Problems Sentence Examples

He had so many problems to face.

She'd always had problems putting on weight.

Take care of yourself, and if you have any problems, call me.

Miss Keller's education, however, is so fundamentally a question of language teaching that it rather includes the problems of the deaf than limits itself to the deaf alone.

In fact, he must be struggling to float on the ocean of problems this family represented.

What part of 'wealthy' were you having problems understanding?

I'm saying their lives will be complicated enough without us adding problems to it.

If you have any problems, call Josh.

She hadn't helped any by turning their past problems into a monetary issue.

Beside his problems, hers seemed trivial.

She has no problems with what I can do?

It was too dreadful to be under the burden of these insoluble problems, so he abandoned himself to any distraction in order to forget them.

I'm having some problems with messages being intercepted after they leave the planet.

I guess he and Lori are having problems and he needed someone to talk to.

He knew the state, the town, and what the problems were.

The rest of their problems aren't my concern.

The outcome of this period of depression was a broadening of his outlook on the problems which he had set himself to solve.

We think that the decay of interest in these writers involves a real loss, and that students of modern problems may do worse than read Ricardo and his school.

They did much to excite thinking, and advanced many problems by more than one step, but they did not furnish a coherent system, and the doctrines which were then new have since been worked out with greater consistency and clearness.

Copious extracts from a diary kept by him at this time are given by Bain; they show how methodically he read and wrote, studied chemistry and botany, tackled advanced mathematical problems, made notes on the scenery and the people and customs of the country.

Four out of the five essays are elaborate and powerful solutions of perplexing technical problems - the distribution of the gains of international commerce, the influence of consumption on production, the definition of productive and unproductive labour, the precise relations between profits and wages.

When the world has settled down to the new conditions, if it ever does so, we may be confronted with problems similar to those which our forefathers had to solve.

In common with other sciences, economics makes use of " abstractions"; but if for some problems we employ symbolic processes of reasoning, we must keep clearly in view the limits of their significance, and neither endow the symbols with attributes they can never possess, nor lose sight of the realities behind them.

As in modern problems, so in those of past times, a man requires for success qualities quite distinct from those conferred by merely academic training and the use of scientific methods.

Suppose we have selected one of the numerous subsidiary problems suggested by the general inquiry, and obtained such full and complete information about one particular industry that we of a can tabulate the wages of the workers for a long series of years.

Under the conditions we have described, many of the most interesting problems of our own time, when they are once defined, resolve themselves into statistical inquiries.

Definite economic problems can very rarely be dealt with by merely quantitative methods.

In modern problems we can watch the economic machine actually at work, cross-examine our witnesses, see that delicate interplay of passions and interests which cannot be set down or described in a document, and acquire a certain sense of touch in relation to the questions at issue which manuscripts and records cannot impart.

We can therefore substitute sound diagnosis for guesswork more frequently in modern than in historical problems.

Suppose, now, we ignore the writers who were inaugurating neit methods, investigating special problems or laboriously collecting facts, and concentrate attention on the dominant school, with its long series of writers from Adam Smith to John Stuart Mill.

Their achievements in the r9th century will be fully acknowledged, but the relevance of their work to the problems of the zoth century will be admitted less than at the present time.

He employed the theory with wonderful success in unravelling the problems of his time.

But the net result of the development of the doctrine of rent is that all problems in which this factor appears, and they embrace the whole range of economic theory, must apparently be treated on their merits.

But a new institution cannot be made on the same terms. The modern industrial system has brought with it an immense variety of practical problems which nations must solve on pain of industrial and commercial ruin.

For these problems we want, not a few old-established general principles which no one seriously calls in question, but genuine constructive and organizing capacity, aided by scientific and detailed knowledge of particular institutions, industries and classes.

Just as the historical school grew up along with the greatest constructive achievement of the 29th century, namely, the consolidation of Germany, so the application to modern problems of the methods of that school has been called forth by the constructive needs of the present generation.

That is, original investigation of special problems has to be carried out on a more gigantic scale than any economist of the historical school ever dreamt of or the world requires, with the certain knowledge that at the end of it all the general theory will not correspond with the facts of life.

The scientific study of practical problems and difficulties is (generally speaking, and with honourable exceptions) far more advanced in almost every civilized country than it is in England, where the limited scale upon which such work is carried on, the indifference of statesmen, officials and business men, and the incapacity of the public to understand the close relation between scientific study and practical success, contrast very unfavourably with the state of affairs in Germany or the United States.

Where his fundamental conception admits of it, he tries to solve historical problems by historical methods.

The early history of the republic is chiefly concerned with the solution of these two problems.

He also shows how his method may be used to determine some curious and long-discussed problems, such as the light of the stars, the ebb and flow of the tide, the motion of the balance.

We cannot do more than refer to Charles for discussions as to how this theory of nature is connected with the metaphysical problems of force and matter, with the logical doctrine of universals, and in general with Bacon's theory of knowledge.

The narrow streets and the traffic congestion of the business district presented difficult problems of urban transit, but the system is of exceptional efficiency.

He published Aristoteles fiber die Farben (1849), Aristoteles' acht Blcher der Physik (1857), and numerous minor articles on smaller points, such as the authenticity of the thirty-eight books of the Problems. The work by which he is best known is the Geschichte der Logik im Abendland (Leipzig, 1855-1870).

The second is that spinners being required to give attention to two distinct classes of problems would be less likely as a body to become complete masters of either.

He made clear his belief that the question was closely connected with the problems of the Pacific and Far East, and invitations were also sent accordingly to China and to the smaller European powers with Far-Eastern interests - Holland, Belgium and Portugal.

The President made it clear that he regarded the conference merely as a step in securing international understanding and good will; he advocated the convening of succeeding conferences as a possible means of securing an international association for the promotion of peace, and he approved the principle of substituting an understanding between the United States, Great Britain, France and Japan regarding Far-Eastern problems, for the existing Anglo-Japanese Treaty.

He had faced difficult problems with independence and yet he had been able to inaugurate something of an " era of good feeling."

He did not deal with the history of the people, with economic or social problems - the dignity of history was to him a reality.

Yet the high court, which decided all problems of descent, would naturally intervene if a problem of descent arose, as it frequently did, in the kingdom; and thus the barons had the right of deciding between different claimants, and also of formally "approving" each new successor to the throne.

Indian affairs furnished the most serious problems of the new Territory of Florida.

Problems in artillery occupy two out of nine books; the sixth treats of fortification; the ninth gives several examples of the solution of cubic equations.

The supreme importance of a study of Greek antiquities on the spot, long understood by scholars in Europe and in America, has gradually come to be recognized in England, where a close attention to ancient texts, not always adequately supplemented by a course of local study and observation, formerly fostered a peculiarly conservative attitude in regard to the problems of Greek archaeology.

