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hence

hence

hence Sentence Examples

  • The roads were covered in ice; hence it was not safe to drive.

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  • The customer was displeased with her meal, hence the chef prepared a replacement.

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  • Hence the Mediterranean region is characteristically one of winter rains, the distinctive feature becoming less sharply defined from south to north, and the amount of total annual fall increasing in the same direction.

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  • Any portion of the underground rhizome when broken off is capable of producing a new plant; hence the difficulty of eradicating them when once established.

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  • ALF, from 1986 to 1990, featured a puppetry alien (or Alien Life Form, hence the acroynm), and from 1996 to 2001, 3rd Rock From the Sun featured a group of extra-terrestrials attempting to pass themselves off as a typical suburban family.

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  • Hence, "managing" the traffic coming through will not succeed in meeting these objectives.

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  • The cups are placed symmetrically on the end of the arms, and it is easy to see that the wind always has the hollow of one cup presented to it; the back of the cup on the opposite end of the cross also faces the wind, but the pressure on it is naturally less, and hence a continual rotation is produced; each cup in turn as it comes round providing the necessary force.

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  • Hence when useful work can be obtained from a system by simply connecting visible portions of it by a train of mechanism, such energy is more readily recognized than is that which would compel us to control the behaviour of molecules before we could transform it into useful work.

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  • Hence according as the trains of oscillations are long or short so is the sound heard in the telephone, and these sounds can be arranged on the Morse code into alphabetic audible signals.

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  • It is not practicable to connect each subscriber directly to all the others, hence a system of exchanges has been adopted.

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  • We mutually agreed the subject of our tests was verboten until we were able to get together again in three weeks hence.

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  • Hence there are advantages in employing a very loose coupling.

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  • If, however, the antenna is inductively or directly coupled to a condenser circuit of large capacity then the amount of energy which can be stored up before discharge takes place is very much greater, and hence can be drawn upon to create prolonged or slightly damped trains of waves.

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  • The roots like all other parts of plants contain protoplasm or living material, which cannot carry on its functions unless it is supplied with an adequate amount of oxygen: hence the necessity for the continuous circulation of fresh air through the soil.

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  • Hence it still seems best to assume some unknown Aramaic form equivalent to 7rapaicX y as, and then to take the latter in the sense of comfort or encouragement.

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  • Hence it is not surprising that, in those more subtle forms in which energy cannot be readily or completely converted into work, the universality of the principle of energy, its conservation, as regards amount, should for a long while have escaped recognition after it had become familiar in pure dynamics.

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  • The smoother we make the pulley the more nearly does the amount of useful work which the weight is capable of doing approach ro foot-pounds, and if we take into account the work done against the friction of the pulley, we may say that the work done by the descending weight is ro foot-pounds, and hence when the weight is in its elevated position we have at disposal r o foot-pounds more energy than when it is in the lower position.

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  • Hence the work done in raising the mass will be represented by mg v 2 /2g, that is, Zmv 2 ergs.

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  • Hence he inferred that the amount of heat given up to the condenser of an engine when the engine is doing work must be less than when the same amount of steam is blown through the engine without doing any work.

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  • Him succeeded, not only in showing that such a difference exists, but in measuring it, and hence determining a tolerably approximate value of the mechanical equivalent of heat.

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  • By continuing this process every unit of mass which enters B will carry with it more energy than each unit which leaves B, and hence the temperature of the gas in B will be raised and that of the gas in A lowered, while no heat is lost and no energy expended; so that by the application of intelligence alone a portion of gas of uniform pressure and temperature may be sifted into two parts, in which both the temperature and the pressure are different, and from which, therefore, work can be obtained at the expense of heat.

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  • Hence the Code allowed a proviso to be inserted in the marriage contract, that the wife should not be seized for her husband's pre-nuptial debts; but enacted that then he was not responsible for her pre-nuptial debts, and, in any case, that both together were responsible for all debts contracted after marriage..

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  • 1 It is evident from equation (13) that the angle of immersion depends solely on the speed of the ship; hence in laying a cable on an irregular bottom it is of great importance that the speed should be sufficiently low.

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  • The form of Morse recorder almost universally used in Europe makes the record in ink- ink, and hence is sometimes called the "ink-writer.".

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  • To each group is connected a set of apparatus; hence during a complete revolution of the arms a pair of instruments (at station A and station B) will be in communication four times, and the intervals during which any particular set of instruments at the two stations are not in connexion with each other become much smaller than in the case of fig.

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  • Hence for sending both a dot and a dash, reverse currents of short duration are sent through the line, but the interval between the reversal is three times as great for the dash as for the dot.

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  • The process of reflection in the case of a wave motion involves the condition that the wave-length shall be small compared with the dimensions of the mirror, and hence the attempt to reflect and converge electric waves loon ft.

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  • Hence we frequently meet with forms which had passed out of the language that was spoken at the time they were engraved, side by side with their equivalents in that language.

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  • This alteration of charge caused a corresponding change in the mutual attraction of the plates of the condenser; hence the flexible plate was made to copy the vibrations of the diaphragm of the transmitter.

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  • The vast number of microphonic contacts present give rise to very strong electrical undulations, and hence to a loud sound.

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  • The resistance of the microphone can thus be made a large fraction of the total resistance of the circuit in which it is placed; hence by using considerable currents, small variations in its resistance can be made to induce somewhat powerful currents in the line wire.

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  • Hence this operator, when signalled in the ordinary way, can put any one of these subscribers in connexion with any subscriber whatever, without the necessity of calling upon another operator to make connexions.

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  • The central range here approaches much nearer to the sea, and hence, with few exceptions, the rivers that flow from it have short courses and are of comparatively little importance.

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  • Below this the watershed of the Apennines is too near to the sea on that side to allow the formation of any large streams. Hence the rivers that flow in the opposite direction into the Adriatic and the Gulf of Taranto have much longer courses, though all partake of the character of mountain torrents, rushing down with great violence in winter and after storms, but dwindling in the summer into scanty streams, which hold a winding and sluggish course through the great plains of Apulia.

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  • Hence this part of the country has a cold winter climate, so that while the mean summer temperature of Milan is higher than that of Sassari, and equal to that of Naples, and the extremes reached at Milan and Bologna are a good deal higher than those of Naples, the mean winter temperature of Turin is actually lower than that of Copenhagen.

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  • Hence his hesitations and vacillations, which Cavour steadily worked to overcome.

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  • Hence a tacit understanding between Bismarck and Austria that the latter should profit by Italian resentment against France to draw Italy into the orbit of the Austro-German alliance.

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  • annus, year; hence annales, sc. libri, annual records), the name given to a class of writers on Roman history, the period of whose literary activity lasted from the time of the Second Punic War to that of Sulla.

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  • Hence the enormous effect of Cranmer's recovery at the final scene.

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  • Hence, early empiricism makes ethics simply a calculus of pleasures ("hedonism").

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  • Hence it naturally has a moral argument in reserve.

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  • Hence F.

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  • Hence there are tendencies even in Plato to build up the ideal world in sharp contrast to the actual world - to the half interpenetrated or half tamed world of matter.

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  • But the Christian bias is sure to make theologians, who borrow a doctrine of the Absolute, interpret it in a Christian sense; hence we may consider it something of an accident that even an Augustine fails exactly to put the argument in form.

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  • Hence both polyp and medusa present characters for classification, and a given species, genus or other taxonomic category may be defined by polyp-characters or medusa-characters or by both combined.

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  • Hence it is necessary to distin guishbetween,first,the"zooids," FIG.

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  • Hence, in a colony of gymnoblastic hydroids, the oldest polyp of each system, that is to say, of the main stem or of a branch, is the topmost polyp; II  ?a ` FIG.

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  • The polyp may then form a second bud, which becomes the starting point of a new system, the beginning, that is, of a new branch; and even a third bud, starting yet another system, may be produced from the same polyp. Hence the colonies of Calyptoblastea may be com plexly branched, and the bud ding may be biserial through out, uniserial throughout, or partly one, partly the other.

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  • Hence it is convenient to consider the morphology of the medusa from these two aspects.

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  • The sub-umbrella invariably shows a velum as an inwardly projecting ridge or rim at its margin, within the circle .of tentacles; hence the medusae of this sub-class are termed craspedote.

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  • The sense-cells form, in the first place, a diffuse system of scattered sensory cells, as in the polyp, developed chiefly on the manubrium, the tentacles and the margin of the umbrella, where they form a sensory ciliated epithelium covering the nerve-centres; in the second place, the sense-cells are concentrated to form definite sense-organs, situated always at the margin of the umbrella, hence often termed " marginal bodies."

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  • In Hydromedusae the sense-organs are always exposed at the umbrellar margin (hence Gymnophthalmata), while in Scyphomedusae they are covered over by flaps of the umbrellar margin (hence Steganophthalmata).

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  • In many Leptomedusae the otocysts are very small, inconspicuous and embedded completely in the tissues; hence they may be easily overlooked in badly-preserved material, and perhaps are present in many cases where they :: r simplest condition of the otocyst is a freely projecting club, a so-called (figs.

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  • Hence the gonads are found on the manubrium in Anthomedusae generally; on the base of the manubrium, or under the gastral pouches, or in both these situations (Octorchidae), or under the radial canals, in Trachomedusae; under the gastral pouches or radial canals, in Narcomedusae.

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  • Hence the budding of medusae exemplifies very clearly a common phenomenon in development, a phylogenetic series of events completely dislocated in the ontogenetic time-sequence.

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  • Hence the alternation is of the type termed metagenesis.

