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factor

factor

factor Sentence Examples

  • The other factor was that he was doing what he had always dreamed of doing.

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  • Another factor was caffeine.

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  • Persia has assumed a comprehensible position as a factor in future Eastern politics.

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  • She didn't factor her transition into a human, either.

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  • She didn't factor her transition into a human, either.

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  • This equation does not give us the value of the unknown factor but gives us a ratio between two unknowns.

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  • Pete was going to be the deciding factor, and all eyes turned to him.

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  • Only then, expressing known historic facts by equations and comparing the relative significance of this factor, can we hope to define the unknown.

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  • The speed at which the journey has to be completed is obviously another important factor, though the increased power of modern locomotives permits trains to be heavier and at the same time to run as fast, and often faster, than was formerly possible, and in consequence the general tendency is towards increased weight as well as increased speed.

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  • The spirit of an army is the factor which multiplied by the mass gives the resulting force.

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  • My guess is that such people have some genetic factor protecting them against the adverse effects of bacon.

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  • Past experience constituted another important factor in establishing the interpretation of signs noted.

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  • In practice, the load factor for electric crane motors varies from 3 to s.

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  • Turning to the non-material external agents, probably no factor, are more responsible for ill-health in plants than temperature anc light.

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  • The effect of the phylogenetic factor in homology may be illustrated in the following cases.

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  • The effect of the phylogenetic factor in homology may be illustrated in the following cases.

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  • Its ready accessibility from the metropolis is the chief factor in its popularity.

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  • The actual load factor to be chosen depends on the nature of the work and the kind of crane.

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  • The actual load factor to be chosen depends on the nature of the work and the kind of crane.

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  • But in the prodigious number of supporting discoveries that have been made no single negative factor has appeared, and the evolution from their predecessors of the forms of life existing now or at any other period must be taken as proved.

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  • This result was apparently confirmed by some independent experiments, but it Is very far from the truth, for it is now known that the actual ratio, or factor as it is commonly called, of the velocity of the wind to that of the cups depends very largely on the dimensions of the cups and arms, and may have almost any value between two and a little over three.

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  • The short period of this evolution is at least one factor in the primitive grade of even the most specialized members of the group. In the advance of their molar teeth from a tritubercular to a grinding type, the author traces a curious parallelism between marsupials and placentals.

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  • A new factor now became apparent in Cretan politics.

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  • When the service is frequent enough to give a good power factor continuously, the steam locomotive cannot compete with the electric motor for the purpose of quick acceleration, because the motors applied to the axles of a train may for a short time absorb power from the central station to an extent far in excess of anything which a locomotive boiler can supply.

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  • Lamarck introduced the conception of the action of an animal on itself as a factor in producing modification.

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  • The speed of a cable is given in words per minute, the conventional number of five letters per word being understood, though in actual practice, owing to the extensive use of special codes, the number of letters per word is really between eight and nine; and this forms a considerable factor in lowering the earning capacity of a cable.

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  • A dock-side crane unloading cargo with high lifts following one another in rapid succession will require a higher load factor than a workshop traveller with a very short lift and only a very occasional maximum load; and a traveller with a very long longitudinal travel will require a higher load factor for the travelling motor than for the lifting motor.

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  • A man may live on in the world by his teaching and example as a power for good, a factor of human progress, and he may also be continuing and completing his course under conditions still more favourable to all most worthy in him.

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  • Copper is not yet universally employed, price being the governing factor in its employment; moreover, the conducting quality of the iron used for telegraphic purposes has of late years been very greatly improved.

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  • In Austria, as in Germany, anti-Semitism is a factor in the parliamentary elections.

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  • As a factor in party politics it was both unnecessary and injurious to the state.

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  • In spite of the statement that the nature of the organism is the most important factor in variation, the tendency amongst evolutionists has been to take much more account of the influence of external conditions.

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  • It is only with the exhaustion of Greek and Jewish civilization that mysticism becomes a prominent factor in Western thought.

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  • Its natural fertility and its commanding position at the meeting-place of trade-routes from every quarter made it a dominant factor until its overthrow.

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  • Its natural fertility and its commanding position at the meeting-place of trade-routes from every quarter made it a dominant factor until its overthrow.

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  • The publication in book form (March 20, 1852) was a factor which must be reckoned in summing up the moving causes of the war for the Union.

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  • The San Pedro, Los Angeles & Salt Lake railway, also an important factor in east and west transcontinental traffic, opened in May 1905, has been of special value in the development of the southern part of the state.

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  • 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.

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  • Hence it is probable that no factor has had a greater influence than these wasps in moulding the protective instincts and habits of spiders.

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  • The grappling of the cable and raising it to the surface from a depth of 2000 fathoms seldom occupy less than twenty-four hours, and since any extra strain due to the pitching of the vessel must be avoided, it is clear that the state of the sea and weather is the predominating factor in the time necessary for effecting the long series of operations which, in the most favourable circumstances, are required for a repair.

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  • Hence it is probable that no factor has had a greater influence than these wasps in moulding the protective instincts and habits of spiders.

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  • The grappling of the cable and raising it to the surface from a depth of 2000 fathoms seldom occupy less than twenty-four hours, and since any extra strain due to the pitching of the vessel must be avoided, it is clear that the state of the sea and weather is the predominating factor in the time necessary for effecting the long series of operations which, in the most favourable circumstances, are required for a repair.

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  • It is only with the exhaustion of Greek and Jewish civilization that mysticism becomes a prominent factor in Western thought.

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  • During the same period we also note the development of certain families, thanks to the accumulation of wealth by trade, and here we get the beginnings of that commercial aristocracy whose evolution was the dominant factor in the constitutional history of the republic.

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  • The influence of man on plants and vegetation is also a biological factor, which is frequently ignored as such, and treated as if it were a thing apart.

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  • If this factor could be discovered it might be applied to the suppression of the disease in malarious localities.

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  • The political factor was the rise during the 7th century B.C. of the Kosala power.

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  • Few can doubt that, if not the whole cause, it is a very important factor in that operation; and that it must play a great part in the sorting out of varieties into those which are transitory and those which are permanent.

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  • interests were sacrificed to that of making Russia a great military power, the guardian of order in Europe and the predominant factor in the Eastern Question, had been tried and found wanting.

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  • At any rate, he spoke at Guildhall on Lord Mayor's Day in a worthy manner; admitting that the growth of the German navy was a main factor in British construction, and pointing out that no power was better able to bear the strain or less likely to fail than Great Britain.

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  • interests were sacrificed to that of making Russia a great military power, the guardian of order in Europe and the predominant factor in the Eastern Question, had been tried and found wanting.

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  • The influence of man on plants and vegetation is also a biological factor, which is frequently ignored as such, and treated as if it were a thing apart.

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  • But the assignment of these various meanings to the factor does not yield results which accord with the historic facts.

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  • The export, moreover, of live sheep and of frozen mutton to Europe has become an important factor in the trade of Argentina.

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  • The vertical relief of the land above the ocean is a very important factor in determining the climate as well as the distribution of the fauna and flora of a continent.

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  • Although his making religion the sole factor of this evolution was a perversion of the historical facts, the book was so consistent throughout, so full of ingenious ideas, and written in so striking a style, that it ranks as one of the masterpieces of the French language in the 19th century.

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  • In most other Mollusca (Anisopleurous Gastropods, Pteropods and Conchifera) there is a want of such continuity; the primitive shell-sac contributes no factor to the permanent shell, or only a very minute FIG.

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  • The political factor was the rise during the 7th century B.C. of the Kosala power.

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  • We can now Indianrs - fully appreciate the factor in practical politics which Afghan- that definite but somewhat irregular mountain system, represents which connects the water-divide north of istan Herat with the southern abutment of the Hindu Kush, near Bamian.

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  • Military science, seeing in history innumerable instances of the fact that the size of any army does not coincide with its strength and that small detachments defeat larger ones, obscurely admits the existence of this unknown factor and tries to discover it--now in a geometric formation, now in the equipment employed, now, and most usually, in the genius of the commanders.

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  • must have already had a wife and son when he escaped from Rome, and it seems to me highly improbable that such a material factor in the situation would have been left out of account in Polybius's full narrative.

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  • This immunity is apparently not due to the absence of favourable conditions, but rather to the presence of some inimical factor which prevents the development of the parasite.

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  • Its great merit is that it proved the necessity of combining another and hitherto much-neglected factor in any natural arrangement, though vitiated as so many other schemes have been by being based wholly on one class of characters.

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  • The greatest benefit conferred by this memoir is probably that it stimulated the efforts, presently to be mentioned, of one of his pupils, and that it brought more distinctly into sight that other factor, originally discovered by Merrem, of which it now clearly became the duty of systematizers to take cognizance.

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  • Poverty in sub-Saharan Africa is a contributing factor in any number of conflicts there.

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  • They have emphasized the statements of Von Mohl, Cohn, and other writers alluded to, that the protoplasm is here also the dominant factor of the body, and that all the peculiarities of the cell-wall can only be interpreted in the light of the needs of the living substance.

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  • The commercial importance of such free interchange of traffic is the controlling factor in determining the gauge of any new railway that is not isolated by its geographical position.

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  • While seafood such as salmon, grouper and mahi-mahi factor primely on the menu, chicken, pork and steak round out the offerings along with salads and appetizers.

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  • To obtain the corresponding theorem concerning the general form of even order we multiply throughout by (ab)2' 2c272 and obtain (ab)2m-1(ac)bxc2:^1=(ab)2mc2 Paying attention merely to the determinant factors there is no form with one factor since (ab) vanishes identically.

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  • Take the time factor.

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  • I guess so, but I wonder sometimes if heredity is the major factor.

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  • He took her to church on Sunday, complimented her attire and fussed over her as if her injured shoulder was a disabling factor.

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  • If AP =p, the element of volume is dx2xpdp, and the number A of particles to be found in it is deduced by the introduction of the factor n.

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  • AMICABLE NUMBERS, two numbers so related that the sum of the factors of the one is equal to the other, unity being considered as a factor.

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  • The "wisdom" personified by the moon-god is likewise an expression of the science of astrology in which the observation of the moon's phases is so important a factor.

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  • motor, with a given load factor.

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  • a motor rated for a quarter load factor means that the motor is capable of exerting its full normal horse-power for three minutes out of every twelve, the pause being nine minutes, or one minute out of every four, the pause being three minutes.

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  • Anaximenes seems to have inclined to a view of cosmic evolution as throughout involving a quasi-spiritual factor.

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  • It is sometimes said that lime acts as a poison on some plants and not on others, and sometimes that it is the physiological dryness of calcareous soils that is the important factor.

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  • The competition of France ceased for a time to be an important factor.

