay, even the use of letters at all suggests that the sort of analysis that actually breaks up its subject-matter is universally or all but universally applicable in nature, and this is not the case.

It is, as it were, a schedule to be filled in, and is connected with the disjunctive judgment as a schematic setting forth of alternatives, not with the hypothetical, and ultimately the apodictic judgment with their suggestion that it is the real movement of thought that is subjected to analysis.

The future of symbolic logic as coherent with the rest of logic, in the sense which the word has borne throughout its history seems to be bound up with the question of the nature of the analysis that lies behind the symbolism, and of the way in which this is justified in the setting of a doctrine of validity.

The atomic weight has been determined by many investigators; the chief methods employed being the analysis and synthesis of the trioxide and the analysis of the hexachloride.

The bibliography attached to this chapter (p. 852) gives a list of all the principal published documents and works, together with some analysis of the unpublished Foreign Office records bearing on the subject.

Stas determined its composition by the analysis of pure silver chlorate.

So far from the recognition of a plan in Acts being inimical to a quest after the materials used in its composition, one may say that it points the way thereto, while it keeps the literary analysis within scientific limits.

He was especially interested in questions relating to the polarization of light, and his observations in this field, which gained him the Rumford medal of the Royal Society in 1840, laid the foundations of the polarimetric analysis of sugar.

The practical problems of fluid motion, which are amenable to mathematical analysis when viscosity is taken into account, are excluded from treatment here, as constituting a separate branch called "hydraulics" (q.v.).

While it is impossible to give here anything like a complete or exact survey of the field - a task rendered almost impossible by the arbitrary manner in which paragraphs are divided, by the difficulty of making Old English enactments fit into modern rubrics, and by the necessity of counting several times certain paragraphs bearing on different subjects - a brief statistical analysis of the contents of royal codes and laws may be found instructive.

On analysis, the law of the Ripuarians, which contains 89 chapters, falls into three heterogeneous divisions.

In the mechanical analysis of the soil, after separation of the stones and fine gravel by means of sieves, the remainder of the finer earth is subjected to various processes of sifting and deposition from water with a view of determining the relative proportions of sand, silt and clay present in it.

The nodules increase in size, and analysis shows that they are exceedingly rich in nitrogen up to the time of flowering of the host plant.

An analysis of the innumerable outbreaks in various parts of Europe indicates that the geological features of the affected districts play a less important part in the incidence of the disease than soil dampness.

When the positive method has been finally extended to society, as it has been to chemistry and physiology, these social facts will be resolved, as their ultimate analysis, into relations with one another, and instead of seeking causes in the old sense of the word, men will only examine the conditions of social existence.

A sociological demonstration lies in the establishment of an accordance between the conclusions of historical analysis and the preparatory conceptions of biological theory.

It was a searching analysis of the financial and moral grounds on which the impost rested, and a historical justification and eulogy of it.

The chief feature in the new venture at first consisted of the analysis of the journals, which Cave undertook personally.

His collaborateurs each agreed to undertake the criticism of a separate literature while Nazzari retained the general editorship and the analysis of the French books.

The actual boundaries between animals and plants are artificial; they are rather due to the ingenious analysis of the systematist than actually resident in objective nature.

Thus, a number of copper-tin alloys when digested with hydrochloric acid leave the same crystalline residue, which on analysis proves to be the compound Cu 3 Sn.

But the comparative study of religions has suggested the lines of reconstitution and the careful analysis of survivals embedded in literature and the evidence of monumental remains, and in particular of the old calendars, has enabled modern scholars to make good progress in the task of separating the elements due to different periods and influences.

No doubt the later indigitamenta (" bidding-prayers") which give us detailed lists of the spirits which preside over the various actions of the infant, or the stages in the marriage ceremony, or the agricultural operations of the farmer, are due in a large measure to deliberate pontifical elaboration, but they are a true indication of the Roman attitude of mind, which reveals itself continually in the analysis of the cults of the household or the festivals of the agricultural year.

It would be out of place to attempt any further analysis of the Conquete here.

The final goal of Greek philosophy was only reached when the great thinkers of the early Christian Church, who had been trained in the schools of Alexandria and Athens, used its modes of thought in their analysis of the Christian idea of God.

Such a riper analysis of the mystery of his own personality enabled him to arrive at a clearer conception of the idea of divine personality, " whose triunity has nothing potential or unrealized about it; whose triune elements are eternally actualized, by no outward influence, but from within; a Trinity in Unity."

The province of reverent theology is to aid accurate thinking by the use of metaphysical or psychological terms. Its definitions are no more an end in themselves than an analysis of good drinking water, which by itself leaves us thirsty but encourages us to drink.

So the Nicene Creed is the analysis of the river of the water of life of which the Sermon on the Mount is a description, flowing on from age to age, freely offered to the thirsty souls of men.

The Assyrians with all their culture, never attained the stage of analysis which demonstrates that only a few fundamental sounds are involved in human speech, and hence that it is possible to express all the niceties of utterance with an alphabet of little more than a score of letters.

Halting just short of this analysis, the Assyrian ascribed syllabic values to the characters of his script, and hence, instead of finding twenty odd characters sufficient, he required about five hundred.