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  • The Trachylinae, on the other hand, are above all oceanic forms, and have no polyp-stage, and hence there is typically no alternation in their life-cycle.

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  • Hence the Trachylinae are termed " hypogenetic " medusae to contrast them with the metagenetic Leptolinae.

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  • Hence only the genus Hydra can be considered as truly representing the order Eleutheroblastea.

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  • Hence the systematic arrangement that follows must be considered purely provisional.

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  • Hence the principal axis of the future medusa corresponds, not to the longitudinal axis of the planula, but to a transverse axis.

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  • Hence the cavity of the air-sack is equivalent to a sub-umbral cavity in which no manubrium is formed, and the pore or orifice of invagination would represent the margin of the umbrella.

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  • The siphons have been compared to the manubrium of a medusa-individual, or to polyps, and hence are sometimes termed gastrozoids.

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  • Hence Huxley's view is not so different from those held by other authors as it seems to be at first sight.

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  • The coast-line sweeps hence south-eastward to the finer promontory of Flamborough Head, beyond which is the watering-place of Bridlington.

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  • iiXrt; hence the name " Hylozoists "), which is at the same time the universal support of things.

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  • Experience forbids our excluding organic activity from natural causes, also our excluding intelligence from purposeful (zwecktdtigen) causes; hence experience forbids our defining the fundamental force or first cause out of which living creatures arose.'

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  • Hence the practice, immediately after Nicaea I., of superadding banishment by the emperor to synodical condemnation.

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  • Hence came the ' jurisdiction of the ordinary in intestacy, for the peace of the soul of the departed.

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  • Hence, even in countries where the Roman Church is established, such as Belgium, Italy, the Catholic states of Germany and cantons of Switzerland, most of the Latin republics of America, and the province of Quebec, and a fortiori where this Church is not established, there is now no discipline over the laity, except penitential, and no jurisdiction exercised in civil suits, except possibly the matrimonial questions of princes (of which there was an example in the case of the reigning prince of Monaco).

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  • Delfzyl, which was formerly an important fortress for the protection of the ancient sluices on the little river Delf (hence its name), has greatly benefited by the construction of the Ems (Eems) shipcanal connecting it with Groningen, and has a good harbour with a considerable import trade in wood.

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  • The Meditations were written, it is evident, as occasion offered - in the midst of public business, and on the eve of battles on which the fate of the empire depended - hence their fragmentary appearance, but hence also much of their practical value and even of their charm.

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  • PHARMACY, a term which in the original Greek form signified the use of any kind of drug (46p,uaKov), potion or spell, and hence also poison and witchcraft.

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  • In 105, Caepio suffered a crushing defeat from the Cimbri at Arausio (Orange) on the Rhone, which was looked upon as a punishment for his sacrilege; hence the proverb Aurum Tolosanum habet, of an act involving disastrous consequences.

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  • Hence such tracheae are only laid down in organs whose growth in length has ceased.

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  • The presence of too much sugar in solution in the sap of the cell inhibits the activity of the chloroplasts; hence the necessity for its removal.

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  • All soils which are physically dry are also physiologically dry; and hence only the physiological dryness or wetness of soils need be considered in ecology.

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  • Hence, in any cosmopolitan treatment of vegetation, it is necessary to consider the groups of plant communities from the standpoint of the climatic or geographical district in which they occur; and this indeed is consistently done by Schimper.

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  • Hygrophytes.Living, as these plants do, under medium conditions as regards soil, moisture and climate, they exhibit no characters which are markedly xerophytic or hydrophytic. Hence, such plants are frequently termed mesophytes.

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  • Again, acidic humus does not form in calcareous soils; and hence one does not expect to find plants characteristic of acidic peat or humus on calcareous soils.

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  • All organs performing the same function and showing similar adaptations are said to be analogous or homoplastic, whatever their morphological nature may be; hence organs are sometimes both homologous and analogous, sometimes only analogous.

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  • Factors in Evo/ution.Evolution in the race involves progressive differentiation in the individual; hence the causes of evolution and of differentiation must be the same.

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  • The territorial divisions and subdivisions often survive the conditions which led to their origin; hence the study of political geography is allied to history as closely as the study of physical geography is allied to geology, and for the same reason.

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  • The symptoms of nerve-poisoning are due to the carbolic acid (or its salts) which circulate in the blood after all the sulphates in the blood have been used up in the formation of sulpho-carbolates (hence, during administration of carbolic acid, the urine should frequently be tested for the presence of free sulphates; as long as these occur in the urine, they are present in the blood and there is no danger).

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  • The former prohibition made it impossible far the unfortunate people to sell their goods which hence fell to the Inquisition.

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  • The red blood-corpuscles are invariably oval disks, with a central nucleus which causes a slight swelling; hence they are oval and biconvex.

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  • (d) Complex Destructive: If A is true, B is true; if C is true, D is true; but B and D are not both true; hence A and C are not both true.

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  • Hence such imperatives have a tendency to dwindle into optatives.

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  • Hence arises Midrash, exposition, from darash to "investigate" a scriptural passage.

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  • (= five nautical miles) an hour; hence the common use of knot as equivalent to a nautical mile.

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  • Deposits of sulphur are frequently formed by the decomposition of hydrogen sulphide, on exposure to the atmosphere: hence natural sulphureous waters, especially hot springs, readily deposit sulphur.

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  • Hence we find that beetles of some kind can hold their own anywhere on the earth's surface.

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  • Hence it is impossible to form a satisfactory linear series.

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  • 18) have the prosternal process just mentioned, capable of movement in and out of the mesosternal cavity, the beetles being thus enabled to leap into the air, hence their popular name of "click-beetles" or "skip-jacks."

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  • - The families of beetles included by Kolbe in this group are distinguished by the possession of six malpighian tubes, and a great reduction in one or two of the tarsal segments, so that there seem to be only four or three segments in each foot; hence the names Tetramera and Trimera formerly applied to them.

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  • Hence their attachment to Peisistratus, the "man of the people," who called upon them to sweep away the last barriers which separated rich and poor, nobles and commoners, city and countryside.

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  • Hence he appears to have encouraged agriculture by abating the tax on small farms, and even by assisting them with money and stock.

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  • So intensely aristocratic (hence his nickname 6 AoXoiSopos, "he who rails at the people") was his temperament that he declined to exercise the regal-hieratic office of 1 3avLAeus which was hereditary in his family, and presented it to his brother.

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  • Hence, although wages are painfully low, the cost of production to the manufacturer is relatively high; and it is still further increased by the cost of the raw materials, by the heavy rates of transport owing to the distance from the sea, by the dearness of capital and by the scarcity of fuel.

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  • Hence family quarrels became very frequent.

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  • Like Alexander in the last period of his reign, Nicholas considered himself the supreme guardian of European order, and was ever on the watch to oppose revolution in all its forms. Hence he was generally in strained relations with France, especially in the time of Louis Philippe, who became king not by the grace of God but by the will of the people.

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  • Hence he attacked Motya and Panormus and the rest of Punic Sicily.

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  • Hence losses in one quarter must be compensated by gains in another - a process which the law, regarding only the gains, renders very difficult.

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  • Except in hard rock, the top width of a cutting, and therefore the amount of material to be excavated, increases rapidly with the depth; hence if a cutting exceeds a certain depth, which varies with the particular circumstances, it may be more economical, instead of forming the sides at the slope at which the material of which they are composed will stand, to make them nearly vertical and support the soil with a retaining wall, or to bore a tunnel.

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  • At this point trains of wagons similarly destined for different places will be arriving from other lines, and hence the necessity will arise of collecting together from all the trains all the wagons which are travelling to the same place.

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  • Hence at A the trucks from a, b, c and d must not only be sorted according as they have to travel along A B, A C, or A D, but also must be marshalled into trains in the order of the stations along those lines.

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  • Hence if all the energy supplied to the train is utilized at one axle there is the fundamental relation RV (I) Continuing the above arithmetical illustration, if the wheels to the axle of which the torque is applied are 4 ft.

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  • Hence Engine resistance, R e = 80 X20 = 1600 lb Vehicle resistance, R v =200 X8.5 = 1700 „ Train resistance, R = 3300 „ The speed, 40 m.

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  • Hence if a train is travelling up the gradient at a speed of V ft.

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  • Hence assuming the mechanical efficiency of the engine to be and substituting !

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  • Hence, if p is the maximum value of the mean effective pressure corresponding to about 85% of the boiler pressure,, uW = pd 2 le /D (26) is an expression giving a relation between the total weight on the coupled wheels, their diameters and the size of the cylinder.

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  • per hour, the tractive force falls to 7400 lb, and this cannot be increased except by increasing the rate of combustion (neglecting any small changes due to a change in the efficiency 7 Knowing the magnitude of R, the draw-bar pull, and hence the weight of vehicle the engine can haul at this speed, can be estimated if the resistances are known.

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  • Hence for a level road the above load could be hauled at 60 m.

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  • The inclusive speed over a long journey is of course a different thing from the average running speed, on account of the time consumed in intermediate stops; the fewer the stops the more easily is the inclusive speed increased, - hence the advantage of the non-stop runs of 150 and zoo m.

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  • Hence less dead weight has to behauled for each ton of paying load.

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  • Homogenesis means simply that such organism comes into existence directly from a parent organism of the same race, and hence of the same species, sub-species, genus and so forth.

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  • The sacrifice of desacralization is, however, also found; hence MM.

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  • The god was originally a stranger, taken into the kin by a rite of blood brotherhood, and this constitutes the dark point of the theory; for Robertson Smith regards the blood bond as relatively late; hence we do not see how the god became associated with the kin.