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  • Wind is another important factor, as cotton does not do well in localities subject to very high winds; and in exposed situations, otherwise favourable, wind belts have at times to be provided.

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  • The Trans-Caspian railway has been an important factor; almost all the cotton exported passes over this line, and the statistics of this trade indicate the progress made.

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  • The political motives of these three princes, and the interaction of their different policies, was thus a great factor in determining the course and the results of the First Crusade.

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  • Henceforth this alliance was a dominant factor in politics.

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  • But an entirely new and far more important factor in the affairs of the Levant was the extension of the empire of the Mongols during the 13th century.

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  • Robert Key at Saham Tony in 1832 won over a young woman who converted her brother, Robert Eaglen, who, eighteen years later at Colchester, proved so decisive a factor in the life of Charles Haddon Spurgeon.

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  • Under the name of "Anti-Masons" able leaders united those who were discontented with existing political conditions, and the fact that William Wirt, their choice for the presidency in 1832, was not only a Mason but even defended the Order in a speech before the convention that nominated him, indicates that simple opposition to Masonry soon became a minor factor in holding together the various elements of which the party was composed.

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  • Orientation of Substituent Groups.-The determination of the relative positions of the substituents in a benzene derivative constitutes an important factor in the general investigation of such compounds.

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  • Since the atomic heat of the same element varies with its state of aggregation, it must be concluded that some factor taking this into account must be introduced; moreover, the variation of specific heat with temperature introduces another factor.

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  • the amount which is equivalent to one part of hydrogen; and (2) a factor which denotes the number of atoms of hydrogen which combines with or is equivalent to one atom of the particular element.

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  • This factor is termed the valency.

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  • The equivalent weight is capable of fairly ready determination, but the settlement of the second factor is somewhat more complex, and in this direction the law of atomic heats is of service.

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  • A factor of considerable importance in determining boiling-points of isomers is the symmetry of the molecule.

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  • Normal values of K were given by nitrogen peroxide, N204, sulphur chloride, S 2 C1 21 silicon tetrachloride, SiC1 4, phosphorus chloride, PC1 3, phosphoryl chloride, POC1 31 nickel carbonyl, Ni(CO) 4, carbon disulphide, benzene, pyridine, ether, methyl propyl ketone; association characterized many hydroxylic compounds: for ethyl alcohol the factor of association was 2.74-2.43, for n-propyl alcohol 2.86-2.72, acetic acid 3.62 -2.77, acetone 1 .

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  • A new factor introduced by Alexander was the foundation of Greek cities at all critical points of intercourse in the conquered lands.

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  • A bipartient factor is a number whose square exactly divides another number.

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  • In the 16th century the capital of the state (in which Arab influence was a decreasing factor) was transferred to Harrar (q.v.).

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  • Here the instinctive factor probably predominates over that which is experiential.

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  • But in the "homing" of pigeons there is little question that the experiential factor predominates.

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  • In 18 To, owing to the growth of Methodism and the lack of ordained ministers, he led the Connexion in the movement for connexionally ordained ministers, and his influence was the chief factor in the success of that important step. From 1811 to 1814 his energy was mainly devoted to establishing auxiliary Bible Societies.

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  • Since about 1880 there have been central factories, and their increase has been a very prominent factor in the development of the industry, as it has been in Cuba.

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  • The religious element has always been a dominating factor in the life of the city.

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  • In the Mediterranean, Crete and Malta yet survived as outposts of Christendom; but the northern coasts of Africa from Egypt to Morocco acknowledged the supremacy of the sultan, whose sea power in the Mediterranean had become a factor to be reckoned with in European politics, threatening not only the islands, but the very heart of Christendom, Italy itself, and capable - as the alliance with France against Charles V.

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  • This concession, given under strong pressure from Russia, aroused the deepest resentment of the Greeks, and was the principal factor in the awakening of the Bulgarian national spirit which subsequent events have done so much to develop. Russian influence at Constantinople had been gradually increasing, and towards the end of 1870 the tsar took advantage of the temporary disabling of France to declare himself no longer bound by those clauses of the Treaty of Paris which restricted Russia's liberty of possessing warships on the Black Sea.

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  • the battle began, but Napoleon was suffering from one of those attacks of illness and depression which henceforth became such an important factor in his fate.

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  • This decline in its prosperity was checked, and the modern development of the port began, when a railway was built from Callao into the heart of the Andes, and Callao is now an important factor in the development of copper-mining.

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  • In intermediate latitudes there is a loss of heat and then the increased density due to equatorial concentration becomes a factor.

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  • It still flows on, however, as a deep current and it then becomes a factor of immense importance with regard to the fisheries in the regions into which it penetrates.

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  • In connexion with the production of rubber the most important factor is the proportion of caoutchouc it contains.

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  • In the history of France, however, the appanage was a very important factor.

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  • From the value of A we may separate those members which contain a particular element a ik as a factor, and write the portion aik A ik; A k, the cofactor of ar k, is called a minor of order n - i of the determinant.

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  • Every factor common to all the elements of a row or of a column is obviously a factor of the determinant, and may be taken outside the determinant brackets.

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  • In the latter case the sign is determined by -I raised to the same power as before, with the exception that Tux., replaces Tusk; but if one of these numbers be even the other must be uneven; hence A ik = - Ais� rk Moreover aik a,, aikarsAik +aisarkAis Aik, rk aik ars rs where the determinant factor is giyen by the four points in which the deleting lines intersect.

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  • We can solve these, assuming them independent, for the - i ratios yl, y2,...yn-i� Now a21A11 +a22Al2 � � � = 0 a31A11+a32Al2 +� �� +a3nAln = 0 an1Al1+an2Al2 +���+annAln =0, and therefore, by comparison with the given equations, x i = pA11, where p is an arbitrary factor which remains constant as i varies.

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  • Now, suppose f and 4) to have a common factor x--y, f(x) =f1(x)(x--y); 4,(x) =4,1(x)(x--y), f l and 41 being of degrees m-1 and ni respectively; we have the identity ch i (x)f(x) =fl(x)4,(x) of degree m+n-I.

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  • and by elimination we obtain the resultant ao 0 bo 0 0 al ao b1 bo 0 a 2 a i b 2 b 1 bo a numerical factor being disregarded.

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  • He forms the equation .f()4(') -.f(x')4)(x) = o, which can be satisfied when f and 4 possess a common factor.

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  • He first divides by the factor x -x', reducing it to the degree m - I in both x and x' where m>n; he then forms m equations by equating to zero the coefficients of the various powers of x'; these equations involve the m powers xo, x, - of x, and regarding these as the unknowns of a system of linear equations the resultant is reached in the form of a determinant of order m.

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  • = 0, we find that, eliminating x, the resultant is a homogeneous function of y and z of degree mn; equating this to zero and solving for the ratio of y to z we obtain mn solutions; if values of y and z, given by any solution, be substituted in each of the two equations, they will possess a common factor which gives a value of x which, corn bined with the chosen values of y and z, yields a system of values which satisfies both equations.

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  • A binary form which has a square factor has its discriminant equal to zero.

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  • This can be seen at once because the factor in question being once repeated in both differentials, the resultant of the latter must vanish.

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  • = 11(1 +�alxl+� g al x2+�3a1x3+...), the product on the right involving a factor for each of the quantities a l, a2, a3..., and u being arbitrary.

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  • If we solve the equations connecting the original and transformed unbrae we find (A �) (- a 2) =A i( - A 2) + �'1A1, (A �) a1 = A2(- A2)+�2A1, and we find that, except for the factor (A /), -a 2 and +ai are trans formed to -A 2 and +A i by the same substitutions as x i and x 2 are transformed to i and E2.

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  • the i t " power of that appertaining to a x and b x multiplied by the j t " power of that appertaining to a x and c x multiplied by &c. If any two of the linear forms, say p x, qx, be supposed identical, any symbolic expression involving the factor (pq) is zero.

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  • The expression (ab) 4 properly appertains to a quartic; for a quadratic it may also be written (ab) 2 (cd) 2, and would denote the square of the discriminant to a factor pres.

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  • The identities are, in particular, of service in reducing symbolic products to standard forms. A symbolical expression may be always so transformed that the power of any determinant factor (ab) is even.

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  • Since, If F = An, 4) = By, 1 = I (Df A4) Of A?) Ab A"'^1Bz 1=, (F, Mn Ax I Ax 2 Axe Ax1) J The First Transvectant Differs But By A Numerical Factor From The Jacobian Or Functional Determinant, Of The Two Forms. We Can Find An Expression For The First Transvectant Of (F, �) 1 Over Another Form Cp. For (M N)(F,4)), =Nf.4Y Mfy.4), And F,4, F 5.4)= (Axby A Y B X) A X B X 1= (Xy)(F,4))1; (F,Ct)1=F5.D' 7,(Xy)(F4)1.

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  • The existence of such forms seems to have been brought to Sylvester's notice by observation of the fact that the resultant of of and b must be a factor of the resultant of Xax+ 12 by and X'a +tA2 for a common factor of the first pair must be also a common factor so we obtain P: = of the second pair; so that the condition for the existence of such common factor must be the same in the two cases.

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  • 'hc has f as a factor, and may be written f.

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  • Moreover the second term on the left contains (a f)' c -2b z 2 = 2 (a f) k-2b x 2 - (b) /0-2a 2 � if k be uneven, and (af)?'bx (i f) of) '-la if k be even; in either case the factor (af) bx - (bf) ax = (ab) f, and therefore (n-k),bk+1 +M�f = k(n-2)f.(uf)uxn-2k-1; and 4 ' +1 is seen to be of the form f .14+1.

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  • If the covariant (f,4) 1 vanishes f and 4 are clearly proportional, and if the second transvectant of (f, 4 5) 1 upon itself vanishes, f and 4) possess a common linear factor; and the condition is both necessary and sufficient.

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  • The discriminant of f is equal to the discriminant of 0, and is therefore (0, 0') 2 = R; if it vanishes both f and 0 have two roots equal, 0 is a rational factor of f and Q is a perfect cube; the cube root being equal, to a numerical factor pres, to the square root of A.

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  • The Hessian in that case is a factor of f, and Q is the third power of u2,...

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  • take and Uk = (af) k ai k the linear factor which occurs to the second power in f.

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  • The quartic will have two pairs of equal roots, that is, will be a perfect square, if it and its Hessian merely differ by a numerical factor.

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  • Remark.-The invariant C is a numerical multiple of the resultant of the covariants i and j, and if C = o, p is the common factor of i and j.

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  • Its symbolic expression, to a numerical factor pres, is (Hbc) (Hbd) (Hcd) (bcd), and it is clearly of degree 6.