Entering the Royal Marines in 1854, he rose to be captain in 1867, retiring in 1869; and thenceforth he devoted himself to the study of naval and military problems, on which he had already published some excellent essays.

Moreover, the higher problems of rhythmic movement in the classical sonata forms are far beyond the scope of academic teaching; which is compelled to be contented with a practical plausibility of musical design; and the instrumental music which was considered the highest style of art in 18 3 0 was as far beyond Wagner's early command of such plausibility as it was obviously already becoming a mere academic game.

These accessories are indispensable if it be proposed to solve the problems usually propounded in books on the " use of the globes," but can be dispensed with if the globe is to serve only as a map of the world.

In biological chemistry he worked at the problems of animal heat and at the phenomena accompanying the growth of plants, and he also devoted much time to meteorological questions and observations.

The presentation was accompanied by a kind of mathematical performance, in which Leonardo solved several hard problems proposed to him by John of Palermo, an imperial notary, whose name is met with in several documents dated between 1221 and 1240.

The methods which Leonardo made use of in solving those problems fill the Liber quadratorum, the Flos, and a Letter to Magister Theodore.

In his Practica geometriae plain traces of the use of the Roman agrimensores are met with; in his Liber abaci old Egyptian problems reveal their origin by the reappearance of the very numbers in which the problem is given, though one cannot guess through what channel they came to Leonardo's knowledge.

They teach further the solution of problems leading to equations of the first and second degree, to determinate and indeterminate equations, not by single and double position only, but by real algebra, proved by means of geometric constructions, and including the use of letters as symbols for known numbers, the unknown quantity being called res and its square census.

In the Letter to Magister Theodore indeterminate problems are chiefly worked, and Leonardo hints at his being able to solve by a general method any problem of this kind not exceeding the first degree.

The new archbishop, without being one of the English divines who have made notable contributions to theological learning, already had a great reputation for ecclesiastical statesmanship; and in subsequent years his diplomatic abilities found ample scope in dealing not only with the difficulties caused in the church by doctrinal questions, but pre-eminently with the education crisis, and with the new problems arising in the enlarged Anglican Communion.

These problems are, however, certain to be solved in the near future, and then probably caoutchouc may be formed in other ways than from isoprene.

And the Church policy, as old as the times of Constantine, to crush utterly the man who brings more problems and pressure than the bulk of traditional Christians can, at the time, either digest or resist with a fair discrimination, seemed to the authorities the one means to save the very difficult situation.

The basin thus presents interesting problems. The existence of wide valleys where the small upper waters of the Cherwell, Evenlode and Coln now flow, the occurrence of waterborne deposits in their beds from the northwest of England and from Wales, and the fact that the Thames, like its lower southern tributaries which pierce the North Downs, has been able to maintain a deep valley through the chalk elevation at Goring, are considered to point to the former existence of a much larger river, in the system of which were included the upper waters of the present Severn, Dee and other rivers of the west.

Seneca even made the discussion of such problems into a regular discipline, claiming that their concrete character gave an interest in morality to those who had no love for abstractions; while they prevented those who had from losing themselves in the clouds.

The determination of this ratio is one of the most difficult problems in the lunar theory.

Nevertheless, many important problems relating to the distribution of magnetic induction may be solved by methods similar to those employed for the solution of analogous problems in electricity.

The question of the rights of the national minorities and the enforcement of the Land Act were among the problems of the day that led on June 3 1921 to the fall of the Cabinet of Ulmanis.

This double cultivation of his scientific powers had the happiest effect on his subsequent work; for the greatest achievements of Riemann were effected by the application in pure mathematics generally of a method (theory of potential) which had up to this time been used solely in the solution of certain problems that arise in mathematical physics.

At the age of nineteen he communicated to Leonhard Euler his idea of a general method of dealing with "isoperimetrical" problems, known later as the Calculus of Variations.

The calculus of variations lay undeveloped in Euler's mode of treating isoperimetrical problems. The fruitful method, again, of the variation of elements was introduced by Euler, but adopted and perfected by Lagrange, who first recognized its supreme importance to the analytical investigation of the planetary movements.

Lagrange saw in the problems of nature so many occasions for analytical triumphs; Laplace regarded analytical triumphs as the means of solving the problems of nature.

To Lagrange, perhaps more than to any other, the theory of differential equations is indebted for its position as a science, rather than a collection of ingenious artifices for the solution of particular problems. To the calculus of finite differences he contributed the beautiful formula of interpolation which bears his name; although substantially the same result seems to have been previously obtained by Euler.

Such is the historical basis which we seem to be able to lay for the study of the exegetical problems of the book.

The name doctor scholasticus was applied originally to any teacher in such an ecclesiastical gymnasium, but gradually the study of dialectic or logic overshadowed the more elementary disciplines, and the general acceptation of " doctor " came to be one who occupied himself with the teaching of logic. The philosophy of the later Scholastics is more extended in its scope; but to the end of the medieval period philosophy centres in the discussion of the same logical problems which began to agitate the teachers of the 9th and 1 oth centuries.

It is divisible into two well-marked periods - the first extending to the end of the 12th century and embracing as its chief names Roscellinus, Anselm, William of Champeaux and Abelard, while the second extended from the beginning of the 13th century to the Renaissance and the general distraction of men's thoughts from the problems and methods of Scholasticism.

Their chief works are in the shape of commentaries upon the writings of "the philosopher."' Their problems and solutions alike spring from the master's dicta - from the need of reconciling these with one another and with the conclusions of Christian theology.

That of Windelband, though going less into detail, is a remarkably fresh treatment of the problems involved.

The beds of these rivers, as well as that of the Danube, are continually changing, forming morasses and pools, and rendering the country near their banks marshy, Notwithstanding the work already done, such as canalizing and regulating the rivers, the erection of dams, &c., the problems of preventing inundations, and of reclaiming the marshes, have not yet been satisfactorily solved.

The ethnographical map of Hungary does much to explain the political problems of the country.

It was at once seen that this elaborate scheme was intended 3 Seton-Watson, Racial Problems, p. 194.

The general working of the great machine was now laid bare, and it needed a further advance of knowledge to bring a fresh set of problems within reach of investigation.

To this lofty quality of intellect he added a rare sagacity in perceiving analogies, and in detecting the new truths that lay concealed in his formulae, and a tenacity of mental grip, by which problems, once seized, were held fast, year after year, until they yielded up their solutions.

These researches derive additional importance from having introduced two powerful engines of analysis for the treatment of physical problems, Laplace's coefficients and the potential function.

The theory of probabilities, which Laplace described as common sense expressed in mathematical language, engaged his attention from its importance in physics and astronomy; and he applied his theory, not only to the ordinary problems of chances, but also to the inquiry into the causes of phenomena, vital statistics and future events.

He was also the first to consider the difficult problems involved in equations of mixed differences, and to prove that an equation in finite differences of the first degree and the second order might always be converted into a continued fraction.