The philological analysis of Wolf and his successors had raised doubts as to the very existence of Homer, and at one time the main current of scholarly opinion had set strongly in the direction of the belief that the Iliad and the Odyssey were in reality but latter-day collections of divers recitals that had been handed down by word of mouth from one generation to another of bards through ages of illiteracy.

His inaugural discourse was on the "new analysis," which he so successfully applied in investigating various problems both in pure and applied mathematics.

This famous book is an analysis of the methods whereby an ambitious man may rise to sovereign power.

That end is the analysis of the conception of the state, studied under two main types, republican and monarchical.

The third volume of the Epopees francaises contains an analysis and full particulars of the chansons de geste immediately connected with the history of Charlemagne.

A small proportion of organic matter including the fat globules of the plankton is mixed with the calcium carbonate, the amount according to Giimbel's analysis being about 1 part in 1000.

The analyses of modern chemists have now revealed the existence of 32 out of the 80 known elements as existing dissolved in sea-water, and it is scarcely too much to say that the remaining elements also exist in minute traces which the available methods of analysis as yet fail to disclose.

Ruppin's analysis of Baltic water, which has an alkalinity of 16 to 18 instead of the 5 or 6 which would be the amount proportional to the salinity, while the water of the Vistula and the Elbe with a salinity of o 1 per mille has an alkalinity of 28 or more.

As the amount of ash varies very considerably in different coals, and stands in no relation to the proportion of the other constituents, it is necessary in forming a chemical classification to compute the results of analysis after deduction of the ash and hygroscopic water.

The atomic weight of caesium has been determined by the analysis of its chloride and bromide.

In 1804 were also delivered the noble lectures entitled Grundziige des gegenwdrtigen Zeitalters (Characteristics of the Present Age, 1804), containing a most admirable analysis of the Aufkltirung, tracing the position of such a movement of thought in the natural evolution of the general human consciousness, pointing out its inherent defects, and indicating as the ultimate goal of progress the life of reason in its highest aspect as a belief in the divine order of the universe.

In his Discourse on the "Residual Analysis," he proposes to avoid the metaphysical difficulties of the method of fluxions by a purely algebraical method.

The foundations of idealism in the modern sense were laid by the thinkers who sought breathing room for mind and will in a deeper analysis of the relations of the subject to the world that it knows.

True, before differences can be united they must have been separated, but this merely proves that differentiation or analysis is only one factor in a single process.

Similarly from the side of logic. It is not the teaching of idealism alone but of the facts which logical analysis has brought home to us that all difference in the last resort finds its ground in the quality or content of the things differentiated, and that this difference of content shows in turn a double strand, the strand of sameness and the strand of otherness - that in which and that by which they differ from one another.

In the " resultant " there is a new direction, and with it a new quality the component forces of which no analysis can discover.'

As little from the side of knowledge is it likely that any theory will find acceptance which reduces all thought to a process of analysis and the discovery of abstract identity.

More precisely, it is a theory of what doctrine ought to be, or a deeper analysis of its nature; it is not a statement of what doctrine has been held to be in the past.

C. Gooch, which has come into common use in quantitative analysis where the solid matter has to be submitted to heating or ignition, consists of a crucible having a perforated bottom.

The Diophantine analysis was a favourite subject with Pell; he lectured on it at Amsterdam; and he is now best remembered for the indeterminate equation ax 2 +1 = y 2, which is known by his name.

Seubert (Ber., 1888, 21, p. 1839) from the analysis of potassium and ammonium osmichlorides, the values obtained being approximately 191.

He belongs distinctly to the romantic school; his forte is vivid and picturesque description, the lively presentation of scenes and actions, characters and states of society, not the subtle analysis of motives, the power of detecting the undercurrents or the generalizing faculty.

In addition to this review, the Bollandists undertook the analysis of the hagiographic MSS.

In the first degree there is a strong persuasion of the propriety of the impression made; the second and third degrees are produced by comparisons of the impression with others associated with it, and an analysis of itself.

Previous to that date, the only step towards compilation of the census results of the empire had been a bare statement of area and population, appended without analysis, comparison or comment, to the reports for England and Wales, from the year 1861 onwards.

The reports for New South Wales and Victoria are especially valuable in their statistical aspect from the analysis they contain of the vital conditions of a comparatively young community under modern conditions of progress.

The information required differs in each group, but the schedule is, as a rule, of a simple character, and the results of the inquiry are usually set forth with comparatively little comment or analysis.

The results of this census were tabulated with care and skill, and a preliminary analysis gave the salient results and in some cases compared them with European figures.

At first he occupied himself with ordinary routine work, but being far from satisfied with the scope which this afforded, he seized eagerly upon the opportunity for novel research, offered by Kirchhoff's discoveries in spectrum analysis.

As a result of the importance both of the formulae obtained by elementary methods and of those which have involved the previous use of analysis, there is a tendency to dissociate the former, like the latter, from the methods by which they have been obtained, and to regard mensuration as consisting of those mathematical formulae which are concerned with the measurement of geometrical magnitudes (including lengths), or, in a slightly wider sense, as being the art of applying these formulae to specific cases.