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  • Thanksgiving, blessing and offering were co-ordinate terms. Hence the Talmudic rule, "A man shall not taste anything before blessing it" (Tosephta Berachoth, c. 4), and hence St Paul's words, "He that eateth, eateth unto the Lord, for he giveth God thanks" (Rom.

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  • 3 Hence the `Ashtaroth or offspring of flocks in Deut.

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  • The trunk line constructed by the Franco-Belgian syndicate connects Lu-Kou-ch'iao, the original terminus, with Hankow - hence the name Lu-Han by which this trunk line is generally spoken of, Lu being short for Lu-Kou-ch'iao and Han for Hankow.

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  • It lies on the main line between Bologna and Milan, and is connected by branch lines with Guastalla and Sassuolo (hence a line to Modena).

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  • At Eleusis, Demeter was venerated as the introducer of all the blessings which agriculture brings in its train - fixed dwelling-places, civil order, marriage and a peaceful life; hence her name Thesmophoros, " the bringer of law and order," and the festival Thesmophoria.

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  • Demeter, clad in black (hence µEXaiva) in token of mourning for her daughter and wrath with Poseidon, retired into a cave.

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  • Hence these measures became the issues on which the first American parties were formed.

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  • Hence its name Curtea, " the court."

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  • Earlier still the sun must have reached to where Neptune now revolves on the confines of our system, but the mass of the sun could not undergo an expansion so prodigious without being made vastly more rarefied than at present, and hence we are led by this mode of reasoning to the conception of the primaeval nebula from which our system has originated.

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  • It is connected by the Zederik and Merwede canals with Amsterdam, and steamers ply hence in every direction.

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  • Hence it is possible, by a comprehensive comparative study of Eastern peoples, in both ancient and modern times, to supplement and illustrate within certain limits our direct knowledge of the early Jewish people, and thus to understand more clearly those characteristics which were [OLD Testament History peculiar to them, in relation to those which they shared with other Oriental peoples.

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  • Hence it is noteworthy that the late editor of Judges has given the first place to Othniel, a Kenizzite, and therefore of Edomite affinity, though subsequently reckoned as a Judaean (Judg i.

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  • Hence the various reconstructions of the earlier history, with all their inherent weaknesses.

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  • Hence, in the absence of more complete external evidence one is obliged to recognize the limitations of Old Testament historical criticism, even though this recognition means that positive reconstructions are more precarious than negative conclusions.

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  • Hence, though this procedure made the Jews intensely obnoxious to the peoples, they became all the more necessary to the rulers.

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  • Hence the Jews are in no sense internationally organized.

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  • White soon returned to England for supplies, and having been detained there until 1591 he found upon his return no trace of the colony except the word " Croatan " carved on a tree; hence the colony was supposed to have gone away with some friendly Indians, possibly the Hatteras tribe, and proof of the assumption that these whites mingled with Indians is sought in the presence in Robeson county of a mixed people with Indian habits and occasional English names, calling themselves Croatans.

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  • barcaruola, a boat-song), properly a musical term for the songs sung by the Venetian gondoliers, and hence for an instrumental or vocal composition, generally in 6-8 time, written in imitation of their characteristic rhythm.

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  • Hence the head of the Babylonian Jews was the exilarch (in Aramaic Resh Galutha) .

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  • Hence the speculative utterances of mysticism are always more or less pantheistic in character.

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  • Hence " negative theology," which ascends from the creature to God by dropping one after another every determinate predicate, leads us nearest to the: truth.

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  • Hence where reason is discarded by the mystic it is merely reason overleaping itself; it occurs at the end and not at the beginning of his speculations.

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  • The intellect combines what the understanding separates; hence Nicolas teaches the principle of the coincidentia contradictoriorum.

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  • When the fungus is grown elsewhere than in the ants' nest it produces gonidia instead of the white masses on which the ants feed, hence it seems that these masses are indeed produced as the result of some unknown cultural process.

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  • Shelving gradually upward from the low flats of Siberia the general continental level rises to a great central waterparting, or divide, which stretches from the Black Sea through the Elburz and the Hindu Kush to the Tian-shan mountains in the Pamir region, and hence to Bering Strait on the extreme north-east.

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  • Hence the study of the mountain ranges of a continent is, for a proper apprehension of its physical conditions and characteristics, as essential as the examination of its extent and position in relation to the equator and poles, and the configuration of its coasts.

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  • causes an accumulation of air over the cold area, The diminution of barometric pressure which takes place all over Asia during the summer months, and the increase in the winter, are hence, no doubt, the results of the alternate heating and cooling of the air over the continent.

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  • The heated body of air carried from the Indian Ocean over southern Asia by the south-west monsoon comes up highly charged with watery vapour, and hence in a condition to release a large body of water as rain upon the land, whenever it is brought into circumstances which reduce its temperature in a notable degree.

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  • Hence, too, Asiatic history has large and simple outlines.

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  • Hence there is clearly a deep-seated difference between the religious feelings of the two continents.

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  • Confucianism is an ethical rather than a religious system, and hence was able to co-exist, though not on very friendly terms, with Buddhism, which reached China about the 1st century A.D.

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  • Owing to its position, the Persian state, when it from time to time became a conquering empire, overlapped Asia Minor, Babylon and India, and hence acted as an intermediary for transmitting art and ideas, sending for instance Greek sculpture to India and the cult of Mithra to western Europe.

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  • It has been men, tioned that in the Nereids a sexual form occurs which differs structurally from the asexual worms, and was originally placed in a separate genus, Heteronereis; hence the name "Heteronereid" for the sexual worm.

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  • Hence the term is applied to states in which the supreme authority is vested in a single person, the monarch, who in his own right is the permanent head of the state.

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  • Hence he must always be rigorously checked where other authorities exist arid used with caution where he is our sole informant.

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  • gradualis, of or belonging to steps or degrees; gradus, step), advancing or taking place by degrees or step by step; hence used of a slow progress or a gentle declivity or slope, opposed to steep or precipitous.

    1
    0
  • Hence we perceive two currents of tendency in the Getica.

    1
    0
  • Mahratta elders hence uttered predictions of military disaster which were in the end more than fulfilled.

    1
    0
  • The Sicilians claimed to be the first on whom Demeter had bestowed the gift of corn, and hence they honoured the two goddesses with many festivals.

    1
    0
  • Hence the nations of antiquity ascribed to it a divine origin; Brahma in Hindustan, Isis in Egypt, Demeter in Greece, and Ceres in Italy, were its founders.

    1
    0
  • Ireland, she possessed six times as many sheep. The cattle population of England alone slightly exceeded that of Ireland, but cattle are more at home on the broad plains of England than amongst the hills and mountains of Wales and Scotland, which are suitable for sheep. Hence, whilst in England sheep were not three times as numerous as cattle, in Wales they were nearly five times, and in Scotland nearly six times as many.

    1
    0
  • The object of this measure is to replace the 1 In 1903 two of the principal sources of supply of mutton shipped in excess of their exportable surplus, for which they suffered severely in 1904 - hence the somewhat irregular movements after 1903.

    1
    0
  • Hence it is that the amount of food consumed to produce a given amount of increase in live weight, as well as that required for the sustentation of a given live weight for a given time, should - provided the food be not abnormally deficient in nitrogenous substance - be characteristically dependent on its supplies of digestible and available non-nitrogenous constituents.

    1
    0
  • Hence, as current fattening food-stuffs go - assuming, of course, that they are not abnormally low in the nitrogenous constituents - they are, as foods, more valuable in proportion to their richness in digestible and available nonnitrogenous than to that of their nitrogenous constituents.

    1
    0
  • Mill's work at the India House, which was henceforth his livelihood, did, not come before the public; hence some have scouted his political writings as the work of an abstract philosopher, entirely unacquainted with affairs.

    1
    0
  • Hence ius Quiritium in Roman law is full Roman citizenship. Subsequently the term lost the military associations due to the original conception of the people as a body of warriors, and was applied (sometimes in a deprecatory sense, cf.

    1
    0
  • The heart lies in front of, instead of to the side of, the attachment of the ctenidium - hence Opisthobranchia as opposed to " Prosobranchia," which correspond to the Streptoneura.

    1
    0
  • Even in the christology, where he is treating of the historical Christ, he entertains critical considerations; hence it is not altogether without reason that in after times he was suspected of "Ebionitic" views of the Person of Christ.

    1
    0
  • He was one of the plenipotentiaries who concluded peace with Lubeck at the congress of Hamburg, and subsequently took an active part in the great work of national reconstruction necessitated by the Reformation, acting as mediator between the Danish and the German parties who were contesting for 2 Hence another of the names - " hurricane-bird " - by which this species is occasionally known.

    1
    0
  • They were, in fact, essentially inadaptive creatures, and hence rapidly died out.

    1
    0
  • Hence the malaise both of mind and body.

    1
    0
  • Hence arise various mistaken beliefs, such as the belief in revelation which not only injures the moral As feudalism passed from its age of supremacy into its age of decline, its customs tended to crystallize into fixed forms.

    1
    0
  • Hence, when the rupture occurred, the fleet was already at its stations in the North Sea, and Adml.

    1
    0
  • This good consists in the realization of personal character; hence the final good, i.e.

    1
    0
  • Hence the treatise of Erastus.

    1
    0
  • dpoE, a pickaxe, hence applied to the animal), the scientific name of a group of African antelopes of relatively large size with long straight or scimitar-shaped horns, which are present in both sexes, and long tufted tails.