Of the four supplements added by the author (1816-1825) he tells us that the problems in the last were contributed by his son.

Ordinary algebra developed very gradually as a kind of shorthand, devised to abbreviate the discussion of arithmetical problems and the statement of arithmetical facts.

The particular problem - a heap (hau) and its seventh makes 19 - is solved as we should now solve a simple equation; but Ahmes varies his methods in other similar problems. This discovery carries the invention of algebra back to about 1700 B.C., if not earlier.

Notwithstanding the prolixity of writers and the number of the writings, all attempts at extracting an algebraic analysis from their geometrical theorems and problems have been fruitless, and it is generally conceded that their analysis was geometrical and had little or no affinity to algebra.

In the body of the work he displays considerable ingenuity in reducing his problems to simple equations, which admit either of direct solution, or fall into the class known as indeterminate equations.

His travels and mercantile experience had led E t u eopre him to conclude that the Hindu methods of computing were in advance of those then in general use, and in 1202 he published his Liber Abaci, which treats of both algebra and arithmetic. In this work, which is of great historical interest, since it was published about two centuries before the art of printing was discovered, he adopts the Arabic notation for numbers, and solves many problems, both arithmetical and algebraical.

So far the development of algebra and geometry had been mutually independent, except for a few isolated applications of geometrical constructions to the solution of algebraical problems. Certain minds had long suspected the advantages which would accrue from the unrestricted application of algebra to geometry, but it was not until the advent of the philosopher Rene Descartes that the co-ordination was effected.

Diophantine problems were revived by Gaspar Bachet, Pierre Fermat and Euler; the modern theory of numbers was founded by Fermat and developed by Euler, Lagrange and others; and the theory of probability was attacked by Blaise Pascal and Fermat, their work being subsequently expanded by James Bernoulli, Abraham de Moivre, Pierre Simon Laplace and others.

Fortunately the new Giolitti and Vesnie Cabinets showed equal moderation and skill in restraining the hotheads on both sides, and the new Foreign Minister, Count Sforza, was assisted by a personal knowledge of Serbian and Balkan problems all too rare among western statesmen.

Here Cuvier was imperfectly formulating, without recognizing the real physical basis of the phenomena, the results of the laws of heredity, which were subsequently investigated and brought to bear on the problems of animal structure by Darwin.

But it must not be forgotten that the problems presented by human communities are extremely complex, and that the absence of any selection of healthy or desirable stock in the breeding of human communities leads to undesirable consequences.

A different treatment is then necessary, and for some of the problems which arise under this head the method of Abbe is convenient.

In theoretical investigations these problems are usually treated as of two dimensions only, everything being referred to the plane passing through the luminous point and perpendicular to the diffracting edges, supposed to be straight and parallel.

Problems not limited to two dimensions, such for example as the shadow of a circular disk, present great difficulties, and have not hitherto been treated by a rigorous method; but there is no reason to suppose that Fresnel's results would be departed from materially.

Wellhausen made his name famous by his critical investigations into Old Testament history and the composition of the Hexateuch, the uncompromising scientific attitude he adopted in testing its problems bringing him into antagonism with the older school of biblical interpreters.

Now the rise of the problems of individual faith is the mark of the age that followed Jeremiah, while the confident assertion of national righteousness under misfortune is a characteristic mark of pious Judaism after Ezra, in the period of the law but not earlier.

One of the first problems which confronted the Botha ministry was the attitude to be adopted towards the other British colonies in South Africa.

The identity and personality of this "Friend of God," who bulks so largely in the great collection of mystical literature, and is everywhere treated as a half supernatural character, is one of the most difficult problems -in the history of mysticism.

That every one who has capacity to understand the law is presumed to know it is a very necessary principle, for otherwise the courts would be continually occupied in endeavouring to solve problems which by their very impracticability would render the administration of justice next to impossible.

The number of field battalions was nearly doubled, two-thirds of the artillery received breech-loading rifled guns, the infantry had for some years had the breech-loading "needlegun," and steps were initiated to train an adequate number of staff officers to a uniform appreciation of strategical problems, based on Moltke's personal interpretation of Clausewitz's Vom Kriege.

This, one of the most difficult problems of pathology, is being attacked by many able workers, who are all striving from different standpoints to elucidate the nature of these new formations, which spring from the normal tissues in which they develop and which they destroy.

For applications of the hodograph to the solution of kinematical problems see Mechanics.

The remarkable discovery of the dual nature of the nervous system, of its duplex development as a lower and upper system of "neurons," has shed much light upon the problems of practical medicine, but this construction is described under Brain; Neuropathology; Muscle And Nerve, &C.

No one shows truer courage, not marred by irreverence, in confronting the great problems of human destiny, or greater strength in triumphing over human weakness.

Dr Hopkinson presented a rare combination of practical with theoretical ability, and his achievements in pure scientific research are not less intrinsically notable than the skill with which he applied their results to the solution of concrete engineering problems. His original work is contained in more than sixty papers, all written with a complete mastery both of style and of subject-matter.

Moreover, his association with glass manufacture led him to study the refractive indices of different kinds of glass; he further undertook abstruse researches on electrostatic capacity, the phenomena of the residual charge, and other problems arising out of Clerk Maxwell's electro-magnetic theory.

One of the most serious administrative problems met with in London is that of locomotion, especially as regards the regulation of traffic in the principal thoroughfares and at the busiest crossings.

The special difficulties which attend deep mining, in addition to the problems of hoisting ore and raising water from great depths, are the increase of temperature of the rocks and the pressure of the overlying strata.

It was more fully developed in his Traite des fluides, published in 1744, in which he gave simple and elegant solutions of problems relating to the equilibrium and motion of fluids.

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.).

In subsequent history there is a good deal of resemblance between the capitularies' legislation of Charlemagne and his successors on one hand, the acts of Alfred, Edward the Elder, ZEthelstan and Edgar on the other, a resemblance called forth less by direct borrowing of Frankish institutions than by the similarity of political problems and condition.

In this section an attempt is made to indicate briefly the causes which have led to so great a diversity of opinion, and to describe in outline the principles underlying the chief schemes of chronology that have been suggested; a short account will then be given of the latest discoveries in this branch of research, and of the manner in which they affect the problems at issue.

The publication of fresh chronological material in 1906 and 1907 placed a new complexion on the problems at issue, and enabled us to correct several preconceptions, and to reconcile or explain the apparently conflicting data.

For further details regarding the formation of Sumerian and Babylonian-Assyrian proper names, as well as for an indication of the problems involved and the difficulties still existing, especially in the case of Sumerian names,' see the three excellent works now at our disposal for the Sumerian, the old Babylonian, and the neoBabylonian period respectively, by Huber, Die Personennamen den Keilschrifturkunden aus der Zeit der Konige von Ur and Nisin (Leipzig, 1907); Ranke, Early Babylonian Proper Names (Philadelphia, 1905); and Tallqvist, Neu-Babylonisches Namenbuch (Helsingfors, 1905).