There are certain special cases where the treatment is really analytical, but where, on account of the simplicity or importance of the figures involved, the analysis does not take a prominent part.

In two pamphlets, by an analysis of the teaching of the Socialists and a survey of Clerical policy during the 19th century, he explained and justified his opinions.

In 1881 he prepared A Primer of Logical Analysis for students of English composition.

His "theorie des debouches" amounts to this, that, products being, in last analysis, purchased only with products, the extent of the markets (or outlets) for home products is proportional to the quantity of foreign productions; when the sale of any commodity is dull, it is because there is not a sufficient number, or rather value, of other commodities produced with which it could be purchased.

Analysis of Contents.-The book's chief break is at xiii.

The above analysis is rough, since even distantly placed sections, indeed the two parts themselves, are interrelated by delicate complex references on and back.

Among the few critically satisfactory French books, Abbe Loisy's Le Quatrieme evangile (1903) stands pre-eminent for delicate psychological analysis and continuous sense of the book's closely knit unity; whilst Pere Th.

Voltaire himself, speaking as a practical man rather than as a metaphysician, declared that if there were no God it would be necessary to invent one; and if the analysis is only carried far enough it will be found that those who deny the existence of God (in a conventional sense) are all the time setting up something in the nature of deity by way of an ideal of their own, while fighting over the meaning of a word or its conventional misapplication.

This opinion is not improbable, as the earlier books of the Old Testament cannot have been unknown in his age; and the critical analysis of the canonical book of Kings is advanced enough to enable us to say that in some of the parallel passages the chronicler uses words which were not written in the annals but by one of the compilers of Kings himself.

Professor Claxton Fidler (Treatise on Bridge Construction, 1887) has made a very careful theoretical analysis of the weights of bridges of different types, and has obtained the following values for the limiting spans.

The passages in which these things are laid bare by Paul's remorseless analysis of his own experience "under Law" seem to have made practically no impression on the Apostolic Fathers as a whole.

Abstraction differs from Analysis, inasmuch as its object is to select a particular quality for consideration in itself as it is found in all the objects to which it belongs, whereas analysis considers all the qualities which belong to a single object.

We might consider that matter and aether can coexist in the same space; this would involve the co-existence and interaction of a double set of properties, introducing great complication, which would place any coherent scheme of physical action probably beyond the powers of human analysis.

With reference to all such further refinements of theory, it is to be borne in mind that the perfect fluid of hydrodynamic analysis is not a merely passive inert plenum; it is also a continuum with the property that no finite internal slip or discontinuity of motion can ever arise in it through any kind of disturbance; and this property must be postulated, as it cannot be explained.

Masaryk's work, Spirit of Russia, is a close analysis of the Russian philosophy of history, and of the Russian religious, moral and political thought.

Dillmann's analysis is as follows.

This analysis has on the whole been accepted by Harnack, Schi rer, Deane and Beer.

This translation is made from Charles's text, and his analysis of the text is in the main accepted by this scholar.

During forty years the resources of analysis, even in the hands of d'Alembert, Lagrange and Laplace, had not carried the theory of the attraction of ellipsoids beyond the point which the geometry of Maclaurin had reached.

Hume's analysis of the conceptions of a permanent world and a permanent self reduces us to the sensationalistic relativism of Protagoras.

He advanced towards the modern view of elements as the undecomposable constituents of material bodies; and understanding the distinction between mixtures and compounds, he made considerable progress in the technique of detecting their ingredients, a process which he designated by the term "analysis."

Proctor in 1877 directed attention to the composition of the slag resulting from the burning of esparto, which they found to be strikingly similar to that of average medical bottle glass, the latter yielding on analysis 66.3% of silica and 25.1% of alkalies and alkaline.

Sodium dioxide is chiefly employed as an oxidizing agent, being used in mineral analysis and in various organic preparations; it readily burns paper, wood, &c., but does not evolve oxygen unless heated to a high temperature.

The above analysis is one of nine by Dr Arthur Voelcker, in which the fat was found to range from about 2 to 124%.

In any region of velocity where it is possible to represent p with sufficient accuracy by an empirical formula composed of a single power of v, say v m, the integration can be effected which replaces the summation in (to), (16), and (24); and from an analysis of the Krupp experiments Colonel Zabudski found the most appropriate index m in a region of velocity as given in the following table, and the corresponding value of gp, denoted by f (v)or v m lk or its equivalent Cr, where r is the retardation.

See further COMBINATORIAL ANALYSIS.

As a mathematician he occupied himself with many branches of his favourite science, more especially with higher algebra, including the theory of determinants, with the general calculus of symbols, and with the application of analysis to geometry and mechanics.

Analysis, &c. - All volatile potassium compounds impart a violet coloration to the Bunsen flame, which is masked, however, if sodium be present.

In 1764 Leonhard Euler employed the functions of both zero and integral orders in an analysis into the vibrations of a stretched membrane; an investigation which has been considerably developed by Lord Rayleigh, who has also shown (1878) that Bessel's functions are particular cases of Laplace's functions.

The literary differences are, moreover, often accompanied by differences of treatment, or representation of the history, which, where they exist, confirm independently the conclusions of the literary analysis.