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  • When R =0, and neither of the expressions AC - B 2, 2AB -3C vanishes, the covariant a x is a linear factor of f; but, when R =AC - B 2 = 2AB -3C =0, a x also vanishes, and then f is the product of the form jx and of the Hessian of jx.

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  • When a z and the invariants B and C all vanish, either A or j must vanish; in the former case j is a perfect cube, its Hessian vanishing, and further f contains j as a factor; in the latter case, if p x, ax be the linear factors of i, f can be expressed as (pa) 5 f =cip2+c2ay; if both A and j vanish i also vanishes identically, and so also does f.

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  • If, however, the condition be the vanishing of i, f contains a linear factor to the fourth power.

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  • If we wish merely to enumerate those whose partitions contain the figure 0, and do not therefore contain any power of a as a factor, we have the generator ze 1-z2.1-z3.1-z4....1-z0.

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  • When the proper degree 0 is < w a factor ao -e must be of course understood.

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  • The number of different symbols a, b, c,...denotes the the covariants are homogeneous, but not in general isobaric functions, of the coefficients of the original form or forms. Of the above general form of covariant there are important transformations due to the symbolic identities: - (�b) 2 2)2 = a b - a b; (x� = as a consequence any even power of a determinant factor may be expressed in terms of the other symbolic factors, and any uneven power may be expressed as the product of its first power and a function of the other symbolic factors.

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  • What does he therefore but resolve to give over toiling, and find himself some factor, to whose care and conduct he may commit the whole managing of his religious affairs - some divine of note and estimation that must be.

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  • The factor of proportionality will be I-41r, so that ' The principal theoretical investigations are summarized in Mascart and Joubert's Electricity and Magnetism, i.

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  • du Bois (Magnetic Circuit, p. 33), the demagnetizing factor, and the ratio of the length of the ellipsoid 2c to its equatorial diameter 2a (=c/a), the dimensional ratio, denoted by the symbol nt.

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  • Denoting its mean value by Hti, and that of the demagnetizing factor by N, we have H=Ho-Hti=Ho-NI.

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  • When the magnetizing current is twice reversed, so as to complete a cycle, the sum of the two deflections, multiplied by a factor depending upon the sectional area of the specimen and upon the constants of the apparatus, gives the hysteresis for a complete cycle in ergs per cubic centimetre.

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  • Taking the density of iron to be 7.7, the factor for reducing the loss in ergs per c.cm.

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  • Since t horse-power= 746 watts, and r ton = 2 240 lb, the factor for reducing horse-power per ton to watts per lb is 746/2240, or just 1/3.

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  • The scale is graduated in such a manner that by multiplying the reading by a simple factor (generally 10 or 2) the absolute value of the magnetization is obtained.

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  • Since the demagnetizing factor was o 052, the strongest field due to the coil was about 1340; but though arrangements were pro vided for cooling the apparatus by means of o ice, great difficulty was experienced owing to heating.

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  • The reward of title and degree and the consequent rise in the esteem of his fellows and himself was also a strong incentive; but the Mithraic faith itself was the greatest factor.

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  • Pazmany was certainly the great civilizing factor of Hungary in the seventeenth century, and indirectly he did as much for the native language as for the native church.

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  • He also showed that every equation of an even degree must have at least one real quadratic factor, reduced the solution of linear differential equations to definite integrals, and furnished an elegant method by which the linear partial differential equation of the second order might be solved.

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  • The numerical factor 6 is called the coefficient of a 5 bc 2 (� 20); and, generally, the coefficient of any factor or of the product of any factors is the product of the remaining factors.

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  • In order that a monomial containing a m as a factor may be divisible by a monomial containing a p as a factor, it is necessary that p should be not greater than m.

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  • (iv.) In algebra we have a theory of highest common factor and lowest common multiple, but it is different from the arithmetical theory of greatest common divisor and least common multiple.

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  • If R= o, then M is said to be a factor of P.

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  • The highest common factor (or common factor of highest degree) of two rational integral functions of x is therefore found in the same way as the G.C.M.

    0
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  • x-a is a factor of P.

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  • (iii.) Conversely, if x-a is a factor of P, then poand plan - 1 +...

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  • Kolliker (Development of Cephalopods, 1844), Remak (Development of the Frog, 1850), and others had laid the foundations of this knowledge in isolated examples; but it was Kovalevsky, by his accounts of the development of Ascidians and of Amphioxus (1866), who really made zoologists see that a strict and complete cellular embryology of animals was as necessary and feasible a factor in the comprehension of their relationships as at the beginning of the century the coarse anatomy had been shown to be by Cuvier.

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  • Another important factor in the present condition of zoological knowledge as represented by classification is the doctrine of degeneration propounded by Anton Dohrn.

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  • It amounts toa new and unprecedented factor in organic development, external to the organism and yet produced by the activity of the organism upon which it permanently reacts.

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  • This factor is the Record of the Past, which grows and develops by laws other than those affecting the perishable bodies of successive generations of mankind, and exerts an incomparable influence upon the educable brain, so that man, by the interaction of the Record and his educability, is removed to a large extent from the status of the organic world and placed in a new and unique position, subject to new laws and new methods of development unlike those by which the rest of the living world is governed.

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  • The middle element alone contributes without deduction; the effect of every other must be found by introduction of a resolving factor, equal to cos 0, if 0 represent the difference of phase between this element and the resultant.

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  • If a formal proof be desired, it may be obtained by introducing into the integral a factor such as P, in which h is ultimately made to diminish without limit.

    0
    0
  • When a, b, X are regarded as constant, the first factor may be omitted, - as indeed should be done for consistency's sake, inasmuch as other factors of the same nature have been omitted already.

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  • The occurrence of sin 4 as a factor in (6) shows that the relative intensities of the primary light and of that diffracted in the direction B depend upon the condition of the former as regards polarization.

    0
    0
  • The factor (I -cos 0) shows in what manner the secondary disturbance depends upon the direction in which it is propagated with respect to the front of the primary wave.

    0
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  • Under these circumstances the double differentiation with respect to t of any quantity is equivalent to multiplication by the factor - n 2, and thus our equations take the form (b 2 v 2 + n2)E+(a2 - b2) ds (b2 2 + n2)n +(a2 - b2 y =0 (7).

    0
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  • Since the dimensions of T are supposed to be very small in com d parison with X, the factor dy (--) is sensibly constant; so that, if Z stand for the mean value of Z over the volume T, we may write TZ y d e T ?

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  • Its connexion with a is expressed by a =c4'/dr; so that TZ sin 05 e'(at - kr) 47b 2 where the factor e int is restored.

    0
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  • Indeed, if the aperture is very small, this method gives the correct result, save as to a constant factor.

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  • From the moment of Emma's marriage Normandy became a chief factor in English politics."/n==Authorities== - The Anglo-Saxon Chronicle (edition by C. Plummer, 2 vols.

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  • His influence was an undoubted factor in the Kruger policy of that time.

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  • Another factor besides climate which has exerted a powerful influence on dress - more perhaps on what is commonly regarded as " jewelry " as distinct from " clothing " - is superstition.

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  • Henceforward he neglected politics, and Louis of France ceased to consider him as a political factor.

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  • The abuse of alcohol may also be mentioned here as a factor in the poduction of disease.

    0
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  • Any of the abnormal conditions that bring about general or local defective nutrition is an important factor in producing fatty degeneration.

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  • Thus, while increased pressure in the blood or lymph vessels may be one factor, and increased permeability of the capillary endothelium another, increased osmotic pressure in the tissues and lymph is probably the most important in the production of dropsy.

    0
    0
  • The disassociation from his local origin involved in this doctrine of the triad gave to Bel a rank independent of political changes, and we, accordingly, find Bel as a factor in the religion of Babylonia and Assyria to the latest days.

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  • The result of his discovery was an entire revolution in the knowledge of diseases of the chest; but it would be a mistake to forget that an essential factor in this revolution was the simultaneous study of the condition of the diseased organs as seen after death.

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  • The government had now no choice but to secure if possible the person of Lord Edward Fitzgerald, whose social position more than his abilities made him the most important factor in the conspiracy.

    0
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  • Anne's only daughter, Suzanne, had married in 1505 her cousin, Charles of Bourbon, count of Montpensier, the future constable; and the question of the succession of Suzanne, who died in 1521, was the determining factor of the treason of the constable de Bourbon (1523).

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  • The growth of popularity of the cycle, and later of the motor-car, has been a principal factor in the wide development of a tendency to leave London during the ” week-end,” that is to say, as a rule, for Saturday afternoon and Sunday.

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  • ordinary steel rope has a breaking strength of about 32 tons, which, with a' factor of safety of six gives a safe working load of 54 tons.

    0
    0
  • (22) Y (F2 x2) Suppose x 3 -F is a repeated factor of X3, then y 3 = G, and X 3 = (x 3 -F)2 [P' _ P(X3+F)2+2' _ G(X +F) -G 2 ], (23) nd putting x3-F=y, (y) 2= 7'3'2- [41' r 1' F 2 -{-4 g r qFG - G2 +2 (2P'r 19F+9 r q G) y+ r y (24) o that the stability of this axial movement is secured if A = 4 P' r ?'F 2 + 4 Y q FG - G 2 (25) s negative, and then the axis makes r J l (-A)/7r nutations per second.

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  • vertical, where Wh tan 0 = N = (c 2 - cl) c2 g2 tan 0, (6) (7) in which we have put k' 2 = ek 2, where E is a numerical factor depending on the shape.

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  • In this respect it was an important factor in the rise of that middle-class literature which found its most virile expression in the period of the Reformation.

    0
    0
  • The quantity of the juice is the test to which recourse must be had in judging the efficiency of the extraction, while the quality is the main factor to be taken into account with regard to the results of subsequent manufacture.

    0
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  • - The influence of different kinds of soil as a factor in the production of disease requires to be considered, in regard not only to the nature and number of the microorganisms they contain, but also to the amount of moisture and air in them and their capacity for heat.

    0
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  • It is impossible to assign any precise date for the beginning of the Hanseatic League or to name any single factor which explains the origin of that loose but effective federation of North German towns.

    0
    0
  • The decisive factor in determining membership in the League was the historical right of the citizens of a town to participate in Hanseatic privileges abroad.

    0
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  • The last wars of the League with the Scandinavian powers in the 16th century, which left it shorn of many of its privileges and of any pretension to control of the Baltic basin eliminated it as a factor in the later struggle of the Thirty Years' War for that control.

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  • "The occurrence of Phylactolaemata in the tropics would show, however, without further evidence, that frost is not a factor essential for germination.

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  • Railways.It is easy to understand that an enterprise like railway construction, requiring a great outlay of capital with returns long delayed, did not at first commend itself to the Japanese, who were almost entirely ignorant of co-operation as a factor of business organization.

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  • Before his western escapade he had taken up the business of hosiery factor.