Old Testament prophecy had addressed itself to both these problems, though it was hardly conscious of the claims of the latter.

But later, with the growing claims of the individual and the acknowledgment of these in the religious and intellectual life, both problems, and especially the latter, pressed themselves irresistibly on the notice of religious thinkers, and made it impossible for any conception of the divine rule and righteousness to gain acceptance, which did not render adequate satisfaction to the claims of both problems. To render such satisfaction was the task undertaken by apocalyptic, as well as to vindicate the righteousness of God alike in respect of the individual and of the nation.

The curve also permits the solution of the problems of duplicating a cube and trisecting an angle.

This knowledge, however, is by no means positivistic or empirical, but on the contrary it is dialectical and a priori synthetic, brought about by the spiritual categories; and from it there constantly arise new problems, an ever new position of the fundamental categories.

The treatment and solution of these problems is what is called " philosophy " in the strict sense of the word, which for that reason coincides with methodology speculatively understood.

Among the most noteworthy workers at the problems involved in the question of the influence of soil in the production of disease we find yen Foder, Pettenkofer, Levy, Fleck, von Naegeli, Schleesing, Muntz and Warrington.

Other nations, indeed, had attempted the highest problems in religion; but Israel alone, in the providence of God, had succeeded, for Israel alone had been inspired.

Although deficient in technical training, he handled with great skill the difficult problems which were presented by the Civil War.

About the same time Francesco Maurolico, or Maurolycus, the eminent mathematician of Messina, in his Theore y nata de Lumine et Umbra, written in 1521, fully investigated the optical problems connected with vision and the passage of rays of light through small apertures with and without lenses, and made great advances in this direction over his predecessors.

The first to take up the camera obscura after Porta was Kepler, who used it in the old way for solar observations in 1600, and in his Ad Vitellionem Paralipomena (1604) discusses the early problems of the passages of light through small apertures, and the rationale of the simple dark chamber.

Most of the writers already noticed worked out the problems connected with the projection of images in the camera obscura more by actual practice than by calculation, but William Molyneux, of Dublin, seems to have been the first to treat them mathematically in his Dioptrica Nova (1692), which was also the first work in English on the subject, and is otherwise an interesting book.

There he came under the influence of Kant, who was just then passing from physical to metaphysical problems. Without becoming a disciple of Kant, young Herder was deeply stimulated to fresh critical inquiry by that thinker's revolutionary ideas in philosophy.

To Kant's lectures and conversations he further owed something of his large interest in cosmological and anthropological problems. Among the writers whom he most carefully read were Plato, Hume, Shaftesbury, Leibnitz, Diderot and Rousseau.

Instead of discoursing on the corporate conscience of the state and the endowments of the Church, the importance of Christian education, and the theological unfitness of the Jews to sit in parliament, he is solving business-like problems about foreign tariffs and the exportation of machinery; waxing eloquent over the regulation of railways, and a graduated tax on corn; subtle on the monetary merits of half-farthings, and great in the mysterious lore of quassia and cocculus indicus.

His love of freedom steadily developed, and he applied its principles more and more courageously to the problems of government.

He has, indeed, described in graphic terms the greatest of the more superficial changes he underwent; how he had " carried into logical and ethical problems the maxims and postulates of physical knowledge," and had moved within the narrow lines drawn by the philosophical instructions of the class-room " interpreting human phenomena by the analogy of external nature "; how he served in willing captivity " the ` empirical ' and ` necessarian ' mode of thought," even though " shocked " by the dogmatism and acrid humours " of certain distinguished representatives "; 1 and how in a period of " second education " at Berlin, " mainly under the admirable guidance of Professor Trendelenburg," he experienced " a new intellectual birth" which " was essentially the gift of fresh conceptions, the unsealing of hidden openings of self-consciousness, with unmeasured corridors and sacred halls behind; and, once gained, was more or less available throughout the history of philosophy, and lifted the darkness from the pages of Kant and even Hegel."

But besides the vocation he had freely selected and assiduously laboured to fulfil, two more external influences helped to shape Martineau's mind and define his problem and his work; the awakening of English thought to the problems which underlie both philosophy and religion, and the new and higher opportunities offered for their discussion in the periodical press.

As thus used, it was a term which governed the problems of speculative theism rather than those connected with the historical origin, the evolution and the organization of religion.

These criticisms mean that his most elaborate discussions came forty years too late, for they were concerned with problems which agitated the middle rather than the end of the 19th century.

A period of interruption now ensued, owing to domestic troubles and foreign complications, and when, in 1878, the government was able to devote attention once again to railway problems, it found the treasury empty.

A failure to solve the problems of metaphysics must always remain a failure, in spite of all protestations that it was inevitable; and it in no wise justifies an advance to so selfcontradictory an asylum ignorantiae as the Unknowable.

This assertion of the divinity of Christ triumphed, but other problems at once emerged.

Aelius Stilo Praeconinus, who was the teacher of Varro and Cicero, much interest had been taken in literary and linguistic problems at Rome.

Only a few problems can be discussed of the many which are raised by the insufficient and conflicting evidence at our disposal.

A very powerful method of attacking problems in electrical distribution was first made known by Lord Kelvin in 1845 and is described as the method of electrical images.'

All philosophy is philosophy of life, the development of a new culture, not mere intellectualism, but the application of a vital religious inspiration to the practical problems of society.

In accordance with this principle, Eucken has given considerable attention to social and educational problems.

This method of representation is applicable to certain kinds of problems, and has been developed by Macfarlane Gray and other writers in its application to the steam engine.

It shows the influence of Arminian theology against Calvinism, which was vigorously upheld in the Quin-particular formula, put forward by the synod of Dort in 1619 to uphold the five points of Calvinism, after heated discussion, in which English delegates took part, of the problems of divine omniscience and human free-will.

It will be sufficient here to point out in general terms the import of the message of archaeological discovery in the Victorian Era in its bearings upon the great problems of world-history.

Notwithstanding the allurements of the subject, such conservative historians as Grote were disposed to regard the problems of early Grecian history as inscrutable, and to content themselves with the recital of traditions without attempting to establish their relationship with actual facts.

He was peculiarly adapted for the wise and skilful treatment of difficult problems in the spirit of an international set, playing the great game of diplomacy with grace and honour.

He proposed the problem of the catenary or curve formed by a chain suspended by its two extremities, accepted Leibnitz's construction of the curve and solved more complicated problems relating to it.

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

One of these problems, illustrated by experiment, deals with an ingenious mode of propelling vessels by the reaction of water ejected from the stern.

But, though this method has been applied in its fullness, and that by the keenest exegetes, there remains a consciousness that it has failed to solve many of the problems of the book.