    1
    0
  • The platy minerals have also a perfect cleavage parallel to their flat surfaces, while the fibrous species often have two or more cleavages following their long axes; hence a schistose rock may split not only by separation of the mineral plates from one another but also by cleavage of the parallel minerals through their substance.

    1
    0
  • The difference between schists and gneisses is mainly that the latter have less highly developed foliation; they also, as a rule, are more coarse grained, and contain far more quartz and felspar, two minerals which rarely assume platy or acicular forms, and hence do not lead to the production of a fissile character in the rocks in which they are important constituents.

    1
    0
  • From these facts it appears that the anterior three divisions of the head differ strongly from the posterior three, which greatly resemble thoracic segments; hence it has been thought possible that the anterior divisions may represent a primitive head, to which three segments and their leg-like appendages were subsequently added to form the head as it now exists.

    1
    0
  • Hence, as has been pointed out by D.

    1
    0
  • Hence the opinion arose that histolysis is a process of phagocytosis.

    1
    0
  • Hence we are inclined to look on the imaginal disks as cellular areas that possess in a latent condition the powers of growth and development that exist in the embryo, powers that only become evident in certain special conditions of the organism.

    1
    0
  • Many of the species are in process of extinction, owing to the extensive changes tha.t are taking place in the natural conditions of the world by the extension of human population and of cultivation, and by the destruction of forests; hence it is probable that a considerable proportion of the species at present existing will disappear from the face of the earth before we have discovered or preserved any specimens of them.

    1
    0
  • Hence the grouping of the orders of winged Hexapoda into the divisions Exopterygota and Endopterygota, as suggested by D.

    1
    0
  • Hence his work, written in French, contains a far greater amount of original matter; and his personal observations made in many countries, from England to Egypt, enabled him to avoid most of the puerilities which disfigure other works of his own or of a preceding age.

    1
    0
  • Hence it is that Gmelin appears as the authority for so much of the nomenclature now in use.

    1
    0
  • The principal theory which he hence conceived himself justified in propounding was that instead of five being (as had been stated) the maximum number of centres of ossification in the sternum, there are no fewer than nine entering into the composition of the perfect sternum of birds in general, though in every species some of these nine are wanting, whatever be the condition of development at the time of examination.

    1
    0
  • Hence it became manifest that a very respectable classification can be found in which characters drawn from these bones play a rather important part.

    1
    0
  • Hence his efforts, praiseworthy as they were from several points of view, and particularly so in regard to some details, failed to satisfy the philosophic taxonomer when generalizations and deeper principles were concerned, and in his practice in respect of certain technicalities of classification he was, in the eyes of the orthodox, a transgressor.

    1
    0
  • Hence they were known in England as "grey amices" (from the ordinary colour of the fur), to distinguish them from the liturgical amice.

    1
    0
  • Hence the noticeable heaviness of Venetian tracery.

    1
    0
  • Two colossal statues of Neptune and Mars at the top of these stairs were executed by Jacopo Sansovino in 1554 - hence the name "giants' staircase."

    1
    0
  • Smith (ed.), The St Clair Papers: Life and Services of Arthur St Clair (2 vols., Cincinnati, 1882); Jacob Burnet, Notes on the Early Settlement of the North-Western Territory (Cincinnati, 1847), written from the Federalist point of view, and hence rather favourable to St Clair; C. E.

    1
    0
  • Hence as a very general rule the coloration makes for concealment under natural conditions of existence, and the instincts which lead to concealment are very highly developed.

    1
    0
  • Hence it is probable that no factor has had a greater influence than these wasps in moulding the protective instincts and habits of spiders.

    1
    0
  • According to the Arabian geographer, Yaqut, Persian scorpions were thrown into the place when it was besieged by Anushirwan; hence their numbex to-day.

    1
    0
  • The royal riding school was removed hence to Hanover in 1867.

    1
    0
  • Hence at first, in 1882, they were used only by a section of the market constituted of members who had voluntarily agreed to do business with one another upon these terms alone.

    1
    0
  • Now frequency of movement, average daily price variation, and range of price movements are matters of fundamental importance to the public. Hence for practical purposes we require several kinds of measurement of price movements, and it is impossible to weigh exactly the one against the other in respect of importance.

    1
    0
  • The mass becomes unduly sanguine or weakly surrenders to panic. Hence the law of error does not apply, and speculation by the public may unsteady prices.

    1
    0
  • Hence Caesar seems to assign more extensive functions to the Druids than they actually possessed.

    1
    0
  • It is evident that accurate knowledge of the character and structure of the rock-formations in petroliferous territories is of the greatest importance in enabling the expert to select favourable sites for drilling operations; hence on well-conducted petroleumproperties it is now customary to note the character and thickness of the strata perforated by the drill, so that a complete section may be prepared from the recorded data.

    1
    0
  • The reason is that the heat produced in a given time in a wire is proportional to the square of the strength of the current passing through it, and hence the rate at which the heat is produced in the wire, and therefore its temperature, increases much faster than the current itself increases.

    1
    0
  • Hence the consequent fusion with Aphrodite, Artemis, Diana, Juno and Venus, and the action and reaction of one upon the other in myth and legend.

    1
    0
  • Two years later the American Congress annexed the portion of West Florida between the Pearl and the Mississippi rivers to Louisiana (hence the so-called Florida parishes of Louisiana), and that between the Pearl and the Perdido to the Mississippi Territory.

    1
    0
  • Oepair€ rrai, literally "attendants" or "physicians," hence "worshippers of God"), a monastic order among the Jews of Egypt, similar to the Essenes.

    1
    0
  • 10, § 12) - hence its highly rhetorical character - from which Eusebius gives the extract about the Essenes; while this in its turn may have constituted the fourth book of a large work entitled ("sarcastically," says Eusebius, H.E.

    1
    0
  • Marine Soap. - These soaps are so named because they are not insoluble in a strong solution of salt; hence they form a lather and can be used for washing with sea-water.

    1
    0
  • Originally a nature goddess (like Venus the garden goddess, with whom she was sometimes identified), she represented at first the hope of fruitful gardens and fields, then of abundant offspring, and lastly of prosperity to come and good fortune in general, being hence invoked on birthdays and at weddings.

    1
    0
  • The supporters of the solar theory look upon Memnon as the son of the dawn, who, though he might vanish from sight for a time, could not be destroyed; hence the immortality bestowed upon him by Zeus.

    1
    0
  • With their resinous to adamantine lustre and their translucency they also present somewhat the appearance of horn; hence the name hornsilver.

    1
    0
  • Hence the number of independent elements assigned to a planet or other body moving around the sun is commonly six.

    1
    0
  • Hence he was on the worst of terms with the king before a year had elapsed.

    1
    0
  • Hence it is referred to as "the Feast" par excellence (Heb.

    1
    0
  • Hence he left for Gotha (1528), resumed teaching, and enjoyed the friendship of Friedrich Myconius.

    1
    0
  • in circuit, is never distant from the city more than five kos (7 m.); hence its name, Panch-kos road.

    1
    0
  • Hence we find them taking part with Ammonites and Midianites (Judg.

    1
    0
  • The entrance to the harbor, which is perfectly sheltered (hence its name), is through a narrow opening in the palm-covered shore.

    1
    0
  • The Maxwells were pursued into Lockerbie and almost exterminated; hence "Lockerbie Lick" became a proverbial expression, signifying an overwhelming defeat.

    1
    0
  • Atargatis, in the capacity of fro?uovxos, wears a mural crown, is the ancestor of the royal house, the founder of social and religious life, the goddess of generation and fertility (hence the prevalence of phallic emblems), and the inventor of useful appliances.

    1
    0
  • Huxley; hence his term Dromaeognathae for the Crypturi.

    1
    0
  • Hence the gaseous atoms of hydrogen and oxygen could not have parts.

    1
    0
  • Lastly, in the production of gaseous hydriodic acid from hydrogen and solid iodine H2 - 1 - 12=HI+HI, so much energy is expended in the decomposition of the hydrogen and iodine molecules and in the conversion of the iodine into the gaseous condition, that the heat which it may be supposed is developed by the combination of the hydrogen and iodine atoms is insufficient to balance the expenditure, and the final result is therefore negative; hence it is necessary in forming hydriodic acid from its elements to apply heat continuously.

    1
    0
  • This compound may be considered as derived from methane, CH 4, by replacing a hydrogen atom by the monovalent group CH 3, known as methyl; hence ethane may be named " methylmethane."

    1
    0
  • We derived this substance from ethane by introducing a meth y l group; hence it may be termed " methylethane."

    1
    0
  • Hence the positions occupied by the nitro groups in the two different nitrobrombenzoic acids must be symmetrical with respect to the carboxyl group. In 1879, Hubner (Ann., 1 95, p. 4) proved the equivalence of the second pair, viz.

    1
    0
  • Hence, unless the radical introduced be one which exercises a special attractive influence, substitution should take place in preference in the previously unsubstituted ring.

    1
    0
  • According to Armstrong, anthracene behaves unsymmetrically towards substituents, and hence one lateral ring differs from the other; he represents the molecule as consisting of one centric ring, the remaining medial and lateral ring being ethenoid.

    1
    0
  • With iodine compounds, iodic acid is likely to be formed, and hence the solution must be reduced with sulphurous acid before precipitation with silver nitrate.

    1
    0
  • Want of data for the elements, however, restricts this method to narrow limits, and hence an indirect method is necessary.

    1
    0
  • 88 These differences do not disappear at the critical point, and hence the critical volumes are not strictly additive.