Father Simon in his Histoire critique du Vieux Testament (1682) also argues that the Pentateuch is the work of more than one author, and makes an important advance towards a systematic analysis of the separate elements by observing that the style varies, being sometimes very curt and sometimes very copious " although the variety of the matter does not require it."

Moses had used different documents, and that of these the two chief were distinguished by their use of different divine names - Elohim and Yahweh; by the use of this clue he gave a detailed analysis of the passages belonging to the several documents.

For subsequent developments, and the fruitful results of documentary analysis as applied to the Pentateuch and other composite books, which cannot be dealt with in any detail here, reference must be made to the special articles on the books of the Old Testament.

He carries through, as Astruc had done, the analysis of Genesis into (primarily) two documents; he draws the distinction between the Priests' Code, of the middle books of the Pentateuch, and Deuteronomy, the people's law book; and admits that even the books that follow Genesis consist of different documents, many incomplete and fragmentary (whence the theory became known as the " Fragment-hypothesis "), but all the work of Moses and some of his contemporaries.

He carried criticism beyond literary analysis and literary appreciation to the task of determining the worth of the documents as records, the validity of the evidence.

Any documentary analysis of the Pentateuch may be right or wrong; but archaeology contributes nothing either one way or another as to the answer.

Von Soden's analysis of numbers, contents and date may be tabulated as follows, but it must be remembered that it reckons many small fragments as separate MSS., especially in the earlier centuries.

Sabine remarked when awarding him the Rumford medal of the Royal Society in 1872, contains a fundamental principle of spectrum analysis, and though for a number of years it was overlooked it entitles him to rank as one of the founders of spectroscopy.

The analysis of manganese dioxide in 1774 led him to the discovery of chlorine and baryta; to the description of various salts of manganese itself, including the manganates and permanganates, and to the explanation of its action in colouring and decolourizing glass.

Papers published in 1776 were concerned with quartz, alum and clay and with the analysis of calculus vesicae from which for the first time he obtained uric acid.

In the measurement of woollen and other textile fabrics, as to quality, strength, number of threads, &c., there exists at Bradford a voluntary standardizing institution known as the Conditioning House (Bradford Corporation Act 1887), the work of which has been extended to a chemical analysis of fabrics.

Relative to the uncertain connexion of length, capacity and weight in the ancient metrological systems of the East, Sir Charles Warren, R.E., has obtained by deductive analysis a new equivalent of the original cubit (Palestine Exploration Fund Quarterly, April, July, October 1899).

Ancient myths are admitted without undergoing analysis; the most naïve realism alternates with daring efforts at spiritualizing.

The mathematical function log x or log x is one of the small group of transcendental functions, consisting only of the circular functions (direct and inverse) sin x, cos x, &c., arc sin x or sin-' x,&c., log x and e x which are universally treated in analysis as known functions.

The logarithmic function is most naturally introduced into analysis by the equation log x= x ?

He was, however, the first whose analysis was sufficiently convincing to exorcise the tyranny of grammatical forms. The categorical and disjunctive judgment reduce to the hypothetical.

As such strainers were further improved, by sorting the sand and gravel, and using the fine sand only at the surface, better clarification of the water was obtained; but chemical analysis indicated, or was at the time thought to indicate, that that improvement was practically confined to clarification, as the dissolved impurities in the water were certainly very little changed.

This was his introduction to modern analysis.

He found time to write two larger works, the History of the Roman Coinage and the Romisches Staatsrecht, a profound analysis of Roman constitutional law, and Romisches Strafrecht, on Roman criminal jurisdiction.

The in-depth analysis has been carried out during the past few months.

It appears from comparison of the work in the two great divisions of vertebrate and invertebrate palaeontology made for the first time in this article that in accuracy of observation and in close philosophical analysis of facts the students of invertebrate palaeontology led the way.

More recent analysis has shown, however, that certain modifications observed within the same stratigraphic level are really grades of mutations which show divergences comparable to those found in successive levels.

Instances of marine and lacustrine analysis have been cited above.

The analysis of continental faunas into those inhabiting rivers, lowlands, forests, plains or uplands, affords a key to physiographic conditions all through the Tertiary.

Dealing with interrupted evidence, however, it becomes necessary to exercise the closest analysis and synthesis as part of his general art as a restorer.

The sum of the primitive characters approximately restores the primitive form; and the gaps in palaeontological evidence are supplied by analysis of the available zoological, embryological and anatomical evidence.

On the other hand, Huxley's summation of the primitive characters of all the mammals led him to an amphibian stem type, a prophecy which has proved faulty because based on erroneous analysis and comparison.

Thus the analysis of George Baur of the ancestral form of the lizards, mosasaurs, dinosaurs, crocodiles and phytosaurs led both to the generalized Palaeohatteria of the Permian and indirectly to the surviving Tuatera lizard of New Zealand.

Primitive ideas on the subject of the soul, and at the same time the origin of them, are best illustrated by an analysis of the terms applied to it.

Iodine has extensive applications in volumetric analysis, being used more especially for the determination of copper.