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    0
  • Hence the end of the Social war, and of the Civil war, which arose out of it, is most clearly a determining factor in Roman literature, and to.

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  • If, however, we defined the strength of the source by the statement that the strength divided 1 The beginner is often puzzled by the constant appearance of the factor 47r in electrical theorems. It arises from the manner in which the unit quantity of electricity is defined.

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    0
  • He was educated at Aurich, where one of his teachers was the philosopher Wilhelm Reuter, whose influence was the dominating factor in the development of his thought.

    0
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  • The 0, 4) diagram is useful in the study of heat waste and condensation, but from other points of view the utility of the conception of entropy as a " factor of heat " is limited by the fact that it does not correspond to any directly measurable physical property, but is merely a mathematical function arising from the form of the definition of absolute temperature.

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  • The discovery of alluvial gold in 1851 brought many immigrants to the district; but the opening up of the quartz reefs in 1872 was the principal factor in the importance of Bendigo.

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    0
  • So certain is the ore-bearing formation that engineers in estimating its auriferous contents feel justified in assuming, as a factor in their calculations, a vertical extension limited only by the lowest depths at which mining is feasible.

    0
    0
  • A high current-density being employed, the turn-over of gold is rapid - an essential factor of success when the costliness of the metal is taken into account.

    0
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  • He was ordained in 1834, and after a short curacy at Bubbenhall in Warwickshire was appointed chaplain of Guy's Hospital, and became thenceforward a sensible factor in the intellectual and social life of London.

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  • The valuable element is the able-bodied immigrant himself as a factor of production.

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  • There is hardly any increase in the intestinal secretion, the drug being emphatically not a hydragogue cathartic. There is no doubt that its habitual use may be a factor in the formation of haemorrhoids; as in the case of all drugs that act powerfully on the lower part of the intestine, without simultaneously lowering the venous pressure by causing increase of secretion from the bowel.

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  • His father was a solicitor, and his mother was the daughter of Matthew Buist, factor to Lord Haddington.

    0
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  • Less accurate formulae are =p W/(W - W 2), the factor involving the density of the air, and the coefficient of the expansion of the solid being disregarded, and 0 =W/(W - W 1), in which the density of water is taken as unity.

    0
    0
  • According to the investigations of Svante Arrhenius the osmotic pressure in atmospheres may be obtained by simply multiplying the temp rature of freezing (r) by the factor -12.08, and it varies with temperature (t) according to the law which holds good for gaseous pressure.

    0
    0
  • Mill has shown that in the North Sea off the Firth of Forth the average depth of visibility of a disk in the winter half-year was 4; fathoms and in the summer half-year 62 fathoms, and, although the greater frequency of rough weather in winter might tend to obscure the effect, individual observations made it plain that the angle of the sun was the main factor in increasing the depth to which the disk remained visible.

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  • in the course of a year, while in the Antarctic regions the season's growth is only half as great; in the latter also the accumulated snow is an important factor in the thickness of the ice, and snow is an even worse conductor of heat.

    0
    0
  • (2) The factor 0 of the product TO is found by means of a revolution counter.

    0
    0
  • To allow for the first of these two factors, Van der Waals finds that v in equation '04) must be replaced by v - b, where b is four times the aggregate space occupied by all the molecules, while to allow for the second factor, p must be replaced by p +a/v 2 .

    0
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  • He at once became a dominant factor in New York politics, and for the next quarter of a century he played a leading role in the history of the commonwealth.

    0
    0
  • 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.

    0
    0
  • Nor is it possible at any point in knowledge to prove the existence of a merely given in whose construction the thinking subject has played no part nor a merely thinking subject in whose structure the object is not an organic factor.

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  • As contrasted with the first it stood for the necessity of recognizing a universal or ideal element as a constitutive factor in all experience whether cognitive or volitional; as contrasted with the latter for the ultimate unity of subject and object, knowledge and reality, and therefore for the denial of the existence of any thing-in-itself for ever outside the range of experience.

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  • Whatever is to be said of ancient Idealism, the modern doctrine may be said notably in Kant to have been in the main a vindication of the subjective factor in knowledge.

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    0
  • Under the kings of Athens it must have closely resembled the Boule of elders described by Homer; and there can be no doubt that it was the chief factor in the work of transforming the kingship into an aristocracy, in which it was to be supreme.

    0
    0
  • 2um) Now, if p is any factor of m, there is a series of equidistant ordinates uo, up, 142p, um - p, um; and the chordal area as determined by these ordinates is ph (2uo + up + u2p +.

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  • Say is considered to have brought out the importance of capital as a factor in production more distinctly than the English economists, who unduly emphasized labour.

    0
    0
  • Others soon followed in spite of the efforts of the chief factor of the Hudson's Bay Company, Dr John M ` Loughlin, and these permanent settlers finally carried the day.

    0
    0
  • If the temperature is t° the length for given frequency must be increased by the factor Id-0.001841.

    0
    0
  • - Consideration of the local conditions affecting the erection of bridges is always important, and sometimes becomes a controlling factor in the determination of the design.

    0
    0
  • Soft steel is used for rivets always, and sometimes for the whole superstructure of a bridge, but medium steel more generally for the plates, angle bars, &c., the weight of the bridge being then reduced by about 7% for a given factor of safety.

    0
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  • The committee recommended that a factor of safety of 4 should be taken for wind stresses.

    0
    0
  • For safety against overturning they considered a factor of 2 sufficient.

    0
    0
  • divided by the factor of safety.

    0
    0
  • It was pointed out as early as 1869 (Unwin, Wrought Iron Bridges and Roofs) that a rational method of fixing the working stress, so far as knowledge went at that time, would be to make it depend on the ratio of live to dead load, and in such a way that the factor of safety for the live load stresses was double that for the dead load stresses.

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  • Factor of Safety twice as great for Live Load as for Dead Load.

    0
    0
  • divided by a factor of safety.

    0
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  • Let that factor be 3.

    0
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  • For stiffened suspension bridges with wire cables, if the dip is 310th of the span the limiting span is 2700 to 3600 ft., and if the dip is *th of the span, 3250 to 4250 ft., according to the factor of safety allowed.

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  • Industry was thus in many ways compensated for the paralysis of trade with private buyers in the home market and for the closing of foreign markets, and it would have been able to continue quietly on the old lines but for the emergence of a new factor which fundamentally altered the conditions.

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  • This factor was the rupture of communications with foreign countries, due in the earlier stages of the war to the limitation, and at one time the prohibition, of exports by neutral countries, the passing over of some of these countries to the enemy, and lastly the blockade by the enemy Powers, which increased in efficiency and made it more and more difficult to import the most essential commodities, until in the end it was almost impossible to obtain from abroad anything, needed either for the soldiers or the civilians.

    0
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  • Again, education, science, art and literature have been secularized: the printing-press carries knowledge into every house, the number of illiterates diminishes from year to year in every civilized country, and the clergy are no longer the exclusive propagators of culture, but merely one factor among a hundred others.

    0
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  • In the development of the state since its admission into the Union the railways have been an important factor.

    0
    0
  • Another factor, and that the determining one, soon came to the aid of the Greeks.

    0
    0
  • The idea underlying these councils was to create, as it were, a certain constitution for factories by which the workman who had hitherto been a mere machine should become a creative factor, closely identified with the organization of the undertaking, conscious of responsibility, and thus making of democracy the same reality in economic life as it had already become in political life.

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  • To this factor was added the revival of national feeling and prejudice, with growing political complications and jealousies.

    0
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  • There is a growing tendency to mixed marriages, which are an important factor in religious changes.

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  • Immediately dependent upon the prince, from whom they obtained their privileges, the most important of which were self-government and freedom from taxation, these traders soon became an important factor in the state, counterpoising, to some extent, the influence of the gentry, enriching the land by developing its resources, and promoting civilization by raising the standard of comfort.

    0
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  • in 1462 Muscovy had been a negligible factor in P olish politics.

    0
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  • Had that dynasty been prolonged for another century, there is every reason to suppose that it would also have dealt satisfactorily with Poland's still more dangerous internal difficulties, and arrested the development of that anarchical constitution which was the ruling factor in the ruin of the Republic. Simultaneously with the transformation into a great power of the petty principalities which composed ancient Poland, another and equally momentous political transformation was proceeding within the country itself.

    0
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  • First, however, it is necessary to describe briefly the origin and previous history of these romantic freebooters who during the second half of the 17th century were the determining factor of Polish and Muscovite politics.

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  • Aristippus and his followers seized upon this, and made it the prime factor in existence, denying to virtue any intrinsic value.

    0
    0
  • In a sense it serves also as a national reserve, and has already been an important factor in the preservation of the American bison.

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  • The resistance R can thus be divided into two factors, one of which is d 2, where d denotes the diameter of the shot in inches, and the other factor is denoted by p, where p is the resistance in pounds at the same velocity to a similar I-in.

    0
    0
  • The factor T becomes of importance in long range high angle fire, where the shot reaches the higher attenuated strata of the atmosphere; on the other hand, we must take about 800 in a calculation of shooting under water.

    0
    0
  • Lastly, to allow for the superior centering of the shot obtainable with the breech-loading system, Bashforth introduces a factor a, called the coefficient of steadiness.

    0
    0
  • In the long range high angle fire the shot ascends to such a height that the correction for the tenuity of the air becomes important, and the curvature 4)-8 of an arc should be so chosen that 4)y 0, the height ascended, should be limited to about moo ft., equivalent to a fall of I inch in the barometer or 3% diminution in the tenuity factor T.

    0
    0
  • After a certain discount for friction and the recoil of the gun, the net work realized by the powder-gas as the shot advances AM is represented by the area Acpm, and this is equated to the kinetic energy e of the shot, in foot-tons, (I) e d2 I + p, a in which the factor 4(k 2 /d 2)tan 2 S represents the fraction due to the rotation of the shot, of diameter d and axial radius of gyration k, and S represents the angle of the rifling; this factor may be ignored in the subsequent calculations as small, less than I %.

    0
    0
  • Sometimes the factor 27.68 is employed, corresponding to a density of water of about 62-4 lb per cub.

    0
    0
  • =C/P, no factor being required.

    0
    0
  • This muzzle velocity is about 5% greater than the 2150 f/s of the range table, so on these considerations we may suppose about 10% of work is lost by friction in the bore; this is expressed by saying that the factor of effect is f =0.9.

    0
    0
  • observing that any factor 1/I-x l is=l+x l +x 2l +..., we see that in the term Nx the coefficient is equal to the number of partitions of n, with the parts I, 2,, ..,withh repetitions.