    1
    0
  • Hence within narrow limits Kopp's determinations were carried out under coincident conditions, and therefore any regularities presented by the critical volumes should be revealed in the specific volumes at the boiling-point.

    1
    0
  • It is found that mercury vapour, helium, argon and its associates (neon, krypton, &c.) have the value 1.67; hence we conclude that these gases exist as monatomic molecules.

    1
    0
  • Hence it may be inferred that this value is typical for diatomic molecules.

    1
    0
  • To take an example: 38 parts of indium combine with 35.4 parts of chlorine; hence, if the formula of the chloride be InCI, InC1 2 or InC1 3, indium has the atomic weights 38, 76 or 114.

    1
    0
  • The series H 2 S = - 61°, CH 3 SH = 21 °, (C 11 3) 2 S=41 ° is an example; in the first case, the molecular weight is increased and the symmetry diminished, the increase of boiling-point being 82°; in the second case the molecular weight is again increased but the molecule assumes a more symmetrical configuration, hence the comparatively slight increase of 20°.

    1
    0
  • Since a/d is the real specific volume of the molecule, it is therefore a constant; hence (N2-I)/(N2+2)d is also a constant and is independent of all changes of temperature, pressure, and of the state of aggregation.

    1
    0
  • Since molecular refractions are independent of temperature and of the state of aggregation, it follows that molecular dispersions must be also independent of these conditions; and hence quantitative measurements should give an indication as to the chemical composition of substances.

    1
    0
  • Hence S may be replaced by (Mv) 3.

    1
    0
  • The gods, as the giants plaintively admit, " rule by beauty"; hence the " Walhalla-motif."

    1
    0
  • The fundamental theme of the epistle is The Unity of Mankind in Christ, and hence the Unity and Divinity of the Church of Christ.

    1
    0
  • Hence in transcription from foreign languages and in works on phonetics it is represented by s or š.

    1
    0
  • DURRA (also written dourah, dhura, &c.; Arabic for a pearl, hence a grain of corn), a cereal grass, Sorghum vulgare, extensively cultivated in tropical and semi-tropical countries, where the grain, made into bread, forms an important article of diet.

    1
    0
  • Cesare, who renounced his cardinalate, was sent on a mission to France at the end of the year, bearing a bull of divorce for the new king Louis XII., in exchange for which he obtained the duchy of Valentinois (hence his title of Duca Valentino) and a promise of material assistance in his schemes to subjugate the feudal princelings of Romagna; he married a princess of Navarre.

    1
    0
  • Hence the scale is r: r,000,000 approximately.

    1
    0
  • Hence the world will last for six thousand years of toil and labour; then will come one thousand years of Sabbath rest for the people of God in the kingdom of the Messiah."

    1
    0
  • They were very conservative of ancient traditions in general, and hence chiliasm survived amongst them to a later date than in Alexandria or Constantinople.

    1
    0
  • Among the ruder or savage tribes they possess but one form; but the ingenuity of man has devised many inventions to increase his comforts; he has varied and multiplied the characters and kinds of domestic animals for the same purpose, and hence the various breeds of horses, cattle and dogs.

    1
    0
  • Hence arose a double negotiation between him and Eugenius IV.

    1
    0
  • Hence we conclude that the Testaments were written between 137 and 107."

    1
    0
  • Hence in reality the passage was preserved only by a originally.

    1
    0
  • Hence at Rome slavery also most properly found its place, so long as that mission was in progress of accomplishment.

    1
    0
  • Hence a regular commerce in slaves was established, which was based on the " systematically-prosecuted hunting of man," and indicated an entire perversion of the primitive institution, which was essentially connected with conquest.

    1
    0
  • Hence the abolition of the external slave trade tended, in fact, to put an end to internal sales, and the slaves became attached to the households or lands of their masters.

    1
    0
  • They had their own households and were hence distinguished as casati.

    1
    0
  • As these waste places have been gradually brought under the plough, in England and Scotland particularly, the haunts and means of subsistence of the linnet have been curtailed, and hence its numbers have undergone a very visible diminution throughout Great Britain.

    1
    0
  • According to Dr Jakob Jakobsen, the name means the voe (waa) of the skollas, or booths, occupied by the men who came to attend the meeting of the ling, or open-air law court, which assembled in former days on an island in the Loch of Tingwall (hence its name), about 3 m.

    1
    0
  • 8, io), and hence only some portions of Deuteronomy (or of an allied production) may be intended.

    1
    0
  • Hence a good herbarium forms an indispensable part of a botanical museum or institution.

    1
    0
  • But in any scientific discussion the term instinct must be used within narrower limits, and hence it is necessary that the term should be defined.

    1
    0
  • Now the wish to become manifest and known, and hence the idea of creation, is co-eternal with the inscrutable Deity, and the first manifestation of this primordial will is called the first Sephirah or emanation.

    1
    0
  • Hence Wisdom, the second Sephirah, and the beginning of development, when it proceeded from the Holy Aged (another name of the first Sephirah) emanated in male and female, for Wisdom expanded, and Intelligence, the third Sephirah, proceeded from it, and thus were obtained male and female, viz.

    1
    0
  • Hence the right is called " the Pillar of Judgment," the left " the Pillar of Mercy," and the centre " the Middle Pillar."

    1
    0
  • Hence the Crown, the first Sephirah, which unites Wisdom and Intelligence to constitute the first triad, is by itself denominated the Intellectual World.

    1
    0
  • Hence nothing in the whole universe can be annihilated.

    1
    0
  • Hence it is most intimately allied to the Deity, and is perfect and immutable.

    1
    0
  • Since these compounds are essential to plant life, it becomes necessary to replace the amount abstracted from the soil, and hence a demand for nitrogenous manures was created.

    1
    0
  • Hence their name Agnoetae and their excommunication.

    1
    0
  • Hence the relation has been called above "one-many."

    1
    0
  • These officers were usually chosen from among the more promising of the youths selected by the devshurme, or system of forced levy for manning the ranks of the Janissaries: hence so many of the statesmen of Turkey were of non-Mussulman origin.

    1
    0
  • Hence the vast majority of the people whom we are accustomed to think of as Ottomans are so only by adoption, being really the descendants of Seljuks or Seljukian subjects, who had derived from Persia whatever they possessed of civilization or of literary taste.

    1
    0
  • But these views obviously could not be published in army orders, hence the discontent and opposition he was destined to encounter.

    1
    0
  • Hence obedience was instinctive and initiative almost undreamt of.

    1
    0
  • With these numbers it was impossible to attain the high degree of individual efficiency required for the old line tactics, hence they were compelled to adopt the French methods of skirmishers and columns, but as yet they had hardly realized the increased density necessary to be given to a line of battle to enable it to endure the prolonged nervous strain the new system of tactics entailed.

    1
    0
  • Hence the extraordinary slowness of their manoeuvres, not because the Austrian infantry were bad marchers, but because the preparation and circulation of orders was still far behind the French standard.

    1
    0
  • It took Blucher time to extricate his troops from the confusion into which the battle had thrown them, and the garrison of Leipzig and the troops left on the right bank of the Elster still resisted obstinately - hence no direct pursuit could be initiated and the French, still upwards of 10o,000 strong, marching rapidly, soon gained distance enough to be reformed.

    1
    0
  • Hence a prolonged halt arose, utilized by the troops in renewing their equipment and so forth, but ultimately the Young German party, led by Blucher and the principal fighting men of the army, triumphed, and on the 1st of January 1814 the Silesian army (50,000) began its passage of the Rhine at Kaub.

    1
    0
  • Hence less than 80,000 remained available for the east and north-eastern frontier.

    1
    0
  • Hence, when on the battlefield the changing course of events left his antagonists mentally exhausted, he was able to face them with will power neither bound nor broken.

    1
    0
  • It is clear that the ancient name, at least, still held firm possession of the site and was hence inherited by the new city.

    1
    0
  • Some, however, of the classic poets he appears to have known only from anthologies; hence he was misled into quoting as from Euripides and others verses which were written by Jewish forgers.

    1
    0
  • Allenlightenment tended to lead up to the truths of Christianity, and hence knowledge of every kind not evil was its handmaid.

    1
    0
  • It was formerly frequented by whaling vessels (hence its name).

    1
    0
  • Hence from the 10th to the 12th centuries there was great intercourse with Iceland and Greenland on the part of the English, Swedish and Danish, but at the end of the 13th century some change occurred, resulting in the southerly emigration of the Eskimos and the extinction of European civilization in Greenland.

    1
    0
  • Histones are a class of albumins soluble in water and acids, but essentially basic in character; hence they are precipitated by alkalies.

    1
    0
  • They are dextrorotatory, and the specific rotation is numerically greater than that of albumin; hence the proteids are, in general, dextrorotatory.

    1
    0
  • When their country was first invaded they fled into the forests, and the Spaniards, coming upon their huts, the doorways of which are built excessively low, supposed them to be dwarfs: hence the name.

    1
    0
  • This important war, the conduct and result of which greatly enhanced the prestige of British arms, had for its main object the freedom of the Peninsula of Spain and Portugal from the domination of Napoleon; and hence it deri'ves its name, though it terminated upon the soil of France.

    1
    0
  • Hence he wrote to Soult, "If the English pass to-day in their position (which he believed to be Sahagun) they are lost."

    1
    0
  • and hence an argument has been drawn against the authority of the relation.

    1
    0
  • In this battle Sigebert, the king of the Ripuarians, was wounded in the knee and limped during the remainder of his life - hence his surname Claudus (the Lame).