Now modern scholars have with varying success used in turn these three hypotheses with a view to the solution of the problems of the New Testament Apocalypse.

It might be supposed that all possible methods had now been considered, and that a combination of the three methods which have established their validity in relation to the interpretation of the Apocalypse would be adequate to the solution of all the problems of the book, but this is not so; for even when each in turn has vindicated the provinces in the book that rightly belong to it, and brought intelligibility into these areas, there still remain outlying regions which they fail to illumine.

See Peace Conference and WAR; also Sir T.Barclay, supplement to Problems of International Practice and Diplomacy, for comparison of texts of 1899 and 1907.

His views on the problems of Arianism, and his attempt to reconcile it with orthodox theology, are contained in A Specimen of True Philosophy (1730, reprinted in Metaphysical Tracts, 1837) and Logology, or a Treatise on the Logos in Seven Sermons on John i.

The value of his work consists not only in the stores of material which he collected, but also in the success with which he dealt with many of the problems raised by the inscriptions.

The remainder of the year he spent at Zurich, slowly perfecting his thoughts on the fundamental problems left for solution in the Kantian philosophy.

Pascal treated these numbers in his Traite du triangle arithmetique (1665), using them to develop a theory of combinations and to solve problems in proba-, bility.

In this way the principle of continuity, which is the basis of the method of Fluxions and the whole of modern mathematics, may be applied to the analysis of problems connected with material bodies by assuming them, for the purpose of this analysis, to be homogeneous.

The planetary theory and other particular dynamical problems likewise occupied his attention from time to time.

Todhunter also published keys to the problems in his textbooks on algebra and trigonometry; and a biographical work, William Whewell, account of his writings and correspondence (1876), in addition to many original papers in scientific journals.

He deals, on the contrary, almost exclusively with the social, financial, educational, industrial and general moral problems of the day.

He published Presidential Problems (New York, 1904), made up in part of lectures at Princeton University, and Fishing and Hunting Sketches (1906).

In these lectures Duchesne touches cleverly upon the most delicate problems, and, without any elaborate display of erudition, presents conclusions of which account must be taken.

That there are many hard problems connected with the fascinating book of Amos cannot be denied.

Mensuration involves the use of geometrical theorems, but it is not concerned with problems of geometrical construction.

This sacrifice of local autonomy was in a measure prepared for by an earlier centralizing movement proper to the churches themselves, whereby those in certain areas met in conference or " synod " to formulate a common policy on local problems. Such inter-church meetings cannot be traced back beyond the latter half of the 2nd century, and were purely ad hoc and informal, called to consider specific questions like Montanism and Easter observance.

But after half a century's further experience, public opinion, stimulated by growing need for common action in relation to certain practical problems of home and foreign work, proved ripe for the realization of the earlier idea in its double form.

The years following the settlement of the four colonies were occupied in the solution of problems in church and civil government and in the preparation for the proper training of ministers.

Since the middle of the 19th century an attempt has been made to meet the problems arising from a rapid industrial and social development by creating bureaus or commissions to exercise a central control over local officials, corporations and even private individuals, and as most of the heads of these bureaus and the commissions are appointed by the governor the importance of that officer has increased.

The defence of the northern frontier was a heavy burden to New York, but by its problems the growth of the union of the colonies was promoted.

It became known as the "Delian problem" or the "problem of the duplication of the cube," and ranks in historical importance with the problems of "trisecting an angle" and "squaring the circle."

Archytas of Tarentum (c. 430 B.C.) solved the problems by means of sections of a half cylinder; according to Eutocius, Menaechmus solved them by means of the intersections of conic sections; and Eudoxus also gave a solution.

These problems were also attacked by the Arabian mathematicians; Tobit ben Korra (836-901) is credited with a solution, while Abul Gud solved it by means of a parabola and an equilateral hyperbola.

Large sections of the old history are devoted to the religion and politics of the ten tribes, which are altogether unintelligible and uninteresting when measured by a strictly Levitical standard; and in general the whole problems and struggles of the prophetic period turn on points which had ceased to be cardinal in the life of the New Jerusalem, which was no longer called to decide between the claims of the Word of Yahweh and the exigencies of political.

By means of this coalition the Ministry succeeded, indeed, in passing the military service reforms on April 24 1911 (reduction of the three years' service to two years, combined with an increase in the contingent of recruits); but this completely exhausted its parliamentary strength, and the first parliamentary suffrage Parliament ended with but poor results in the midst of unsolved national problems.

Immediately afterwards the Reichsrat adjourned for the summer holidays (July 26), without having ventured on any steps towards the solution of the great problems of State.

Marat declares that physiology alone can solve the problems of the connexion between soul and body, and proposes the existence of a nervous fluid as the true solution.

How far such adaptations are produced afresh in each generation, whether or no their effects are transmitted to descendants and so directly modify the stock, to what extent adaptations characteristic of a species or variety have come about by selection of individuals capable, in each generation, of responding favourably, or how far by the selection of individuals fortuitously suitable to the environment, or, how far, possibly by the inheritance of the responses to the environment, are problems of biology not yet definitely solved.

Metaphysics, again, is concerned with the ultimate problems of matter and spirit; it endeavours to go behind the phenomena of sense and focus its attention on the fundamental truths which are the only logical bases of natural science.

For the scientific problems connected with oscillation see Mechanics and Oscillograph.

The problems particularly of the primitive history were first brought into clear light by him, and all subsequent work upon the subject must acknowledge its indebtedness to him.

But the controversy about predestination, which, in the 9th century, Hincmar and Hrabanus fought out with the monk Gottschalk of Fulda, as well as the discussions that arose from the definition of the doctrine of transubstantiation of Radbert, enable us to gauge the intellectual energy with which theological problems were once more being handled.

Among other publications by him were An American Four-in-hand in Britain (1883), Round the World (1884), The Empire of Business (1902), a Life of James Watt (1905) and Problems of To-day (1908).

The Letters contain a discussion of many of the principal problems in psychology and ethics.

The second volume (1817) relates to the Eulerian integrals, and to various integrals and series, developments, mechanical problems, &c., connected with the integral calculus; this volume contains also a numerical table of the values of the gamma function.

They ranged from such problems as the land settlement of the Punjab, or the introduction of civil marriage to provide for the needs of unorthodox Hindus, to the question how far the study of Persian should be required or encouraged among European civil servants.

For in requiring these religions to impart certain prescribed religious truths, and to inculcate the highest moral tone, it burdened them with problems to which they were unequal.

This correlative numerical problem and the two purely geometrical problems are inseparably connected historically.

In his theses as well as in his early writings - such as De la subrogation Keene, La Bonorum possessio, and Sur la duree des effets de la minorite (1870) - he endeavoured to explain the problems of laws by means of history, an idea which was new to France at that time.