Stas, from the analysis of pure silver iodate, and by C. Marignac from the determinations of the ratios of silver to iodine, and of silver iodide to iodine; the mean value obtained for the atomic weight being 126.53.

He wrote numerous papers on photometry and spectrum analysis in Poggendorff's Annalen and Berichte der k.

But an analysis of his results leaves the reader in more perplexity than satisfaction at the kind of information imparted, and he reverts insensibly to the sources from which his instructor has himself been instructed.

Nevertheless the mountains are of especial interest to the physiographer who wishes to make a comparative study of land forms as affected by normal and by glacial sculpture, in order to give due attention to process as well as to structure and stage in the analysis and description of mountain topography.

The work of Wallis had evidently an important influence on the next notable personality in the history of the subject, James Gregory, who lived during the period when the higher algebraic analysis was coming into power, and whose genius helped materially to develop it.

Each of these was divided into two books, and, with the Data, the Porisms and Surface-Loci of Euclid and the Conics of Apollonius were, according to Pappus, included in the body of the ancient analysis.

Restorations have been given by Marino Ghetaldi, by Hugo d'Omerique (Geometrical Analysis, Cadiz, 1698), and (the best) by Samuel Horsley (1770).

As the result of an exhaustive analysis of the text and of the political and religious events of the time, Mayer comes to the conclusion that the document was forged about 775, i.e.

This analysis does not disclose, nor indeed is it possible to discover, what was the determining element for Tertullian; in fact he was under the dominion of more than one ruling principle, and he felt himself bound by several mutually opposing authorities.

But in spite of this great logical achievement, he continued throughout the discourse to accept Plato's grammatical analysis of all sentences into noun and verb, which indeed applies to the proposition as a sentence but does not give its particular elements.

Nor does the work get further than the analysis of some propositions into noun and verb with " is " added to the predicated verb; an analysis, however, which was a great logical discovery and led Aristotle further to the remark that " is " does not mean " exists "; e.g.

How then did Aristotle get further in the logical analysis of the proposition?

It is nearer to Plato's analysis of the sentence, and no logician would have gone back to it, after the Prior Analytics.

These considerations make it probable that the author of all three treatises was Aristotle himself; while the analysis of the treatises favours the hypothesis that he wrote the Eudemian Ethics and the Magna Moralia more or less together as the rudimentary first drafts of the mature Nicomachean Ethics.

We cannot write a history of the varied origin of logic, beyond putting the rudimentary logic of the proposition in the De Interpretatione before the less rudimentary theory of categories as significant names capable of becoming predicates in the Categories, and before the maturer analysis of the syllogism in the Analytics.

He means that the logical analysis of demonstration in the Analytics would teach them beforehand that there cannot be demonstration, though there must be induction, of an axiom, or any other principle; whereas, if they are not logically prepared for metaphysics, they will expect a demonstration of the axiom, as Heraclitus, the Heraclitean Cratylus and the Sophist Protagoras actually did, - and in vain.

Hence, when the number of any proposed year in each of the cycles is known, its number in the Julian period can be determined by the resolution of a very simple problem of the indeterminate analysis.

It was evident that a similar analysis might have been applied to tactual consciousness which does not give externality in its deepest significance any more than the visual; but with deliberate purpose Berkeley at first drew out only one side of his argument.

In ultimate analysis, then, nature is conscious experience, and forms the sign or symbol of a divine, universal intelligence and will.

Berkeley is compelled to see that an immediate perception is not a thing, and that what we consider permanent or substantial is not a sensation but a group of qualities, which in ultimate analysis means sensations either immediately felt or such as our experience has taught us would be felt in conjunction with these.

Thus he devoted one summer vacation to the careful analysis of Comte's Politique positive.

An analysis of his works has been written by Mrs Meynell (1900).

Spectrum analysis thus passed quickly out of the stage in which its main purpose was " analysis " and became our most delicate and powerful method of investigating molecular properties; the old name being no longer appropriate, we now speak of the science of " Spectroscopy."

This analogy is useful because the application of Fourier's analysis to the optical theory of spectroscopes has been doubted, and it may be urged in answer to the objections raised that the instrument acts in all respects like a mechanical analyser,' the applicability of which has never been called into question.

A treatise on the analysis of thought (Sur la decomposition de la pensee), although sent to press, was never printed.

In it de Gerando, after a rapid review of ancient and modern speculations on the origin of our ideas, singles out the theory of primary ideas, which he endeavours to combat under all its forms. The latter half of the work, devoted to the analysis of the intellectual faculties, is intended to show how all human knowledge is the result of experience; and reflection is assumed as the source of our ideas of substance, of unity and of identity.

Leibnitz, again, having become equally dissatisfied with Cartesianism, Spinozism and the Epicurean realism of Gassendi, in the latter part of his life came still nearer than Spinoza to metaphysical idealism in his monadology, or half-Pythagorean,half-Brunistic analysis of bodies into monads, or units, or simple substances, indivisible and unextended, but endowed with perception and appetite.

Up to this point, then, Leibnitz opened one of the chief avenues to metaphysical idealism, the resolution of the material into the immaterial, the analysis of bodies into mental elements.

His theory of bodies involved an idealistic analysis neither into bodily atoms nor into mathematical units, but into mentally endowed simple substances.