    1
    0
  • As the rock was highly viscous and the surface over which it moved was often irregular the motion was disturbed and fluctuating; hence the sinuous and contorted appearance frequently assumed by the banding.

    1
    0
  • Hence it may be regarded as diagnostic of rocks which were vitreous when they consolidated.

    1
    0
  • When an electric current flows round a circuit, there is no accumulation of electricity anywhere in the circuit, hence the current strength is everywhere the same, and we may picture the current as analogous to the flow of an incompressible fluid.

    1
    0
  • Hence there can be no reverse forces of polarization inside the liquid itself, such forces being confined to the surface of the electrodes.

    1
    0
  • Hence experiments without separating diaphragms are to be preferred, and the apparatus may be considered effective when a consideraable bulk of intervening solution is left unaltered in composition.

    1
    0
  • Hence it is probable that in cases where the transport number keeps constant with 00000 0 0.

    1
    0
  • Hence the absolute velocities of the two ions can be determined, and we can calculate the actual speed with which a certain ion moves through a given liquid under the action of a given potential gradient or electromotive force.

    1
    0
  • The number of undissociated molecules is then I - a, so that if V be the volume of the solution containing I gramme-molecule of the dissolved substance, we get q= and p= (I - a)/V, hence x(I - a) V =yd/V2, and constant = k.

    1
    0
  • Hence zinc can only dissolve when some more easily separable.

    1
    0
  • Hence we get the equation Ee = Le +Te (dE/dT) or E = L+T(dE/dT), as a particular case of the general thermodynamic equation of available energy.

    1
    0
  • Hence for the electrochemical unit of zinc or 0.003388 gramme, the thermal evolution is 5.66 calories.

    1
    0
  • Hence, if we assume that, in the Daniell's cell, the temperature coefficients are negligible at the individual contacts as well as in the cell as a whole, the sign of the potential-difference ought to be the same at the surface of the zinc as it is at the surface of the copper.

    1
    0
  • in three days, has a strong ammoniacal odour, which rapidly disappears, and in consequence of the loss of ammonia the latex will not keep for longer than a day unchanged; hence when it has to be carried to a distance from the place of collection, 3% of ammonia solution is added.

    1
    0
  • The four inner stamens are longer than the two outer; and the stamens are hence collectively described as tetradynamous.

    1
    0
  • He represented the antiFranco-Prussian portion of her council, and his object was to bring about an Anglo-Austro-Russian alliance which, at that time, was undoubtedly Russia's proper system, Hence the reiterated attempts of Frederick the Great and Louis XV.

    1
    0
  • Hence processes have been patented in which the objects to be plated are suspended in revolving drums between the anodes, the rotation of the drum causing the constant renewal of surfaces and affording a burnishing action at the same time.

    1
    0
  • The air, after being chilled on the plateaus during the winter, drifts, owing to its greater density, down upon the lowlands; hence in the region of the lower Lena there obtains an exceedingly low temperature throughout the winter, and Verkhoyansk, in 67°N., is the pole of cold of the eastern hemisphere.

    1
    0
  • Hence she is called 7roXuis,.

    1
    0
  • In principle it was even held to be the debtor for the amount; hence the inhabitants were jointly responsible, a state of affairs which was not suppressed till the time of Turgot, and even then not completely.

    1
    0
  • Hence there is water communication with the Neckar, and so to the Rhine and into the interior of France.

    1
    0
  • Hence the transposition of columns merely changes the sign of the determinant.

    1
    0
  • Hence anAu = auk t a22a33...ann, where the cofactor of an is clearly the determinant obtained by erasing the first row and the first column.

    1
    0
  • Hence we have the development A = a11A11 +a12Al2 +a13A13+��� +ainAin, proceeding according to the elements of the first row and the corresponding minors.

    1
    0
  • 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.

    1
    0
  • bin respectively, and Hence A11= 0 0 ...

    1
    0
  • Hence the product determinant has the principal diagonal elements each equal to A and the remaining elements zero.

    1
    0
  • Now the determinant has the value - {AiA11+A2A22+A3A33+2A2A3A23+2A3AIA31+2A1A2Al2{ = -Eata r r-2EA r A 8 A rs in general, and hence by substitution {A I V A n+ A 211 A22+��� +A71 Ann}2.

    1
    0
  • Hence 0 = - O or ., =o.

    1
    0
  • For the second order we may take Ob - I - A, 1 1 +A2, and the adjoint determinant is the same; hence (1 +A2)x1 = (1-A 2)X 1 + 2AX2, (l +A 2)x 2 = - 2AX1 +(1 - A2)X2.

    1
    0
  • Hence the produc J1 t theorem (21, Z2,...zn / (y1, Y2,...y.n) = ?

    1
    0
  • Hence if A does not vanish x 1 = x 2 =...

    1
    0
  • each of them satisfied by a common system of values; hence the equation R =o is derived on this supposition, and the vanishing of R expresses the condition that the equations can be satisfied by a common system of values assigned to the variables.

    1
    0
  • If al, a2, ...a, n be the roots of f=o, (1, R2, -Ai the roots of 0=o, the condition that some root of 0 =o may qq cause f to vanish is clearly R s, 5 =f (01)f (N2) � �;f (Nn) = 0; so that Rf,q5 is the resultant of f and and expressed as a function of the roots, it is of degree m in each root 13, and of degree n in each root a, and also a symmetric function alike of the roots a and of the roots 1 3; hence, expressed in terms of the coefficients, it is homogeneous and of degree n in the coefficients of f, and homogeneous and of degree m in the coefficients of 4..

    1
    0
  • The resultant being a product of mn root differences, is of degree mn in the roots, and hence is of weight mn in the coefficients of the forms; i.e.

    1
    0
  • aj Hence the system of values also causes to vanish in this case; dx and by symmetry aj and Fz also vanish.

    1
    0
  • Hence in all there are mn such systems. If, therefore, we have a third equation, and we substitute each system of values in it successively and form the product of the mn expressions thus formed, we obtain a function which vanishes if any one system of values, common to the first two equations, also satisfies the third.

    1
    0
  • Hence this product is the required resultant of the three equations.

    1
    0
  • Hence, finally, the resultant is expressed in terms of the coefficients of the three equations, and since it is at once seen to be of degree mn in the coefficient of the third equation, by symmetry it must be of degrees np and pm in the coefficients of the first and second equations respectively.

    1
    0
  • It is the resultant of k polynomials each of degree m-I, and thus contains the coefficients of each form to the degree (m-I)'-1; hence the total degrees in the coefficients of the k forms is, by addition, k (m - 1) k - 1; it may further be shown that the weight of each term of the resultant is constant and equal to m(m-I) - (Salmon, l.c. p. loo).

    1
    0
  • af Expression in Terms of Roots.-Since x+y y =mf, if we take cx any root x 3, y1, ofand substitute in mf we must obtain, y 1 C) zaZ1 �; hence the resultant of and f is, disregarding numerical factors, y,y2...y,,.

    1
    0
  • Hence the theorem.

    1
    0
  • Hence the theorem is established.

    1
    0
  • Hence the theorem of expressibility enunciated above.

    1
    0
  • Hence, if f(ai, a 2, ...a n) _ (?i?2%?3���), 1 2 3 +,01(X2A3...) +02(X1X3.�.) +IlA'(XlX2.�.) +...

    1
    0
  • Hence we derive the particular cases 1 1 expel ' =exp(d1 -2d2+5d3 - ...); exp/ld 1 = exp(Ad1p2d2 +/13d3 - ...), and we can express D.

    1
    0
  • To operate with D2 upon (213) (214) (15), we have D (2)f = (13) (214) (15) + (213) (14) (15), D c1 2)f = (122) (213) (15) +(213) (213) (14) + (212) (214) (14), and hence D2f = (214) (15) (13) +(213) (15) (14) +(213) (212) (15) +(213)2(14) +(214) (212) (14).

    1
    0
  • - If, in the identity 1 (1 +anx = 1+aiox+aoly+a20x 2 +allxy+a02y 2 +..., we multiply each side by (I -�-P.x+vy), the right-hand side becomes 1 +(aio+1.1 ') x +(a ol+ v) y +...+(a p4+/ 1a P-1,4+ va Pr4-1) xPyq - - ...; hence any rational integral function of the coefficients an, say f (al °, aol, ...) =f exp(�dlo+vdol)f d a P-1,4, dot = dapg The rule over exp will serve to denote that i udio+ vdo h is to be raised to the various powers symbolically as in Taylor's theorem.

    1
    0
  • 1 1 Hence it becomes necessary to have more than one set of umbrae, so that we may have more than one symbolical representation of the same real coefficients.

    1
    0
  • Hence the condition is i+k+...

    1
    0
  • Now D A xA k = (n - k) A k; A� A k = k A?1; D �A A k = (n - k) A k+1;D m� A k = kA k; (n - k)A ka - w Ak - 1 aA k = O; a _ J (n - k) A k +l A k = O; kA k Ak = wJ; equations which are valid when X 1, X 2, � 1, �2 have arbitrary values, and therefore when the values are such that J =j, A k =ak� Hence °a-do +(n -1)71 (a2aa-+...

    1
    0
  • we find that Di must be equal to p x g x for then t x (p x) 3 +, u (g x) 3, Hence, if px, qx be the linear factors of the Hessian 64, the cubic can be put into the form A(p x) 3 +�(g x) 3 and immediately solved.