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  • Among his other works may be named Paroles d'un revolte (1884); La Conquete du pain (1888); L' Anarchic: sa philosophie, son ideal (1896); The State, its Part in History (1898); Fields, Factories and Workshops (1899); Memoirs of a Revolutionist (1900); Mutual Aid, a Factor of Evolution (1902); Modern Science and Anarchism (Philadelphia, 1903); The Desiccation of Asia (1904); The Orography of Asia (1904); and Russian Literature (1905).

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  • From 1875 onwards Smith contributed to the 9th edition of the Encyclopaedia Britannica a long series of important articles, which, together with the articles of Cheyne, Wellhausen and others, made that work an important factor in the change which was to pass over English thought in regard to the Bible; in 1878, by his pleadings in the trial for heresy brought against him on the ground of these articles, he turned a personal defeat in the immediate issue into a notable victory for the cause which led to his condemnation; and subsequently (in 1880), in two series of lectures, afterwards published 2 and widely read, he gave a brilliant, and, as it proved, to a rapidly increasing number a convincing exposition of the criticism of the literature, history and religion of Israel, which was already represented in Germany 2 The Old Testament in the Jewish Church (1881); The Prophets of Israel (1882).

    0
    0
  • The principle on which the instrument works is as follows: Suppose any circuit, such as an electric motor, lamp or transformer, is receiving electric current; then the power given to that circuit reckoned in watts is measured by the product of the current flowing through the circuit in amperes and the potential difference of the ends of that circuit in volts, multiplied by a certain factor called the power factor in those cases in which the circuit is inductive and the current alternating.

    0
    0
  • It is not as a philosophy, then, nor as a new religion, that Neoplatonism became a decisive factor in history, but, if one may use the expression, as a " mood."

    0
    0
  • The power of io, which occurs as a factor in the tables of both Napier and Byrgius, was rendered necessary by the fact that the decimal point was not yet in use.

    0
    0
  • As has been stated, Abraham Sharp's table contains 61-decimal 10 b= log 24 = - log (1-160) d =10g 49 = - log (1-160) 17253 8 35 62 21868 Briggian logarithms of primes up to I ioo, so that the logarithms of all composite numbers whose greatest prime factor does not exceed this number may be found by simple addition; and Wolfram's table gives 48-decimal hyperbolic logarithms of primes up to 10,009.

    0
    0
  • By means of these tables and of a factor table we may very readily obtain the Briggian logarithm of a number to 61 or a less number of places or of its hyperbolic logarithm to 48 or a less number of places in the following manner.

    0
    0
  • Multiplying by 50, we have 50X43,867=2,193,350, and on looking in Burckhardt's Table des diviseurs for a number near to this which shall have no prime factor greater than 10,009, it appears that 2,193,349 = 23 X 47 X 2029; thus 43,867= Au (23X47X2029 -{-1), and therefore log e 43,867 = log e 23+loge 47+logy 2029 - log e 50 +2,193,349 2 (2,193,349) 2 + (2,193,349)3 &c. The first term of the series in the second line is whence, taking out the logarithms from Wolfram's table, log e 43, 86 7 = Io 68891 76079 60568 10191 3661.

    0
    0
  • The principle of the method is to multiply the given prime (supposed to consist of 4, 5 or 6 figures) by such a factor that the product may be a number within the range of the factor tables, and such that, when it is increased by I or 2, the prime factors may all be within the range of the logarithmic tables.

    0
    0
  • If the number is incommensurable or consists of more than seven figures, we can take the first seven figures of it (or multiply and divide the result by any factor, and take the first seven figures of the result) and proceed as before.

    0
    0
  • The determining factor is no doubt to be sought in his relationship with C. Marius, the husband of his aunt Julia.

    0
    0
  • The birds - the largest factor in the fauna - have become very greatly reduced through the introduction of cats, dogs and pigs, as well as by the constant persecution of every sort of animal by the natives.

    0
    0
  • The Jesuits established themselves in 1572, devoting themselves actively to the education both of whites and of natives, and were a powerful factor in the exploring and civilizing of the northern districts.

    0
    0
  • Hence the stress laid on will as the realizing factor, in opposition to thought, a view through which Schelling connects himself with Schopenhauer and Von Hartmann, and on the ground of which he has been recognized by the latter as the reconciler of idealism and realism.

    0
    0
  • One very helpful factor in determining which is the principal carrier of any form is the coincidence of the zone of a particular insect with that of any disease.

    0
    0
  • In many cases, at any rate, this indicates a difference in sexuality; and it is particularly necessary to bear this factor in mind when considering the avian Trypanosomes, where, perhaps, the extremes of form are to be met with.

    0
    0
  • His philosophy consisted in an attempt to reconcile the doctrines of his teachers Philo of Larissa and Mnesarchus the Stoic. Against the scepticism of the former, he held that the intellect has in itself a sufficient test of truth; against Mnesarchus, that happiness, though its main factor is virtue, depends also on outward circumstances.

    0
    0
  • They are the chief factor in surviving Irish superstition.

    0
    0
  • The initial settlement of the Pacific coast following the discovery of gold in California in 1848, and of the eastern base of the Rocky Mountains after the discovery of gold in 2859, ifiustrates the same factor.

    0
    0
  • The ten years from 1860 to 1870 witnessed the operation of the first great factor which reduced the rate of national increase, namely the Civil War.

    0
    0
  • Turning to the factor of sex, it may be stated that the t umber of the gainfully employed in 1900 above give1~ included 8 / of all the men and boys, and 18-8% of all the women and gi in the country.

    0
    0
  • Deducing from the figures of production since 1859 an equation of increase, one finds that in each nine years as much oil has been produced as in all preceding years together, and in recent years the factor of increase has been higher.

    0
    0
  • With the reservations that only in the case of certain red haematite bedded deposits can any estimate be made of relative accuracy, say within 10%; that the concentration deposits of brown ore can be estimated only with an accuracy represented by a factor varying between 0.7 and 3; and that the great Lake Superior and the less known Adirondack deposits can be estimated within 15 to 20%, the total supply of the country was estimated at 79,594,220,000 long tons73,21o,415,000 of which were credited to haematite ores and 5,054,675,000 to magnetite.

    0
    0
  • Nevertheless the state is (as will be explained later) a slightly declining factor in the public life of the nation, because public interest tends more and more to centre in the Federal or national government.

    0
    0
  • But occasionally one or more drafts are mixed together, when price is the determining factor.

    0
    0
  • This concert of the great powers, as its name implies, in contradistinction to the " balance of power," was essentially a factor for the preservation of peace.

    0
    0
  • Whatever value may attach to the consolidation of the British Empire itself as a factor in spreading the peace which reigns within it, it is also a great contribution to the peace of the world that the British race should have founded practically independent states like the Dominion of Canada, the Commonwealth of Australia, the South African Union and the Dominion of New Zealand.

    0
    0
  • Chemical action has frequently been suggested as being a necessary factor in the luminosity of flame, not only in the sense that it causes a sufficient rise of temperature but as furnishing some special and peculiar though undefined stimulus.

    0
    0
  • The facts, as quoted, point to the closeness of the packing of molecules as the factor which always accompanies and perhaps causes the widening of lines.

    0
    0
  • We have now reduced the law for the bands to a form which we have found applicable to a series of lines, but with this important difference that while a in the case of line spectra is a small corrective term, it now forms the constant on which an essential factor in the appearance of the band depends.

    0
    0
  • When we compare together electric discharges the intensity of which is altered by varying, the capacity, we are unable to form an opinion as to whether the effects observed are due to changes in the density of the luminous material or changes of temperature, but the experiments of Sir William and Lady Huggins 1 with the spectrum of calcium are significant in suggesting that it is really the density which is also the determining factor in cases where different concentrations and different spark discharges produce a change in the relative intensities of different lines.

    0
    0
  • It also involves, of course, the distance between the needles and the distribution of the magnetism of the needles;: but this factor is determined by comparing the value given by the instrument, at a shore station, with that given by an ordinary magnetometer.

    0
    0
  • The determining factor in politics was the conduct of the war.

    0
    0
  • The Liberal leaders had given public pledges of their adhesion to Lord Lansdowne's foreign policy, and the fear of their being unable to carry it on was no longer a factor in the public mind.

    0
    0
  • His literary attainments attracted the notice of Charlemagne, and Paulus became a potent factor in the Carolingian renaissance.

    0
    0
  • There may be room for dispute, as to the extent to which the king's share in the schism was due to the instigation of the revolted cardinals; there can be not the slightest doubt that his attitude was the decisive factor in perpetuating and widening the breach.

    0
    0
  • It may be admitted that he clung to his native Florence and to his family with warm affection; but the really decisive factor which governed his attitude throughout was his anxiety for the temporal and spiritual independence of the Holy See.

    0
    0
  • Though this factor was perhaps not prominent in the case of Holland (1853) or Scotland (1878) it was Irish immigration which made it feasible in England (1850).

    0
    0
  • In fact, experiments upon the changes of velocity of bodies, due to a mutual influence between them, bring to light a property of bodies which may be specified by a quantity proportional to their volumes in the case of bodies which are perceived by other tests to be of one homogeneous substance, but otherwise involving also another factor.

    0
    0
  • Of course, such travellers are not peculiar to the cotton trade, but cotton goods in various forms are an important factor in the home trade.

    0
    0
  • The decisive factor in the separation of Silesia from Poland was furnished by a partition of the Polish crown's territories in 1138.

    0
    0
  • For most experimental purposes the small terms involving the factor (- p') may be neglected, and we have, approximately, PoV'=Rt log (ply).

    0
    0
  • The security of the Zuider Zee for trade and fishing purposes was the first factor in the commercial development of North Holland, and the cities of Medemblik, Enkhuizen, Hoorn, Edam and Monnikendam, though now little more than market centres for the surrounding district, possessed a large foreign commerce in the 16th and 17th centuries.

    0
    0
  • Colour, therefore, must be correlated with some determinant (determining factor) for pattern, and it cannot, therefore, exist alone in an animal's coat.

    0
    0
  • His sympathy with men of other ways and thought, and with the truth in other ecclesiastical systems gained for him the confidence and affection of men of varied habits of mind and religious traditions, and was thus a great factor in gaining increasing support for the Episcopal Church.

    0
    0
  • A new Islam is also a factor of the situation.

    0
    0
  • Their natural devotion and their susceptibility to pomp and ritual was a factor skilfully used by the priests, but hardly anything was done to strengthen their moral power.

    0
    0
  • It is, however, probable that conduction is to some extent a factor in the process.

    0
    0
  • In connexion with this he emphasizes a too generally neglected factor in economic phenomena, " the constant and insatiable desire of the mind for exercise and employment."

    0
    0
  • The total power developed is 600 H.P., and though the load factor varies very greatly in this case, the differential type of governor used secures perfect control of the running of the wheels.