Ober Anmut and Wiirde, published in 1793, was a further contribution to the elucidation and widening of Kant's theories; and in the eloquent Briefe fiber die cisthetische Erziehung des9Menschen (1795), Schiller proceeded to apply his new standpoint to the problems of social and individual life.

His whole conception of life and character had deepened since Don Carlos, and under the influence of Kant's philosophy the drama became the embodiment of ethical problems that are essentially modern.

In addition to his purely chemical work, Lavoisier, mostly in conjunction with Laplace, devoted considerable attention to physical problems, especially those connected with heat.

The relation of the state to corporations and industrial problems has been a subject of important legislation.

A Bureau of Labor Statistics (1879), whose members are styled Commissioners of Labor, makes a study of economic and financial problems and publishes biennial reports; a Mining Board (1883) and an inspector of factories and workshops (since 1893) have for their duty the enforcement of labour legislation.

Among the first problems of the new state were those relating to lands and Indians.

Municipal problems have also reacted upon state politics.

For this unfortunate issue Louis was not without blame; for from the very first, owing to an exaggerated idealism and love of antiquity, he had totally misunderstood the national character of the Greeks and the problems involved in the attempts to govern them by bureaucratic methods.

He sometimes altered and contorted the facts; he very often unduly simplified his problems; he was very apt when he had proved a favourite opinion true to infer it to be the whole truth.

With the general acceptance of its main principle that the real is the rational, there came in the eighties a more critical examination of the precise meaning to be attached to it and its bearing on the problems of religion.

But they have both been urged with sufficient ability to arrest its progress and to call for a reconsideration and restatement of the fundamental principle of idealist philosophy and its relation to the fundamental problems of religion.

A hero, who was probably originally intended to demonstrate the failure of the vacillating temperament when brought face to face with the problems of art, proved ill-adapted to demonstrate those precepts for the guidance of life with which the Lehrjahre closes; unstable of purpose, Wilhelm Meister is not so much an illustration of the author's life-philosophy as a lay-figure on which he demonstrates his views.

Problems of the relation of the individual to society and industrial questions were to have formed the theme of the Wanderjahre; but since the French Revolution these problems had themselves entered on a new phase and demanded a method of treatment which it was not easy for the old poet to learn.

Yet, the conditions in Palestine during the monarchies reveal grave and complex social problems, marked class distinctions, and constant intercourse and commercial enterprise.

The antiquity of certain principles and details is undeniable - as also in the Talmud - but since one must start from the organic connexions of the composite sources, the problems necessitate proper attention to the relation between the stages in the literary growth (working backwards) and the vicissitudes which culminate in the postexilic age.

Only common geometrical problems are involved in the case of sheets of sensible thickness, and allowances are made for thickness.

These, together with independent researches into the heat treatment of steel and iron, have opened up many unsolved problems fraught with deepest interest and importance.

One of the most difficult problems with which the metal-worker who handles constructional forms has to deal is the maintenance of a due relation between absolute strength and a useful degree of elasticity.

Analytical problems, such as the isolation of certain organic radicals, attracted his attention to begin with, but he soon turned to synthetical studies, and he was only about twenty-five years of age when an investigation, doubtless suggested by the work of his master, Bunsen, on cacodyl, yielded the interesting discovery of the organo-metallic compounds.

In language, which he appears to regard as somehow acquired, he finds a solution for the problems of reason which Kant had discussed in the Kritik der reinen Vernunft.

Baldwin was a man of a subtler type - a man capable of dealing with the intrigues of a court and with problems of law, and, as such, suited for guiding the middle age of the kingdom, which the different qualities of his predecessors had been equally suited to found.

The immense and incalculable problems involved in the rise of Japan, the awakening of China, and their relations to the European powers and to America - known as the Far Eastern Question - are comparatively but affairs of yesterday.

The Eastern Question thus developed, in the latter years of the 19th century, from that of the problems raised by the impending break-up of a moribund empire, into the even more complex question of how to deal with an empire which showed vigorous evidence of life, but of a type of life which, though on all sides in close touch with modern European civilization, was incapable of being brought into harmony with it.

But in 1890 a great stir was created by the publication, under his editorship, of Lux Mundi, a series of essays by different writers, being an attempt "to succour a distressed faith by endeavouring to bring the Christian Creed into its right relation to the modern growth of knowledge, scientific, historic, critical; and to modern problems of politics and ethics."

These methods have reached their highest development in connexion with the determination of the mechanical equivalent of heat, but they may be applied with great advantage in connexion with other problems, such as the measurement of the variation of specific heat, or of latent heats of fusion or vaporization.

These clusters present many unsolved problems. Thus Perrine, from an examination of ten globular clusters (including Messier 13 and Centauri), has found in each case that the stars can be separated into two classes of magnitudes.

One of the problems, which has engaged a large share of the attention of astronomers in the last century, has been the determination of the direction of this " solar motion."

We now arrive at the greatest of all the problems of sidereal astronomy, the structure and nature of the universe as a whole.

Clerke's The System of the Stars (2nd ed., 1905), which contains full references to original papers; Problems in Astrophysics, by the same author,, may also be consulted.

He had now secured a leading if not the foremost place among the chemists of the French capital, and the demand for his services as adviser in technical problems and matters of practical interest made great inroads on his available time.

He saw the necessity of going back to Kant in the sense of demanding a critical reconsideration of the epistemological problems which Kant had made but a partially successful attempt to solve.

The present article is divided into The Problems of Logic, History.

History Logic cannot dispense with the light afforded by its history so long as counter-solutions of the same fundamental problems continue to hold the field.

The problems raised by the relativism of Protagoras are no less fundamentally problems of the nature of knowledge and of the structure of thought.

In the mathematics we determine complex problems by a construction link by link from axioms and simple data clearly and distinctly conceived.

It was because the aftermath of Newtonian science was so rich that the scientific faith of naturalism was able to retain a place besides its epistemological creed that a logician of the school could arise whose spirit was in some sort Baconian, but who, unlike Bacon, had entered the modern world, and faced the problems stated for it by Hume and by Newton.

They had devised canons for the investigation of the concrete problems of this, but had either ignored altogether the need to give an account of the mirroring mind, or, in the alternative had been, with some naïveté, content to assume that their nominalist friends, consistently their allies in the long struggle with traditionalism, had adequately supplied or could adequately supply the need.

His grasp of the procedure by which the man of science manipulated his particular concrete problems was admirable.

It is the oscillation which Mill manifests between the conception of his formula as it is actually applicable to concrete problems in practice, and the conception of it as an expression of a theoretical limit to practical procedure.

Existent subjects, containing eternally all their successive predicates in the time-series, are substances, which when the problems connected with their activity, or dynamically speaking their force, have been resolved, demand - and supply - the metaphysic of the Monadology.