The analysis of bodies into immaterial elements by Leibnitz incited Lotze.

He accepted the Leibnitzian fallacy that unity is indivisibility, which led to the Leibnitzian analysis of material bodies into immaterial monads, indivisible and therefore unextended, and to the theory of monadic souls and entelechies.

But, in thus adapting to his own purposes the Leibnitzian analysis of material into immaterial, he drew his own conclusions according to his own metaphysics, which required that the supposed centres of force are not Leibnitzian " monads," nor Herbartian " reals," nor divine modifications such as Lotze afterwards supposed, but are elements of a system which in outer aspect is bodily and in inner aspect is spiritual, and obeying laws of spirit.

But the idealists are only too glad to get any excuse for denying bodily substances and causes; and, while Leibnitz supplied them with the fancied analysis of material into immaterial elements, and Hume with the reduction of bodies to assemblages of sensations, Mach adds the additional argument that bodily forces are not causes at all.

If judgment is an analysis of an aggregate idea into subject and predicate, it follows, as he says, that " as judgment is an immediate, so is inference a mediate, reference of the members of any aggregate of ideas to one another " (System der Philosophie, 66, first ed.).

If knowledge is experience of ideas distinguished by inner will of apperception into subject and object in inseparable connexion, if the starting-point is ideas, if judgment is analysis of an aggregate idea, if inference is a mediate reference of the members of an aggregate of ideas to one another, then, as Wundt says, all we can know, and all reason can logically infer from such data, is in our ideas, and consciousness without an object of idea is an abstraction; so that reason, in transcending experience, can show the necessity of ideas and " ideals," but infer no corresponding reality beyond, whether in nature, or in Man, or in God.

Weber, whose Metaphysik, completed in 1891, starting from the ego and the analysis of consciousness, aims at arriving at the distinction between spirit and nature, and at rising to the spirit of God the Creator.

At the same time, like Cousin, his works show a tendency to underrate body, tending as they do to the Leibnitzian analysis of the material into the immaterial, and to the supposition that the unity of the body is only given by the soul.

If an iron ship be swung when upright for deviation, and the mean horizontal and vertical magnetic forces at the compass positions be also observed in different parts of the world, mathematical analysis shows that the deviations are caused partly by the permanent magnetism of hard iron, partly by the transient induced magnetism of soft iron both horizontal and vertical, and in a lesser degree by iron which is neither magnetically hard nor soft, but which becomes magnetized in the same manner as hard iron, though it gradually loses its magnetism on change of conditions, as, for example, in the case of a ship, repaired and hammered in dock, steaming in an opposite direction at sea.

Instead of observing the deviation solely for the purposes of correcting the indications of the compass when disturbed by the iron of the ship, the practice is to subject all deviations to mathematical analysis with a view to their mechanical correction.

He developed a great research laboratory of experimental physics, attracting numerous workers from many countries and colonies; advances were made in the investigation of the conduction of electricity through gases, in the determination of the charge and mass of the electron and in the development of analysis by means of positive rays.

It can only be contrived by means of complicated mathematical analysis.

Such general statements of the theory of motion as that of Lagrange, while releasing us from the rather narrow and strained view of the subject presented by detailed analysis of motion in terms of force, have also suggested a search for other forms which a statement of elementary principles might equally take as the foundation of a logical scheme.

Professor Maximowicz concludes from an analysis of the Prjevalsky collection that the flora of Tibet is extremely ancient, and that it is chiefly composed of immigrants from the Himalaya and Mongolia.

The analysis of air was conducted by determining the amount of oxygen present and assuming the remainder to be nitrogen.

The attack made by David Hume on the causal relation led directly to the new rationalism of Kant, who argued that it was wrong to regard thought as mere analysis.

From about 1864 he occupied himself almost exclusively with spectrum analysis, both of stars (Catalogo delle stelle di cui si e determinato lo spettro luminoso, Paris, 1867, 8vo; "Sugli spettri prismatici delle stelle fisse," two parts, 1868, in the Atti della Soc. Ital.) and of the sun (Le Soleil, Paris, 1870, 8vo; 2nd ed., 1877).

A fuller analysis, and some notice of the predecessors of Grotius, will be found in Hely, Etude sur le droit de la guerre de Grotius (Paris, 1875).

The volume contains also dissertations on Logarithms and on the Limits of Quantities and Ratios, and a few problems illustrative of the ancient geometrical analysis.

The view of the dual nature of lichens had hitherto been based on analysis; the final proof of this view was now supplied by the actual synthesis of a lichen from fungal and algal constituents.

It has been supposed that this theory was suggested to him either by researches on olefiant gas and carburetted hydrogen or by analysis of "protoxide and deutoxide of azote," both views resting on the authority of Dr Thomas Thomson (1773-1852), professor of chemistry in Glasgow university.

He proceeds to give what has been quoted as his first table of atomic weights, but on p. 248 of his laboratory notebooks for 1802-1804, under the date 6th of September 1803, there is an earlier one in which he sets forth the relative weights of the ultimate atoms of a number of substances, derived from analysis of water, ammonia, carbon-dioxide, &c. by chemists of the time.