    0
    0
  • He held a unique position among foreign residents in Japan, alike as a profound student of its history and art, and as a powerful factor in international politics.

    0
    0
  • In all these lesser orders may be discerned the tendency of a return to the elements of Eastern monasticism discarded by St Benedict - to the eremitical life; to the purely contemplative life with little or no factor of work; to the undertaking of rigorous bodily austerities and penances - it was at this time that the practice of self-inflicted scourgings as a penitential exercise was introduced.

    0
    0
  • It is the law of diminishing returns from land, involving as it does - though only hypothetically - the prospect of a continuously increasing difficulty in obtaining the necessary sustenance for all the members of a society, that gives the principal importance to population as an economic factor.

    0
    0
  • It would be difficult even to prove any ground of affinity among them beyond a desposition to take sense as a prime factor in the account of subjective experience: their common interest in physical science was shared equally by rationalist thinkers of the Cartesian school, and was indeed begotten of the time.

    0
    0
  • One important factor in keeping down the amount per person is the substitution in use, which for a generation has been in progress, of the stronger teas of India and Ceylon for the old-fashioned weaker produce of China.

    0
    0
  • Lowness of price has not been the only factor in increasing the rate of consumption.

    0
    0
  • The imperial budget, like that of most European nations, is divided into two portions, the ordinary and the extraordinary; and the increase under both heads (especially for army and navy) became a recurrent factor.

    0
    0
  • The old pagan faith was not yet entirely destroyed, and traces of its influence may still be detected in popular beliefs and customs. But still Christianity was dominant, and soon became an important factor in the process of civilization, while the close alliance of the German church with the papacy was followed by results of the utmost consequence for Germany.

    0
    0
  • They were no longer, as in the old days, the leading factor.

    0
    0
  • The most striking effect of the development of this antagonism was the gradual disappearance as a factor in politics of the Liberals, the chief builders of the Empire.

    0
    0
  • The Tromholt-Schroeter data for Scandinavia as a whole commenced with 1761; the figures for earlier years were obtained by multiplying the data for Sweden by 1.356, the factor being derived by comparing the figures for Sweden alone and for the whole of Scandinavia from July 1761 to June 1783.

    0
    0
  • War, this war was fought almost exclusively in the Aegean Sea, the enemy was primarily Sparta, and the deciding factor was Persian gold.

    0
    0
  • The most striking meteorological factor in Egypt is the persistence of the north wind throughout the year, without which the climate would be very trying.

    0
    0
  • But the main factor in evolutionary process was undoubtedly the formation of hs, which brought gods of independent origin into relation ii one another, and thus imbued them with human passions virtues.

    0
    0
  • The second factor inducing the assimilative change is the withdrawal of the nervous system from sensual, stimulation.

    0
    0
  • But a potent - according to some, the most potent - factor in hypnotism, namely, suggestion, is unrepresented in the production of so-called animal hypnotism.

    0
    0
  • Later, in keeping with his position, he opposed all concessions to the Protestants; but still showed himself so vacillating that the papacy ceased to be regarded as a serious political factor, and was entirely ignored in the final settlement of Westphalia, 1648.

    0
    0
  • The fundamental factor in these dissensions was the rivalry between the princes of Spoleto and the Carolingian house, represented by the king of Germany.

    0
    0
  • Wallace, however, brought into his scheme a factor excluded by Darwin.

    0
    0
  • It is equally impossible to draw an exact line between variation induced by the environment and variation that may be termed intrinsic. Extrinsic and intrinsic factors are involved in every case, although there is a range from instances in which the external factor appears to be extreme to instances where the intrinsic factor is dominant.

    0
    0
  • Even the results of mutilation involve an intrinsic factor, for they range, according to the organ and organism affected, from complete regeneration to the most imperfect healing.

    0
    0
  • In the effects of exercise, of physiological activity and the gross results of such external agencies as food, temperature, climate, light, pressure and so forth the intrinsic factor appears to become more important.

    0
    0
  • And finally, there are a series of variations, amongst which no doubt are the mutations of de Vries and the disintegrations and recombinations of the unit factors with which Mendel and his followers have worked, in which the external or environmental factor is most remote from the actual result.

    0
    0
  • - Transportation facilities have been an important factor in the economic development of Illinois.

    0
    0
  • He compiled a systematic account of the fiscal system of the canton Bern, but the main factor in his mental growth came from his study of Christianity.

    0
    0
  • Another factor of importance in Goethe's Strassburg life was his love for Friederike Brion, the daughter of an Alsatian village pastor in Sesenheim.

    0
    0
  • Too little is known of the north as a factor in Palestinian development to allow hasty inferences, but it is certainly noteworthy, at all events, that the names Amor and Hatti appear to move downwards, and that " Hittite " is applied to Palestine and Philistia by the Assyrians, and to Hebron in the Old Testament, and that Ezekiel (xvi.

    0
    0
  • But with the establishment of (relatively) universal peace Palestine ceased to be a factor in general history.

    0
    0
  • Weeden, Indian Money as a Factor in New England Civilization (Baltimore, 1884); E.

    0
    0
  • 6.) workers, and unfertilized eggs in "drone-cells," virgin reproduction or parthenogenesis being therefore a normal factor in the life of these insects.

    0
    0
  • An association of sugar planters is a very important factor in the economic development of the island.

    0
    0
  • The destruction of the U.S. battleship "Maine" in the harbour of Havana on the 15th of February 1898 was an influential factor in causing the outbreak of the Spanish-American War, and during the war the city was blockaded by a United States fleet.

    0
    0
  • He found that pressure increases luminosity, so that hydrogen, for example, the flame of which in normal circumstances gives no light, burns with a luminous flame under a pressure of ten or twenty atmospheres, and the inference he drew was that the presence of solid particles is not the only factor that determines the light-giving power of a flame.

    0
    0
  • Caste has, in fact, come to be the chief dominating factor in the life of the ordinary native of India.

    0
    0
  • An important factor which thus served to maintain the rites in a more or less stable condition was the predominance of what may be called the astral theology as the theoretical substratum of the Babylonian religion, and which is equally pronounced in the religious system of Assyria.

    0
    0
  • The popular factor is the belief in the influence exerted by the movements of the heavenly bodies on occurrences on earth - a belief naturally suggested by the dependence of life, vegetation and guidance upon the two great luminaries.

    0
    0
  • The ritual alone which accompanied divination practices and incantation formulae and was a chief factor in the celebration of festival days and of days set aside for one reason or the other to the worship of some god or goddess or group of deities, is free from traces of the astral theology.

    0
    0
  • Though, in accounting for the anger of the gods, no sharp distinction is made between moral offences and a ritualistic oversight or neglect, yet the stress laid in the hymns and prayers, as well as in the elaborate atonement ritual prescribed in order to appease the anger of the gods, on the need of being clean and pure in the sight of the higher powers, the inculcation of a proper aspect of humility, and above all the need of confessing one's guilt and sins without any reserve - all this bears testimony to the strength which the ethical factor acquired in the domain of the religion.

    0
    0
  • This factor appears to less advantage in the unfolding of the views concerning life after death.

    0
    0
  • Religion or revelation is one element or factor in the divine process, a stage or phase of the ultimate rational life.

    0
    0
  • Thought as form would thus be a factor or an element in a composite unit.

    0
    0
  • From the purely geometrical point of view, a quaternion may be regarded as the quotient of two directed lines in space - or, what comes to the same thing, as the factor, or operator, which changes one directed line into another.

    0
    0
  • He saw that he could get a hint from the simpler case, already thoroughly discussed, provided the two factor lines were in one plane through the real unit line.

    0
    0
  • But the numerical factor appears to be yz'+zy', while it is the quantity yz' - zy' which really vanishes.

    0
    0
  • And when the two factor lines are at right angles to one another, or 0=42, the product is simply ix" -}-jy"-}-kz", the unit line perpendicular to both.

    0
    0
  • In other words, if the system (considered as rigid) be made to turn about till the first factor coincides with i and the second with j, the product will coincide with k.

    0
    0
  • Also let us assume (a) space to have the same properties in all directions, and make the convention (b) that to change the sign of any one factor changes the sign of a product.

    0
    0
  • If it be perpendicular to the factor lines, (a) shows that it must have simultaneously every such direction.

    0
    0
  • For the reversal of either factor must, by (b), change its sign.

    0
    0
  • But there is nothing to prevent its being represented by a directed line if, as further applications of (a) and (b) show we must do, we take it perpendicular to each of the factor lines.

    0
    0
  • It was first employed in the case of steam by Peabody as a means of estimating the wetness of saturated steam, which is an important factor in testing the performance of an engine.

    0
    0
  • An important factor in the victory of the Romans was their use of Greek fire.

    0
    0
  • His speeches breathe the very spirit of the storm, and they were perhaps the greatest single factor in the development of the events of the time.

    0
    0
  • Another weather factor is the winds, which are extremely regular in their movements.

    0
    0
  • The question of the economic development of the state, and of trade to the Orient, the views of the mercenary labour-contractor and of the philanthropist, the factor of " upper-race " repugnance, the " economic-leech" argument, the " rat-rice-filth-and-opium " argument, have all entered into the problem.

    0
    0
  • Another factor gives it still greater interest for the student of religion, - in it the progress of religious thought can be traced, and the varying elements of the religious life seen in harmony and in conflict.

    0
    0
  • Nevertheless the latter continues because of its presence in the primary sources, but it is no longer a determining factor, since its presupposition - the Messianic kingdom on earth - has been obscured.

    0
    0
  • The Holy Spirit, the determining factor in the religious life, uses the Bible as his means, and calls the intelligence into action.

    0
    0
  • The establishment of Dutch trading-posts on the west coast of Borneo dates from 1604, nine years after the first Dutch fleet, under Houtman, sailed from the Texel to dispute with the Portuguese the possession of the Eastern trade, and in 1608 Samuel Blommaert was appointed Dutch resident, or head factor, in Landak and Sukedana.

    0
    0
  • The factor (P+P) cos 0h sin 0 is called the vIrtual coefficient of the two screws which define the types of the wrench and twist, respectively.

    0
    0
  • For a complete solution of (34) we must of course superpose the free vibration (30); but owing to the factor ehlt the influence of the initial conditions gradually disappears.

    0
    0
  • Analytically, it is convenient to put Q~ equal to eirt multiplied by a complex coefficient; owing to the linearity of the equations the factor e~ni will run through them all, and need not always be exhibited.

    0
    0
  • The n formulae of this type represent a normal mode of free vibration; the individual particles revolve as a rule in elliptic orbits which gradually contract according to the law indicated by the exponential factor.

    0
    0
  • To determine the free oscillations we assume a time factor e~1 the equations then become linear differential equations between the dependent variables of the problem and the independent variables x, or x, y, or x, y, 1 as the case may be.