    1
    0
  • of f=0, :and notices that they become identical on substituting 0 for k, and -f for X; hence, if k1, k2, k 3 be the roots of the resolvent -21 2 = (o + k if) (A + k 2f)(o + k 3f); and now, if all the roots of f be different, so also are those of the resolvent, since the latter, and f, have practically the same discriminant; consequently each of the three factors, of -21 2, must be perfect squares and taking the square root 1 t = -' (1)�x4; and it can be shown that 0, x, 1P are the three conjugate quadratic factors of t above mentioned.

    1
    0
  • The transformation to the normal form, by the solution of a cubic and a quadratic, therefore, supplies a solution of the quartic. If (X�) is the modulus of the transformation by which a2 is reduced to 3 the normal form, i becomes (X /2) 4 i, and j, (Ap) 3 j; hence?

    1
    0
  • Hence, solving the cubic, R 2 j = (S -m i a) (S - m 2 a) (S - m3a) wherein m 1 m2, m 3 are invariants.

    1
    0
  • Now, evidently, the third transvectant of f, expressed in this form, with the cubic pxgxrx is zero, and hence from a property of the covariant j we must have j = pxgxrx; showing that the linear forms involved are the linear factors of j.

    1
    0
  • Hence, from the identity ax (pq) = px (aq) -qx (ap), we obtain (pet' = (aq) 5px - 5 (ap) (aq) 4 pxg x - (ap) 5 gi, the required canonical form.

    1
    0
  • Hence, excluding ao, we may, in partition notation, write down the fundamental solutions of the equation, viz.

    1
    0
  • In order to obtain the seminvari ants we would write down the (w; 0, n) terms each associated with a literal coefficient; if we now operate with 52 we obtain a linear function of (w - I; 8, n) products, for the vanishing of which the literal coefficients must satisfy (w-I; 0, n) linear equations; hence (w; 8, n)-(w-I; 0, n) of these coefficients may be assumed arbitrarily, and the number of linearly independent solutions of 52=o, of the given degree and weight, is precisely (w; 8, n) - (w - I; 0, n).

    1
    0
  • 1-az2....1-azn' Hence (w; 0, n) - (w - I; 0, n) is given by the coefficient of aez'° in the fraction 1-z 1 -a.1-az.

    1
    0
  • These latter forms are enumer ated by I - z 24 I -z 4; hence the generator of quartic perpetuants must be z4 z4 z7 1-z 2.1 -z 3.1z 4 1-z 2.1-s 4 1-22.1-z3.1-z4' and the general form of perpetuants is (4 K+ 1 3A+1 2�).

    1
    0
  • Hence every product of A 1, A2, A3, A4, which contains the product A 4 A 3 disappears before reduction; this means that every seminvariant, whose partition contains the parts 4, 3, is a perpetuant.

    1
    0
  • Again, if 0 is uneven =20+I, the condition is a 1 a 2 ...cr 241 II(a 1 +a 2)II(cr 1 +a 2 +(73)...II(a 1 +a 2 +...+ac) =0; and the degree, in the quantities a, is 20+1 + (42+1) +(21) �...-F(254)�1) =22°-1= 2e-1-1 Hence the lowest weight of a perpetuant is 2 0 - 1 -1, when 0 is >2.

    1
    0
  • 1 And The Actual Forms For The First Three Weights Are 1 Aobzo, (Ao B 1 A 1 B O) Bo, (A O B 2 A 1 2 0 Bo, Ao(B2, 3 A1B2 A2B1 A O (B L B 2 3B O B 3) A I (B 2 1 2B 0 B 2); Amongst These Forms Are Included All The Asyzygetic Forms Of Degrees 1, 1, Multiplied By Bo, And Also All The Perpetuants Of The Second Binary Form Multiplied By Ao; Hence We Have To Subtract From The 2 Generating Function 1Z And 1 Z Z2, And Obtain The Generating Function Of Perpetuants Of Degrees I, 2.

    1
    0
  • Hence, in both cases, contragrediency and cogrediency are identical, and contravariants are included in covariants.

    1
    0
  • Hence in the above general form of covariant we may suppose the exponents h 1, h2, h3,...ki, k2, k3,...

    1
    0
  • Hence a beautiful road, immortalized by Goethe in Dichtung and Wahrheit, leads across the Vosges to Pfalzburg.

    1
    0
  • The determination of the true relation between the length of a pendulum and the time of its oscillation; the invention of the theory of evolutes; the discovery, hence ensuing, that the cycloid is its own evolute, and is strictly isochronous; the ingenious although practically inoperative idea of correcting the "circular error" of the pendulum by applying cycloidal cheeks to clocks - were all contained in this remarkable treatise.

    1
    0
  • Lead unites readily with almost all other metals; hence, and on account of its being used for the extraction of (for instance) silver, its alchemistic name of saturnus.

    1
    0
  • Strong sulphuric acid dissolves it, forming an acid salt, Pb(HS04)2, which is hydrolysed by adding water, the normal sulphate being precipitated; hence the milkiness exhibited by samples of oil of vitriol on dilution.

    1
    0
  • Hence the disastrous effects supposed to follow a breach of taboo; the offender has thrust his hand into the divine fire, which shrivels up and consumes him on the spot" (Frazer, The Golden Bough, i.

    1
    0
  • Hence the rise of sacred books among most Eastern peoples.

    1
    0
  • Hence they were resolutely opposed to any idea of reform; for to begin making changes in the Church's system would be a tacit admission that Luther had some show of reason on his side.

    1
    0
  • Hence they deliberately refuse to engage in casuistry of the old-fashioned sort.

    1
    0
  • cauda, hence couart or coward.

    1
    0
  • The term, with its adjective " formal " and the derived nouns " formality " and " formalism," is hence contemptuously used for that which is superficial, unessential, hypocritical: chap. xxiii.

    1
    0
  • They are distinguished by having one of the five blue or yellow coloured sepals (the posterior one) in the form of a helmet; hence the English name monkshood.

    1
    0
  • Hence it is not very easy to determine experimentally the law of magnetic force between poles.

    1
    0
  • A south pole would be urged oppositely to the conventional " direction " of the line; hence it follows that a very small magnetic needle, if placed in the field, would tend to set itself along or tangentially to the line of force passing through its centre, as may be approximately verified if the compass be placed among the filings on the cardboard.

    1
    0
  • Where the lines are crowded together, as in the neighbourhood of the poles, the force is greater (or the field is stronger) than where they are more widely separated; hence the strength of a field at any point can be accurately specified by reference to the concentration of the lines.

    1
    0
  • Hence I = M/v = ml/v = m/a, v being the volume and a the sectional area.

    1
    0
  • Hence if the induction per square centimetre at any point is denoted by B, then in empty space B is numerically equal to H; moreover in isotropic media both have the same direction, and for these reasons it is often said that in empty space (and practically in air and other nonmagnetic substances) B and H are identical.

    1
    0
  • Hence B =µH and I =KH.

    1
    0
  • (35) Du Bois has shown that _when the dimensional ratio in (= length/ diameter) exceeds t00, Nm 2 =constant=45, and hence for long thin rods N = 45/ m2.

    1
    0
  • Hence the difficulty of imparting any considerable permanent magnetization to a short thick bar not possessed of great coercive force.

    1
    0
  • For small bodies other than spheres the coefficient will be different, but its sign will always be negative for diamagnetic substances and positive for others; hence the forces acting on any small body will be in the same directions as in the case of a sphere' Directing Couple acting on an Elongated Body.

    1
    0
  • Hence any apparatus, such as a galvanometer, may be partially shielded from extraneous magnetic action by enclosing it in an iron case.

    1
    0
  • Hence, whatever the position of the body, if the field be resolved into three components parallel to the 1 For all except ferromagnetic substances the coefficient is sensibly equal to See W.

    1
    0
  • The distinguishing feature of the first is the steepness of its outlines; this indicates that the induction increases rapidly in relation to the magnetic force, and hence the metal is well suited for the construction of dynamo magnets.

    1
    0
  • For simplicity of calculation, the clear length of each rod between the yokes is made 12.56 (=47r) centimetres, while the coil surrounding the standard bar contains 100 turns; hence the magnetizing force due to a current of n amperes will be ion C.G.S.

    1
    0
  • Hence the changes of volume undergone by a given sample of wrought iron under increasing magnetization must depend largely upon the state of the metal as regards hardness; there may be always contraction, or always expansion, or first one and then the other.

    1
    0
  • The force acting on the magnetism of one of the faces, and urging this face towards the other, will be less than B by 27r1, the part of the total force due to the first face itself; hence the force per unit of area with which the faces would press against each other if in contact is P = (B-27rI)I =27rT 2 +HI = (B 2 -H 2) =/81r.

    1
    0
  • pressure is 0'00141 grm., the mass at any absolute temperature 0 is by Charles's law o oo 141 X 2 739 = 0 3 849/9 grm.; hence the susceptibility per unit of volume at 760 mm.

    1
    0
  • Hence in performing a cycle there is a waste of energy corresponding to what has been termed hysteresis-loss.

    1
    0
  • According to the best determinations the value of elm does not exceed 1.8X Io', and T is of the order of Io 15 second, the period of luminous vibrations; hence OM/M must always be less than 109 H, and therefore the strongest fields yet reached experimentally, which fall considerably short of Io %, could not change the magnetic moment M by as much as a ten-thousandth part.

    1
    0
  • Hence may be deduced an explanation of the fact that, while the susceptibility of all known diamagnetics (except bismuth and antimony) is independent of the temperature, that of paramagnetics varies inversely as the absolute temperature, in accordance with the law of Curie.