It appears, then, that, confronted with the "problem of ascertaining the relative diameter of the particles of which, he was convinced, all gases were made up, he had recourse to the results of chemical analysis.

In one of them, read in 1814, he explains the principles of volumetric analysis, in which he was one of the earliest workers.

An analysis of Lie's works is given in the Bibliotheca Mathematica (Leipzig, 1900).

Indeed, an analysis of the composition of the alpine flora as a whole leads to the conclusion that the chief bond of union between its members consists in the treeless character of their habitat.

Rain-water is the best, next to that river or pond water, and last of all that from springs; but a chemical analysis should be made of the last before introducing it, as some spring waters contain mineral ingredients injurious to vegetation.

The aim of Laokoon, which ranks as a classic, not only in German but in European literature, is to define by analysis the limitations of poetry and the plastic arts.

Invisible to the microscope, but rendered visible by reagents, are glycogen, Mucor, Ascomycetes, yeast, &c. In addition to these cell-contents we have good indirect evidence of the existence of large series of other bodies, such as proteids, carbohydrates, organic acids, alkaloids, enzymes, &c. These must not be confounded with the numerous substances obtained by chemical analysis of masses of the fungus, as there is often no proof of the manner of occurrence of such bodies, though we may conclude with a good show of probability that some of them also exist preformed in the living cell.

A problem to which he returned repeatedly was that of separating nickel and cobalt from their ores and freeing them from arsenic; and in the course of his long laboratory practice he worked out numerous processes for the preparation of pure chemicals and methods of exact analysis.

As this in turn has been due to the very men who have developed the iron industry, it can hardly be questioned that, on further analysis, this development must in considerable part be referred to racial qualities.

Probably his greatest service to scholarship is this analysis of the principles of orthography in Latin.

His disappointment at its reception was great; and though he never entirely relinquished his metaphysical speculations, though all that is of value in his later writings depends on the acute analysis of human nature to which he was from the first attracted, one cannot but regret that his high powers were henceforth withdrawn for the most part from the consideration, of the foundations of belief, and expended on its practical applications.

So far as analysis of knowledge is concerned they are in harmony, and Hume's sceptical conclusions regarding belief in matters of fact are the foundations on which Butler's defence of religion rests.

It is remarkable that Hume does not appear to have been acquainted with Spinoza's analysis of the affections.

This solution presupposes a peculiar conception of the general relation between the mind and things which in itself requires justification, and which, so far at least as the empirical theory was developed by Locke and his successors, could not be obtained from psychological analysis.

For purposes of psychological analysis the conscious experience of the individual mind is taken as given fact, to be known, i.e.

While, then, the general idea of a theory of knowledge as based upon psychological analysis is the groundwork of the Treatise, it is a particular consequence of this idea that furnishes to Hume the characteristic criterion applied by him to all philosophical questions.

The foundations of cognition must be discovered by observation or analysis of experience so conceived.

But it is to be recollected that, according to Hume, an idea is actually a representation or individual picture, not a notion or even a schema, and that he never claims to be able to extract the predicate of a geometrical judgment by analysis of the subject.

As in the case of the previous problem, it is unnecessary to follow the steps of his analysis, which are, for the most part, attempts to self substitute qualities of feeling for the relations of thought The .

The results of Hume's theoretical analysis are applied by him to the problems of practical philosophy and religion.

There can be no doubt that Hume has continually in mind the theological questions then current, and that he was fully aware of the mode in which his analysis of knowledge might be applied to them.

It remains to give a brief analysis of the qualifications and functions of the archons after the year 487 B.C. After election (in the time of Aristotle in the month Anthesterion; in the 3rd century in Munychion) a short time had to elapse before entering on office to allow of the dokimasia (examination of fitness).

There cannot be said to be any standard or recognized analysis.

There seems to be no relationship between the commercial value and the analysis, the arbitrary personal methods of the expert tea-taster being controlled by factors that chemistry does not appear to deal with.

Most countries have a close check upon this at the time of importation, and the customs authorities in Great Britain submit to analysis all samples of a doubtful character.

Impure teas are not permitted to pass into consumption, but the quantity condemned after analysis as unfit for food in the year 1906 was 41 packages, out of a total of 317,000,000 lb.

The mathematical theory of probability and the allied theory of the combinatorial analysis were in effect created by the correspondence between Pascal and Fermat, concerning certain questions as to the division of stakes in games of chance, which had been propounded to the former by the gaming philosopher De Mere.

After an analysis of the religious consciousness, which yields the doctrine of an absolute personal and spiritual God, Rothe proceeds to deduce from his idea of God the process and history of creative development, which is eternally proceeding and bringing forth, as its unending purpose, worlds of spirits, partially self-creative and sharing the absolute personality of the Creator.

In 1829 appeared the Analysis of the Human Mind.

By his Analysis of the Mind and' his Fragment on Mackintosh Mill acquired a position in the history of psychology and ethics.

He carried out the principle of association into the analysis of the complex emotional states, as the affections, the aesthetic emotions and the moral sentiment, all which he endeavoured to resolve into pleasurable and painful sensations.

But the salient merit of the Analysis is the constant endeavour after precise definition of terms and clear statement of doctrines.