    0
    0
  • The ratio in which the utmost stress before breaking exceeds the safe working stress is called the factor of safety, and is determined empirically.

    0
    0
  • Then, if possible, B and, C themselves are to be resolved each into rnI factors (counting 1 as a factor), which factors, or multiples of them, shall be not less than t nor greater than 6t; or if B and C contain inconveniently large prime factors, an approximate velocity ratio, found by the method of continued fractions, is to be substituted for B/C as before.

    0
    0
  • - -)Engelso In order that these conditions may obtain, the quantities in the brackets must be zero, since the factor aug is not zero.

    0
    0
  • Whilst community of occupation was an important factor in the original formation of non-tribal castes, the practical exigencies of life have led to considerable laxity in this respect - not least so in the case of Brahmans who have often had to take to callings which would seem altogether incompatible with the proper spiritual functions of their caste.

    0
    0
  • The Saktas, as we have seen, are worshippers of the sakti, or the female principle as a primary factor in the creation and reproduction of the universe.

    0
    0
  • In regard to the necessity of taking into consideration the factor of age in the return of marriage-rates, an example may be here given from the data for England.

    0
    0
  • Next to the proportion of the married to the total marriageable the most important factor connected with the natural increase of the population is the age at which marriage takes place.

    0
    0
  • In the above countries, therefore, abstinence from matrimony may be said to have been a factor of some importance in the decline.

    0
    0
  • Age is a factor still more important than sex in a return intended to serve as an index of mortality.

    0
    0
  • The great difference between the serial rank occupied in the respective lists by Russia, Servia and Galicia, with remarkably high rates of natural growth, as well as that found in the case of most of the other countries in question, shows that this factor is by no means a trustworthy guide in the estimate of hygienic balance.

    0
    0
  • But a far more potent factor in swelling the numbers of the Catholics has been the immigration of the Irish, which began early in the 19th century, but was enormously stimulated by the famine of 1846.

    0
    0
  • The Revival of Learning will be treated as a decisive factor in this process of evolution on a new plan.

    0
    0
  • While the success of the new government was the work of many men and many causes, one cannot resist the conviction that the factor of chief importance was the existence, at the head of the executive department, of such a character as Washington.

    0
    0
  • Peirce for the theories which make chance an objective factor in the process of the Universe.

    0
    0
  • Theoretically, if both type and press were new, little or no preparation should be necessary, but practical experience proves that this need of preparation has not yet been entirely obviated and still remains an important factor.

    0
    0
  • Thus Edom formed a prominent centre for traffic from Arabia and its seats of culture to Egypt, the Philistine towns, Palestine and the Syrian states, and it enjoyed a commercial importance which made it a significant factor in Palestinian history.

    0
    0
  • In other words, the forms of knowledge were the main factor in making objects.

    0
    0
  • For the last hundred years the peasants had been a leading factor in the political life of the land; and perhaps in no other contemporary European state could so self-reliant The a class of yeomen have been found.

    0
    0
  • an entirely incalculable factor had entered into Swedish politics.

    0
    0
  • The oligarchy composed of the great landowners have always been an important factor in the political life of the republic; when President Balmaceda found that he was not a persona grata to this circle he determined to endeavour to govern without their support, and to bring into the administration a set of men who had no traditions and with whom his personality would be all-powerful.

    0
    0
  • Their business was to enforce these rights; from the first they were very unpopular, and their arbitrary behaviour was a factor in bringing about the formation of the Lombard league and the rising against Frederick in 1167.

    0
    0
  • Oysters are more valuable than any other single product of the fisheries, and in at least twenty-five countries are an important factor in the food-supply.

    0
    0
  • Consequently, it is at once a product of, and a main factor in civilization; and is thereby sharply differentiated from the Israelite religion, with whose moral precepts it otherwise coincides so frequently.

    0
    0
  • Thus the creed became a powerful factor in the development of an united Iranian nationality, That a.

    0
    0
  • The decisive factor was of course their military superiority.

    0
    0
  • He appears at this time to have already formed the belief that important achievements as a thinker were possible to him, and at more than one critical period in his career this belief was the decisive factor in determining his conduct.

    0
    0
  • In his writings he dwelt upon important contributions of historical Christianity, and maintained especially that, in continuing the work of the Caesars, the Catholic church had been the most potent factor in civilizing the invading barbarians and in organizing the life of the middle ages.

    0
    0
  • of Spain in his Council of the Indies in 1544, by Luis Hernandez de Biedma, who had accompanied De Soto as His Majesty's factor.

    0
    0
  • Then, too, an increasingly important factor was the competition of Louren90 Marques for the Rand trade.

    0
    0
  • The strategical position of Great Britain in Baluchistan is a very important factor in the problem of maintaining order and good administration in the country.

    0
    0
  • To this result another important factor contributed.

    0
    0
  • Differentiating equation 9 with respect to s we obtain, after dividing by 27 as a common factor, pyds - T cos a ds + Ty s i n ad s =o...

    0
    0
  • In observations upon ripples the factor involving h may usually be omitted, and thus in the case of water (p= I) ?3 g ?2 T = 2 2 4, r (3) simply.

    0
    0
  • An all important factor in this remarkable progress was the introduction by Koch of solid culture media, of the " platemethod," &c., an account of which he published in 1881.

    0
    0
  • There is, however, another all-important factor concerned, viz.

    0
    0
  • With regard to the subject of infection the chief factor is susceptibility; with regard to the bacterium virulence is allimportant.

    0
    0
  • Further, there is the very important factor of acquired susceptibility.

    0
    0
  • We cannot, however, say that these play an important part in immunity, and even if it were so, the essential factor would be the development of the substances which act in this way.

    0
    0
  • This, as already pointed out, depends upon the increase of opsonins, though it is also to be noted that in many infective conditions there is another factor present, namely a leucocytosis, that is, an increase of the leucocytes in the blood, and the defensive powers of the body are thereby increased.

    0
    0
  • Yet while the seed they sowed was taking deep root in France and in Germany, the English deists, the most notable men of their time, were soon forgotten, or at least ceased to be a prominent factor in the intellectual life of the century.

    0
    0
  • None the less it is unquestionable that in the period preceding the Revolution the bulk of French thinkers were ultimately deists in various degrees, and that deism was a most potent factor not only in speculative but also in social and political development.

    0
    0
  • from Hamburg and 84 from Stettin, its situation, so far from being prejudicial to its growth and prosperity, as was formerly often asserted, has been, in fact, the principal determining factor in its rapid rise to the position of the greatest industrial and commercial city on the continent of Europe.

    0
    0
  • The recognition of Germany as a leading factor in the world's counsels had been given, and the people of Berlin could indulge in the task of embellishing the capital in a manner befitting its position.

    0
    0
  • His uncles, John Breckinridge (1797-1841), professor of pastoral theology in the Princeton Theological Seminary in1836-1838and for many years after secretary of the Presbyterian Board of Foreign Missions, and Robert Jefferson Breckinridge (1800-1871), for several years superintendent of public instruction in Kentucky, an important factor in the organization of the public school system of the state, a professor from 18J3 to 1871 in the Danville Presbyterian Theological Seminary at Danville, Kentucky, and the temporary chairman of the national Republican convention of 1864, were both prominent clergymen of the Presbyterian Church.

    0
    0
  • The large number of hostile Indians was also a factor in making the Territory unattractive.

    0
    0
  • It has been a powerful factor in the development of several of the churches already spoken of, especially those of Servia and Montenegro, which are usually very much subject to Russian influences (`PcoQV60povE S or `PWVVWc¢tXoc).

    0
    0
  • It is in this way that weight forms a factor in flight, the wings and the weight of the body reciprocating and mutually assisting and relieving each other.

    0
    0
  • Casimir was to be a leading factor in this combination, and he took advantage of it to procure the election of his son Wladislaus as king of Bohemia.

    0
    0
  • But his personal popularity suffered not the slightest diminution, while his clear, almost intuitive, outlook and his unconquerable faith in the future of his country made him, during those difficult years, a factor of incalculable importance in the public life of Denmark.

    0
    0
  • His aunt, Miss Mary Moody Emerson, a brilliant old maid, an eccentric saint, was a potent factor in his education.

    0
    0
  • - The general type of true grasses is familiar in the cultivated cereals of temperate climates - wheat, barley, rye, oats, and in the smaller plants which make up pastures and meadows and form a principal factor of the turf of natural downs.

    0
    0
  • The Po is the dominating factor in north Italian geography, north Italy practically consisting of the Po basin, with the surrounding slopes of the Alps and Apennines.

    0
    0
  • Until greater knowledge of protoplasm and particularly of proteid has been acquired, there is no scientific room for the suggestion that there is a mysterious factor differentiating living matter from other matter and life from other activities.

    0
    0
  • According to Duhm there are many passages in which metre (see also Amos) may also be a factor in our critical conclusions.

    0
    0
  • Instead of making the motive to choice a factor within the concrete process of volition, he regards it as a cause antecedent to the exercise of a special mental faculty.

    0
    0
  • If, on the other hand, "infection of the germ" is impossible, telegony will not count as a factor in variation, and breeders will no longer be either justified in regarding mares and other female animals as liable to be "corrupted" by ill-assorted unions, or benefited by first having offspring to a high-class, or it may be more vigorous, mate.

    0
    0
  • Rates are even a more important factor in direct taxation than the income tax, and they have given rise to even greater complaints and discussion.

    0
    0
  • But in the result he became the dominant factor in American railway matters.

    0
    0
  • He also set up three courts of justice: a tribunal for petty causes under a factor with native assessors, a court of appeal under the deputy governor and members of council, and a court-martial.

    0
    0
  • Probably the factor which thus diminishes the effective 10° 20' 30' 40' 50° 60' 70' 80' 90° FIG.

    0
    0
  • Hence, if no other agency is invoked, at an epoch say xXmoo years ago, the sun's heat would have been greater than now by the factor 1-+x/3n, where n X 6000° is taken for the sun's present mean temperature.

    0
    0
  • It seems possible that n is not a large number, and if we take x equal, say, to 200, we come to the most recent estimate - the astronomical - of the date of the earth's glacial epoch, when the sun's radiation was certainly not much more than it is now, while this factor would differ materially from unity.

    0
    0
  • Such a rate of change would be quite insensible, and we can affirm that for recent times there is no reason to look for any other factor than contraction; but if we consider the remote past it is a different matter.

    0
    0
  • The line n shows the factor by which the index of refraction of the transmitted vibration is multiplied, and the curve p the intensity of the absorbed vibration for that wave-length.

    0
    0
  • Another disturbing factor in connexion with native affairs was the revolt of the Hottentots and Hereros in German SouthWest Africa (q.v.).