Apart from politics he took a deep and active interest in the problems of capital and labour, was one of the organizers (1901) and the first president of the National Civic Federation, whose purpose was to solve social and industrial problems, and in December 1901 became chairman of a permanent board of conciliation and arbitration established by the Federation.

Others, such as the Barycentrische Calciil of Mobius, and the Methode des equipollences of Bellavitis, give elegant modes of treating space problems, so long as we confine ourselves to projective geometry and matters of that order; but they are limited in their field, and therefore need not be discussed here.

By reason of the co-operative effort demanded for the large problems of irrigation, packing and marketing, the citrus industry has done much for the permanent development of the state, and its extraordinary growth made it, towards the close of the 19th century, the most striking and most potent single influence in the growth of agriculture.

Rapid settlement, excessive prices, reckless waste of money, and wild commercial ventures that glutted San Francisco with all objects usable and unusable made the following years astounding from an economic point of view; but not less bizarre was the social development, nor less extraordinary the problems of state-building in a society " morally and socially tried as no other American community ever has been tried " (Royce).

He also discussed many other problems, such as stellar distribution, the extent of the universe, &c., whilst at Brera.

The problems which had devolved upon McKinley's administration had been far advanced towards final settlement.

Moreover, it is a human weakness to manipulate one's ancestry, and the common claim to be descended from the local godling is not to be confused with the Arunta type of reincarnation.4 Again, in the part taken by women in serpent-lore other problems of primitive society and religion intermingle.

The pre-eminence was not to be of rank and glory but of service and again made prominent though not yet supreme, and the metaphysical problems are so close at hand that their discussion is imperative.

In theology the fundamental problems of ontological philosophy were faced; the relationship of unity to multiplicity, of noumenon to phenomena, of God to man.

New problems have arisen out of the book which relates to him, but here we can only attempt to consider what, in a certain sense, may be called the surface meaning of the text.

The founding and the growth of such communities furnish matter for an interesting chapter in the history as well of ancient as of modern civilization; and the regulation of the relations between the parent state and its dependencies abroad gives rise to important problems alike in national policy and in international economics.

In the problems of government raised by the organization of the British dominions beyond the seas the system of colonization has been developed to an extent unknown under any other national flag.

The exploration of Greenland has been continued, with few exceptions, by Danes who, besides throwing much light on problems in physical geography and Eskimo ethnography, have practically completed the map of the coasts.

Epidemic outbreaks of other diseases - for instance, cholera, diphtheria and typhoid fever - are often preceded and followed by the prevalence of mild illness of an allied type; and t he true significance of this fact is one of the most important problems in epidemiology.

As a simple example of the geometrical method of treating statical problems we may consider the equilibrium of a particle on a rough inclined plane.

In problems of impact we have to deal with cases of practically instantaneous impulse, where a very great and rapidly varying force produces an appreciable change of momentum in an exceedingly minute interval of time.

Free Motion of a Solid.Before proceeding to further problems of motion under extraneous forces it is convenient to investigate the free motion of a solid relative to its mass-centre 0, in the most general case.

Motion of a Solid of Revolution.In the case of a solid of revolution, or (more generally) whenever there is kinetic syminetry about an asks through the mass-centre, or through a fixec point 0, a number of interesting problems can be treated almost directly from first principles.

This principle of least resistance renders determinate many problems in the statics of structures which were formerly considered indeterminate.

Motions ClassedIn problems of mechanism, each solid piece of the machine is supposed to be so stiff and strong as not to undergo any sensible change of figure or dimensions by the forces applied to ita supposition which is realized in practice if the machine is skilfully designed.

From this principle arise problems of a kind which will be referred to in treating of Trains of Mechanism.

This classification is founded on the kinds of problems arising from the combinations.

Enough, however, remains to show that Aristarchus had a clear notion of the chief problems of philology (except perhaps those concerning etymology).

If men were really to be made obedient, it could only be by stopping them from thinking for themselves about the everyday problems of conduct; and the best way to do this was to furnish them beforehand with a ready-made code of answers to such problems, warranted to meet all needs.

It had undoubtedly done much to awaken interest in social problems, and to call forth philanthropic zeal; but the movement soon travelled far beyond the limits that Leo would have set to it.

A study of his works reveals an unusual combination of skill and originality in the mathematical treatment of many of the most difficult problems of astronomy, an unfailing patience and sagacity in dealing with immense masses of numerical results, and a talent for observation of the highest order.

Humanism, as it actually appeared in Italy, was positive in its conception of the problems to be solved, pagan in its contempt for medieval mysticism, invigorated for sensuous enjoyment by contact with antiquity, yet holding in itself the germ of new religious aspirations, profounder science and sterner probings of the mysteries of life than had been attempted even by the ancients.

They attempted to explain the fundamental problems of existence by the unaided evidence of the new natural science.

Having come to the consideration of these philosophical problems late in life, he was at some disadvantage; but he endeavoured to join as he best could in the current of contemporary German thought.

In no part of the semi-arid region of the country are the irrigation problems so diverse and difficult.

In electricity Abel studied the construction of electrical fuses and other applications of electricity to warlike purposes, and his work on problems of steel manufacture won him in 1897 the Bessemer medal of the Iron and Steel Institute, of which from 1891 to 1893 he was president.

Each of these large divisions presents a series of problems of which the practical treatment is illustrated in the financial history of the great nations of the world.

Until the 18th century no scientific treatment of financial problems was attained, though there had been great advances on the administrative side.

Apart from the special problems that this system of borrowing raises, there is the general one of its aid in making national finance continuous and orderly.

Finally, there is the same set of problems in respect to accounting and control in local as in central finance.

While British philosophizing up to a recent date has been notably lacking in width of metaphysical outlook, it has taken a very high place in its handling of the more practical problems of conduct.

Stearn in England, succeeded in completely solving the practical problems. From and after that date incandescent electric lighting became commercially possible, and was brought to public notice chiefly by an electrical exhibition held at the Crystal Palace, near London, in 1882.

Robertson (London, 1905); besides the original introductions, it contains a useful summary by the editor of the various problems of Bacon's life and thought.

On the problems afforded by the chronology of Gerbert's (Pope Silvester II.) letters and by the notes in cipher in the MS. of his letters, he wrote L'Ecriture secrete de Gerbert (1877), which may be compared with his Notes tironiennes dans les dipldmes merovingiens (1885).

The various problems which arise are still under discussion, and are of great importance for the study of Palestinian thought at the age of the parting of the ways.

Like all problems of origins, the question is necessarily extremely obscure, and cannot be definitely settled by historical evidence.

In 1859 he was appointed director of Kew Observatory, and there naturally became interested in problems of meteorology and terrestrial magnetism.

This was fgllowed by Through Scylla and Charybdis, in which he developed his favourite view of revelation as experience; Mediaevalism, a vigorous apologia in reply to a Lenten pastoral of Cardinal Mercier, archbishop of Malines, who had attacked him as the chief exponent of Modernism; and Christianity at the Cross Roads, which emphasizes the distinction between his own position and that of the Liberal Protestants, and is of special interest for its treatment of the eschatological problems of the Gospels.