This impression can in some degree be modified only by the application of a critical analysis with the assistance of Arabian tradition.

The death of Heinrich Brugsch in 1895 was a very severe blow to demotie studies; but it must be admitted that his brilliant gifts lay in other directions than exact grammatical analysis.

By tonic contraction is meant a prolonged and equable state of tension which yields under analysis no element of intermittent character.

Among prose writers should be mentioned the grammarian Peder Syv,5 (1631-1702); Bishop Erik Pontoppidan (1616-1678), whose Grammatica Danica, published in 1668, is the first systematic analysis of the language; Birgitta Thott (1610-1662), a lady who translated Seneca (1658); and Leonora Christina Ulfeld, daughter of Christian IV., who has left a touching account of her long imprisonment in her Jammersminde.

The First Plagues of Egypt.-In this section the analysis again reveals three main sources, which are clearly marked off from one another both by their linguistic features and by their difference of representation.

Now it is obvious that the results obtained by the foregoing analysis of J and E have an important bearing on the history of the remaining section of E's legislation, viz.

The evidence, However, afforded (a) by the parallel version of Deuteronomy and (b) by the literary analysis of J and E not only fails to support this tradition, but excites the gravest suspicions as to the originality both of the form and of the position in which the Decalogue now appears.

Logical analysis, after assuming that truth is independent and not of our making, has to confess that all logical operations involve an apparently arbitrary interference with their data (Bradley).

The following analysis may be taken as typical of cements made from chalk and clay on the Thames and 100.0 There may be variations from this composition according to the nature of the raw materials employed.

Although the ultimate composition of cement, that is, the percentage of each base and acid present, can be accurately determined by analysis, its proximate composition, i.e.

The quality of Portland cement is ascertained by its analysis and by determining its specific gravity, fineness, mechanical strength Tesfing.

Cement for all important work is submitted to a rigorous system of testing and analysis before it is accepted and used.

In 1804 he was appointed professor of mathematics at the Lycee, in 1809 professor of analysis and mechanics, and in 1816 examiner at the Ecole Polytechnique.

Weismann, however, from theoretical considerations and from analysis of supposed cases has at the least thrown doubt on the transmission of acquired characters.

Analysis of any acquired character, however, shows that there are two factors involved.

Those who have followed up the work of Mendel believe that the qualities of the new individual are a precise selection from and reconstruction of the parental qualities, and that were complete analysis possible, the characters of the new individual could be predicted with chemical accuracy.

A little later this same knowledge led him to the beginnings of quantitative organic analysis.

The simple nature of the alkalies Lavoisier considered so doubtful that he did not class them as elements, which he conceived as substances which could not be further decomposed by any known process of analysis - les molecules simples et indivisibles qui composent les corps.

Strauss has given an exhaustive analysis of the whole work in his book on Reimarus.

Kant's analysis of knowledge had disclosed the a priori element as the necessary complement of the isolated a posteriori facts of experience.

Accordingly Fries, like the Scotch school, places psychology or analysis of consciousness at the foundation of philosophy, and called his criticism of knowledge an anthropological critique.

From this point of view the parts of the book are by no means all of equal value; critical analysis shows that often parallel or distinct narratives have been fused together, and that, whilst the older stories gave more prominence to ordinary human motives and combinations, 1 This is confirmed by the circumstance that in Judg.

Chemical analysis, like common experience, shows that Indian corn is a very nutritious article of food, being richer in albuminoids than any other cereals when ripe (calculated in the dry weight).

A lengthened analysis of them would be out of place here, and all that is possible is a brief mention of the more important.

Belief is, according to Hamann, the groundwork of knowledge, and he accepts in all sincerity Hume's analysis of experience as being most helpful in constructing a theological view.

That the effect is due to a real difference in the character of the light from the two components has been shown by spectrum analysis, but it is probably exaggerated by contrast.

At the same time he was working with Thenard at the improvement of the methods of organic analysis, and by combustion with oxidizing agents, first potassium chlorate and subsequently copper oxide, he determined the composition of a number of organic substances.

Among his research work of this period may be mentioned the improvements in organic analysis and the investigation of fulminic acid made with the help of Liebig, who, gained the privilege of admission to his private laboratory in 1823-1824.

Turning his attention to technical chemistry, he became chemist at several works both in Germany and England, and in 1876 he was appointed professor of technical chemistry at Zurich polytechnic. Lunge's original contributions cover a very wide field, dealing both with technical processes and analysis.

In 1822 he published in the Morning Chronicle (April) a letter against Canning's attack on Lord John Russell, and edited, or rather re-wrote, some discursive papers of Bentham, which he published under the title Analysis of the Influence of Natural Religion on the Temporal Happiness of Mankind by Philip Beauchamp (1822).

On the other hand, the demonstrations of mathematical sciences of his time, and the logical forms of deduction evinced in Plato's dialogues, provided him with admirable examples of deduction, which is also the inference most capable of analysis.

Aristotle's analysis of the syllogism showed man how to advance by combining his thoughts in trains of deductive reasoning.

As then the reasoning of the syllogism was the main problem of Aristotle's logic, what was his analysis of it?