    0
    0
  • In the next place, it is necessary to confine the pressure, at every point of the masonry, to an intensity which will give a sufficient factor of safety against crushing.

    0
    0
  • - Factor of Safety Diagram.

    0
    0
  • It is clear that the material upon which any high masonry dam is founded must also have a large factor of safety against crushing under the greatest load that the dam can impose upon it, and this consideration unfits any site for the construction of a masonry dam where sound rock, or at least a material equal in strength to the strongest shale, cannot be had; even in the case of such a material as shale the foundation must be well below the ground.

    0
    0
  • at much more distant intervals, a proper factor of safety will be allowed.

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  • Its provisions were a most potent factor in assisting the expansion of England's colonial empire and also in the building up of the country's commercial greatness.

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  • Fortunately for the Americans, however, the company in 1824 sent to the Columbia river as its chief factor and governor west of the Rocky Mountains Dr John McLoughlin (1784-1857), who ruled the region with an iron hand, but with a benevolent purpose, for twenty-two years.

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  • The Peabody Institute, founded in 1859 by George Peabody, who was for some years a resident of Baltimore, is an important factor in the promotion of science, literature and the fine arts.

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  • 8 vertical series commencing 9 9 with a number n (other than Io Io I) then n is said to be a factor 12 12 12 12 ..

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  • A number (other than I) which has no factor except itself is called a prime number, or, more briefly, a prime.

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  • If a number is a factor of another number, it is a factor of any multiple of that number.

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  • Thus 12 has 6 for a factor; but 6 is not a prime, one of its factors being 2; and therefore 2 must also be a factor of 12.

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  • Dividing 12 by 2, we get a submultiple 6, which again has a prime 2 as a factor.

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  • The following are the most important properties of numbers in reference to factors: (i) If a number is a factor of another number, it is a factor of any multiple of that number.

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  • (ii) If a number is a factor of two numbers, it is a factor of their sum or (if they are unequal) of their difference.

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  • (The words in brackets are, inserted to avoid the difficulty, at this stage, of saying that every number is a factor of o, though it is of course true that o.

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  • If two numbers have no factor in common (except 1) each is said to be prime to the other.

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  • If we resolve two numbers into their prime factors, we can find their Greatest Common Divisor or Highest Common Factor (written G.C.D.

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  • the greatest number which is a factor of both.

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  • The process depends on (ii) of § 45, in the extended form that, if x is a factor of a and b, it is a factor of pa-qb, where p and q are any integers.

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  • factor; or to be reduced to its lowest terms when it is replaced by such a fraction.

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  • The conversion of the unit may be represented as multiplication by a factor 4 boy apples, so that the operation is 4 apples X 5 boysboy 4 apples r boy Y 5 X I X I boy = 5 X 4 apples= 20 apples.

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  • Similarly, to convert £153 into shillings we must multiply it by a factor 2 £I ' ' so that we get 2£I.

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  • if we regard this converting factor as unity.

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  • The converting factor mentioned under (i) therefore represents a rate; and partition, applied to concrete cases, leads to a rate.

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  • In reference to the use of the sign X with the converting factor, it should be observed that " lb X " symbolizes the replacing of so many times 4 lb by the same number of times 7 lb, while " 4 X " symbolizes the replacing of 4 times something by 7 times that something.

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  • ., and that if we go up to the factor i ?n4n+1 the product of these factors differs from the true value of the number by less than gngn -{-1 In certain cases two or more factors can be combined so as to produce an expression of the form i where k is an integer.

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  • The citizens of London welcomed him, but he was not secure of his success till by a swift swoop on Winchester he obtained possession of the royal treasurean all-important factor in a crisis, as Henry I.

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  • The question of election to bishoprics and abbacies went back to the stage which it had reached in the time of Henry I.; the choice was made in canonical form, by the chapters or the monasteries, but the kings recommendation was a primary factor in that choice.

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  • The individual character of the reigning king was still the main factor in political history, Edwa,ilII.

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  • the king once more became an important factor in English politics.

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  • But the English Liberals were already a little weary of allies who were quarrelling among themselves, and whose disputes were introducing a new factor into politics.

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  • Thirdly, for the double tangents; the points of contact of these are obtained as the intersections of the curve by a curve II = o, which has not as yet been geometrically defined, but which is found analytically to be of the order (m-2) (m 2 -9); the number of intersections is thus = m(rn - 2) (m 2 - 9); but if the given curve has a node then there is a diminution =4(m2 - m-6), and if it has a cusp then there is a diminution =6(m2 - m-6), where, however, it is to be noticed that the factor (m2 - m-6) is in the case of a curve having only a node or only a cusp the number of the tangents which can be drawn from the node or cusp to the curve, and is used as denoting the number of these tangents, and ceases to be the correct expression if the number of nodes and cusps is greater than unity.

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  • a property independent of the particular axes of co-ordinates used in the representation of the curve by its equation; for instance, the curve may have a node, and in order to this, a relation, say A = o, must exist between the coefficients of the equation; supposing the axes of co-ordinates altered, so that the equation becomes u' = o, and writing A' = o for the relation between the new coefficients, then the relations A = o, A' = o, as two different expressions of the same geometrical property, must each of them imply the other; this can only be the case when A, A' are functions differing only by a constant factor, or say, when A is an invariant of u.

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  • Exact analysis is difficult and tedious, and consequently the laboratory methods are not employed in technology, where time is an important factor and moderate accuracy is all that is necessary.

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  • Associative tendency, individual or inherited, has since been the favourite constructive factor of human experience in Empirical Philosophy.

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  • This factor is not prominent in Locke's Essay.

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  • And the'tendency; to associate is there presented, not as the fundamental factor of human knowledge, but as a chief cause of human error.

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  • An important factor to be mentioned in this connexion is the change in the distribution of the acreage under wheat, consequent upon falling prices.

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  • Thus we have a new zoological factor in the history of the moral sentiments; which, though in no way opposed to the older psychological theory of their formation through coalescence of more primitive feelings, must yet be conceived as controlling and modifying the effects of the law of association by preventing the formation of sentiments other than those tending to the preservation of human life.

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  • By what precedes it appears that there exists a function of the n 2 elements, linear as regards the terms of each column (or say, for shortness, linear as to each column), and such that only the sign is altered when any two columns are interchanged; these properties completely determine the function, except as to a common factor which may multiply all the terms. If, to get rid of this arbitrary common factor, we assume that the product of the elements in the dexter diagonal has the coefficient + 1, we have a complete definition of the determinant, and it is interesting to show how from these properties, assumed for the definition of the determinant, it at once appears that the determinant is a function serving for the solution of a system of linear equations.

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  • a, b, c a' b' c', a"b" c", b", that is, every term which does not vanish contains as a factor the abc-determinant last written down; the sum of all other factors a0'y" is the a/37-determinant of the formula; and the final result then is, that the determinant on the left-hand side is equal to the product on the right-hand side of the formula.

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  • Moreover, representing the remaining three lines by a" b" c" d" e" b /r c a, d N, e"' a " c 'N d"N err" it is further seen that the factor which multiplies the determinant formed with any two columns of the first set is the determinant of the third order formed with the complementary three columns of the second set; and it thus appears that the determinant of the fifth order is a sum of all the products of the form ' a b c" d" e" a, b"c"'dN, ear the sign being in each case such that the sign of the term .c"d"'e" obtained from the diagonal elements of the component determinants may be the actual sign of this term in the determinant of the fifth order; for the product written down the sign is obviously +.

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  • The other factor in Venizelos' defeat was the blind over-confidence of his partizans; many Venizelists in Athens and the larger cities neglected to vote.

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  • The consciousness of being saved in this sense is now transmitted and mediated by the Christian church, but in the case of Jesus, its originator, it was an entirely new and original factor in the process of religious development, and in so far, like every new and higher stage of being, a supernatural revelation.

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  • A very important factor in the movement of the population is the large over-sea emigration, mostly to the United States of America, which has grown very much during the last quarter of the 19th century, and which shows a tendency to become still larger.

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  • The crying abuses of the old rgime, an insignificant factor at the outset, soon combined with the widespread agrarian distress, due to the unjust distribution of land, the disastrous exploitation of the soil, the actions of the government, and the severe winter of 1788.

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  • Bonaparte thus gained the good opinion of peace-loving Frenchmen; he partitioned Venetian territory with Austria, contrary to French interests but conformably with his own in Italy, and henceforward was the decisive factor in French and European policy, like Caesar or Pompey of old.

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  • The enormous water-power of the Falls of St Anthony, yielding about 40,000 h.p., has been the principal factor in making Minneapolis a great manufacturing centre.

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  • And, therefore, finding on reflection any particular concrete factor contingent, we abstract the position from that which occupies it, and so reach the speculative notion of the pure Ego.

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  • Now Fresnel's formulae were obtained by assuming that the incident, reflected and refracted vibrations are in the same or opposite phases at the interface of the media, and since there is no real factor that converts cos T into cos (T+p), he inferred that the occurrence of imaginary expressions for the coefficients of vibration denotes a change of phase other than 7r, this being represented by a change of sign.

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  • If this be so, it is clear that the factor A / - 1 denotes a change of phase of 42, since this twice repeated converts cos T into cos (T+ir) = - cos T, and hence that the factor a+b A l - I represents a change of phase of tan1 (b/a).

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  • There can be no doubt, in spite of the apology for his action published by Guizot in his memoirs, that Louis Philippe made a deliberate attempt to overreach the British government; and, if the attempt issued in disaster to himself, this was due, not to the failure of his statecraft so much as to his neglect of the obvious factor of human nature.

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  • This theory must be taken into consideration as a factor in accounting for the persistent hold which even at the present day astrology still maintains on many minds.

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  • Jigg, or Jig, is a very important factor, as will be seen hereafter.

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  • With it also moisture is a great factor in its productivity.

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  • The spiritual enthusiasm of Lady Conway was a considerable factor in some of More's speculations, none the less that she at length joined the Quakers.

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  • The individual components required weaker curvatures and permitted of being more correctly manufactured, and, more particularly, the advantage of reduced aberrations was the predominant factor.

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  • On the other hand, a study of the plant-life of past ages tends to the conviction that too much stress may be laid on the imperfection of the geological record as a factor in the interpretation of palaeontological data.

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  • When we apply predicates to the sense-manifold regarded in isolation, we make that which is only a factor in the experience of objects into a separate, independent object, and use our predicates transcendently.

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  • Pete was going to be the deciding factor and all eyes turned to him.

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  • Dean knew Cynthia desperately wanted to photograph the display but both knew time was a factor if they were to visit the mine before the Dawkinses were free of their legal meetings to make the trip themselves.

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  • She didn't factor Gabriel's transition into Death into the equation.

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