The true character and origin of this enigmatical woman were, until quite recently, among the most obscure problems of Russian history.

The problems to be solved were the frontier difficulty with Argentina, the question of the possession of Tacna and Arica with Peru, and the necessity of fulfilling the obligation contracted with Bolivia to give that country a seaport on the Pacific coast.

Even the problems of its integrity are quite secondary.

Lipsius (2nd ed., Hand.-Commentar, 1892), and Zockler (2nd ed., 1894) may still be consulted with advantage, while Hilgenfeld's commentary (1852) discusses acutely the historical problems of the epistle from the standpoint of Baur's criticism.

Chrystal's Algebra, where also may be found details of the application of continued fractions to such interesting and important problems as the recurrence of eclipses and the rectification of the calendar.

The preaching of Zoroaster is directed to each individual man, and requires of him that he shall choose his position with regard to the fundamental problems of life and religion.

His Studies in Deductive Logic, consisting mainly of exercises and problems for the use of students, was published in 1880.

A gifted addressed himself with energy and diligence to the great problems awaiting him.

He first properly recognized its scope and problems, and began many of its most important discussions.

But his keen criticism of Hesse and Knoke is more successful than his positive explanation of the textual phenomena, and a more thorough-going process of literary criticism is necessary in order to solve the problems of the epistle.

His intellect was profound and comprehensive, thoroughly qualified to grapple with the deepest problems of metaphysics, but by natural preference occupying itself mainly with the practical and moral.

It would be unfair to Butler's argument to demand from it answers to problems which had not in his time arisen, and to which, even if they had then existed, the plan of his work would not have extended.

The Analogy, in fact, has and can have but little influence on the present state of theology; it was not a book for all time, but was limited to the problems of the period at which it appeared.

Subsequently Ames entered into a controversy in print with Grevinchovius on universal redemption and election, and cognate problems. He brought together all he had maintained in his Coronis ad Collationem Hagiensem - his most masterful book, which figures largely in Dutch church history.

For any large treatment of moral and political questions he seems to have been alike by nature and preparation unfitted; and there is no evidence of his having had any but the most ordinary and narrow views of the great social problems. He shows no trace of that hearty sympathy with the working classes which breaks out in several passages of the Wealth of Nations; we ought, perhaps, with Held, to regard it as a merit in Ricardo that he does not cover with fine phrases his deficiency in warmth of social sentiment.

The analogues therefore of metaphysical problems must be sought in physics; particularly that problem of the causes of things for which the Platonic idea and the Peripatetic " constitutive form " had been, each in its turn, received solutions.

Yet problems of interest bearing upon psychology and natural theology continued to be discussed.

There were also urgent economic problems to be solved.

Berthollet's most remarkable contribution to chemistry was his Essai de statique chimique (1803), the first systematic attempt to grapple with the problems of chemical physics.

The startling and romantic changes of earlier years long ago gave way to normal municipal problems and ordinary municipal routine.

Of his other compositions, the most individual are those in which, deeply impressed by the problems of his day, he has sought to reconcile science and religion, especially the fine dialogue between Milton and Galileo, where the former, impressed by Galileo's predictions of the intellectual consequences of scientific progress, resolves "to justify the ways of God to man."

A branch of bacteriology which offers numerous problems of importance is that which deals with the organisms so common in milk, butter and cheese.

This is the most satisfactory, as it is the most obvious, explanation of his utter indifference in presence of one of the most momentous problems that ever pressed for solution on an English statesman.

Moreover, the influence of the deistic writers had an incalculable influence in the gradual progress towards tolerance, and in the spread of a broader attitude towards intellectual problems, and this too, though, as we have seen, the original deists devoted themselves mainly to a crusade against the doctrine of revelation.

His life was divided between two great pursuits - the career of a surgeon, and the mastery and solution of many of the great problems of sanitary science and reform.

The problems of the self may be summed up as follows.

In ethics, egoistic doctrines disregard the ultimate problems of selfhood, and assume the self to consist of a man's person and those things in which he is or ought to be directly interested.

Details of his experimental work in magnetism and the problems of electricity and light are given in 17.3 8 9, 39 1 and 346, 6.859, 9.206, 21.936.

Another discussed conduction in curved sheets; a third the distribution of electricity in two influencing spheres; a fourth the deter mination of the constant on which depends the intensity of induced currents; while others were devoted to Ohm's law, the motion of electricity in submarine cables, induced magnetism, &c. In other papers, again, various miscellaneous topics were treated - the thermal conductivity of iron, crystalline reflection and refraction, certain propositions in the thermodynamics of solution and vaporization, &c. An important part of his work was contained in his Vorlesungen fiber mathematische Physik (1876), in which the principles of dynamics, as well as various special problems, were treated in a somewhat novel and original manner.

Psychology has been drawn upon to interpret the movements of revolutions or religions, anthropology and ethnology furnish a clue to problems to which the key of documents has been lost.

Of the many scientific problems of modern times, there are few possessing a wider or more enduring interest than that of aerial navigation (see also Aeronautics).

Before publishing his results he proposed these problems for public competition in 1658 under the assumed name of Amos Dettonville.

This effort made under the direction of the Bureau of Education has been eminently successful, and in the future the reindeer seems certain to contribute very greatly to the food, clothing, means of shelter and miscellaneous industries of the natives; and not less to the solution of the problems of communication and transportation throughout the interior.

The interpretation of the Avesta is one of the most difficult problems of oriental philology.

Not only have many travellers of many nationalities directed their steps towards the Bam-i-dunya ("the Roof of the World") in search of adventure or of scientific information, but the government surveys of Russia and India have met in these high altitudes, and there effected a connexion which will help to solve many of the geodetic problems which beset the superficial survey of Asia.

This whole prophecy, which is perhaps the most interesting in the Book of Daniel, presents problems which can never be thoroughly understood, first because the author must have been ignorant of both history and chronology, and secondly, because, in his effort to be as mystical as possible, he purposely made use of indefinite and vague expressions which render the criticism of the passage a most unsatisfactory task.

Of his prose works, the Juvenilia appeared in 1633; the Lxxx Sermons in 1640; Biathanatos in 1644; Fifty Sermons in 1649; Essays in Divinity, 1651; his Letters to Several Persons of Honour, 1651; Paradoxes, Problems and Essays, 1652; and Six and Twenty Sermons, 1661.

In science he was the first among modern men to set himself most of those problems which unnumbered searchers of later generations have laboured severally or in concert to solve.

But there is no warrant for restricting the term to any special mode of approaching the problems indicated; and as these form the central subject of metaphysical inquiry, no valid distinction can be drawn between natural theology and general metaphysics.