    1
    0
  • In particular, he found that the calculated velocity with which it transmitted electromagnetic disturbances was equal to the observed velocity of light; hence he was led to believe, not only that his medium and the ether were one and the same, but, further, that light itself was an electromagnetic phenomenon.

    1
    0
  • A sum of money (aes equestre) was given to each eques for the purchase of two horses (one for himself and one for his groom), and a further sum for their keep (aes hordearium); hence the name equites equo publico.

    1
    0
  • The central eyes are " simple eyes," that is to say, have a single lens, and are hence called " monomeniscous."

    1
    0
  • (For details the reader is referred to Watase (11) and to Lankester and Bourne (5).) The structure of the central eyes of Scorpio and spiders and also of Limulus differs essentially from that of the lateral eyes in having two layers of cells (hence called diplostichous) beneath the lens, separated from one another by a membrane (figs.

    1
    0
  • Hence the name of the sub-class signifying tri-lobed, a condition realized also in the Xiphosurous Arachnids.

    1
    0
  • with the other books, and with no marks of distinction, they were practically employed by the Greek Fathers in the same way as the other books; hence Origen, Clement and others often cite them as " scripture," " divine scripture," " inspired," and the like.

    1
    0
  • Two well-defined views in this way prevailed, to which was added a third, according to which the books, though not to be put in the same rank as the canonical scriptures of the Hebrew collection, yet were of value for moral uses and to be read in congregations, - and hence they were called " ecclesiastical " - a designation first found in Rufinus (ob.

    1
    0
  • Hence Christ is represented as coming to destroy the work of the female (Clem.

    1
    0
  • Hence Zahn gives its date as 90 -100 at latest; Dobschiitz, as loo -110; and Harnack, as 110 -130.

    1
    0
  • Hence the land connexions must have formerly been much easier and far more continuous than at present.

    1
    0
  • It continued to be a royal residence during the reigns of her three sons, and hence the first rapid growth of the upper town may be referred to the 12th century.

    1
    0
  • Hence, though the village of Canongate grew up beside the abbey of David I., and Edinburgh was a place of sufficient importance to be reckoned one of the four principal burghs as a judicatory for all commercial matters, nevertheless, even so late as 1450, when it became for the first time a walled town, it did not extend beyond the upper part of the ridge which slopes eastwards from the castle.

    1
    0
  • The Schoolmen had no historical sense and little historical information; hence they fell into one error after another on the essentials in the rite of ordination.

    1
    0
  • Hence the Lutheran churches exhibit great variety of constitution.

    1
    0
  • But this is only to say again that Erigena is more of a Neoplatonist than a Scholastic. Hence Cousin suggested in respect of this point a threefold chronological division - at the outset the absolute subordination of philosophy to theology, then the period of their alliance, and finally the beginning of their separation.

    1
    0
  • Hence the strength with which a champion of the faith like Anselm insists on the subordination of reason.

    1
    0
  • And hence at a much later date (in the beginning of the 13th century) his name was invoked to cover the pantheistic heresies of Amalrich of Bena.

    1
    0
  • Hence it may be said that the universals are in the individuals, constituting their essential reality (and it is an express part of Erigena's system that the created but creative Word, the second division of Nature, should pass into the third stage of created and non-creating things); or rather, perhaps, we ought to say that the individuals exist in the bosom of their universal.

    1
    0
  • Hence rebellions of satraps became frequent from the middle of the 5th century; under Artaxerxes II.

    1
    0
  • Hence his cautious, dilatory tactics: the encouragement of Italian propagandists, who were few, the discouragement of German propagandists, who were many.

    1
    0
  • Hence the council of Constance to depose three rival popes; hence the council of Basel to pacify the Hussites, and promote another anti-Moslem league.

    1
    0
  • Hence the October Diploma (Oct.

    1
    0
  • He followed as his chief source the prose history of Myron of Priene, an untrustworthy writer, probably of the 2nd century B.C.; hence a good deal of his story must be regarded as fanciful, though we cannot distinguish accurately between the true and the fictitious.

    1
    0
  • Hence we can separate the numbers from the common unit, and replace 3 lb - I - 5 lb - 7 lb +2 lb by (3+5-7+2) lb, the additions and subtractions being then performed by means of an addition-table.

    1
    0
  • Hence the successive remainders are successively smaller multiples of L, but still integral multiples, so that the series of quotients k, s, t,.

    1
    0
  • Hence u is the greatest common measure of p and q.

    1
    0
  • Hence the change can be made in 3.4.5 ways.

    1
    0
  • Hence the formula (2) is also true for the nth power of A-I-a.

    1
    0
  • Hence it is true for all positive integral powers of n.

    1
    0
  • (iii.) From (21) of � 43 (iv.) we see that I R r l is less than m[r+l]xr+1 if x is positive, or than 1 m [r+1] x m+1 (I+x)- m I if x is negative; and it can hence be shown that, if 1 x I < 1, 1 R r I can be made as small as we please by taking r large enough, so that we can make S r approximate as closely as we please to (r +x)-1n.

    1
    0
  • Then a+a = as = a; hence numerical coefficients and indices are not required.

    1
    0
  • If A=ZaE, then, by definition, IA=EajE, and hence AI(B+C) =AIB+AIC.

    1
    0
  • Hence many structures which are obvious to the eye, and serve as distinguishing marks of separate species, are really not themselves of value or use, but are the necessary concomitants of less obvious and even altogether obscure qualities, which are the real characters upon which selection is acting.

    1
    0
  • Hence there is no necessity for an assumption of the perpetuation of direct adapta tions.

    1
    0
  • Hence, whatever else may happen, there must be a system of dark rings formed, the same as from a single small aperture.

    1
    0
  • Hence a spherical mirror of 3 ft.

    1
    0
  • Hence, in order that a double line may be resolved whose components have indices and A ct--S i ., it is necessary that t should exceed the value given by the following equation: - t= X/S / 8.

    1
    0
  • Hence, if a be the width of the diffracted beam, and do the angle through which the wave-front is turned, ado = dX, or dispersion = /a ..

    1
    0
  • Hence a wide beam demands treatment with further apparatus (usually a telescope) of high magnifying power.

    1
    0
  • Hence, as CA increases, viz.

    1
    0
  • Hence there is much doubt as to his exact meaning.

    1
    0
  • Hence the references to the Scyths in the Hebrew prophets (Jer.

    1
    0
  • Hence the Greek names, Abii, Hippemolgi, Hamaxobii.

    1
    0
  • Similar movements from the same regions appear also to have penetrated Iran itself; hence the resemblance between the dress and daggers of certain classes of warriors on the sculptures of Persepolis and those shown on the Kul Oba vase.

    1
    0
  • Similarly it may be shown that each internal reflection introduces a supplementary deviation of 7r - 2r; hence, if the ray be reflected n times, the total deviation will be D =2(i - r) +n (7r - 2r) .

    1
    0
  • Since the value of µ for water is about, it follows that n must be at least unity for a rainbow to be formed; there is obviously no theoretical limit to the value of n, and hence rainbows of higher orders are possible.

    1
    0
  • The third and fourth bows are situated between the observer and the sun, and hence, to be viewed, the observer must face the sun.

    1
    0
  • The smaller the drops, the greater the distance; hence it is that the spurious bows are generally only observed near the summits of the bows, where the drops are smaller than at any lower altitude.

    1
    0
  • A tin ingot is distinctly crystalline; hence the characteristic crackling noise, or "cry" of tin, which a bar of tin gives out when being bent.

    1
    0
  • But it is expensive, and tin vessels have to be made very heavy to give them sufficient stability of form; hence it is generally employed merely as a protecting coating for utensils made essentially of copper or iron.

    1
    0
  • Hence all tin crystals as kept in the laboratory give with water a turbid solution, which contains stannic in addition to stannous chloride.

    1
    0
  • Hence the semi-dramatic character of the style.

    1
    0
  • Hence the great dispute about the application to the Virgin Mary of the epithet OEoTOKOS.

    1
    0
  • Hence priests would remove their ceremonial dress before leaving the sanctuary " that they sanctify not the people with their garments " (Ezek.

    1
    0
  • Later still, this portion, instead of forming a bundle of folds in the centre, was carefully folded over and carried up over the left shoulder, and in course of time these folds were carefully arranged in several thicknesses resembling boards, tabulae, hence called contabulatio (Plate, fig.

    1
    0
  • Hence, unless a later Pheidon is assumed, the statement of Ephorus must be considered unhistorical.

    1
    0
  • Hence he publicly celebrated Mass, prohibited preaching against Catholicism, and showed exceptional favour to renegades from the Establishment.

    1
    0
  • Hence it may be considered to terminate where the Rio Cojedes, which drains the elevated valley in which Barquisimeto stands, after rising on its western slopes flows eastwards into the basin of the Orinoco.

    1
    0
  • Hence, though they were only a few miles apart, each was ignorant Bohemian Campaign 1866 - ?

    1
    0
  • It was considered to be a sulphur compound, hence its name sulphur ether; this idea was proved to be erroneous by Valentine Rose in about 1800.

    1
    0
  • Hence not only must the study of our subject include the diseases peculiar to man and the higher animals, but those of the lowest forms of animal life, and of plant life, must be held equally worthy of attention.

    1
    0
  • Until, however, further evidence is forthcoming in support of this syncytial theory of structure, it would be unwise to regard it as established sufficiently to constitute a serviceable working hypothesis; hence, for the time being, we must accept the assertion that the cell represents the ultimate tissue-unit.

    1
    0
  • They supposed that it was accompanied by a peculiar hyaline thickening of the arterial wall, usually of the tunica intima, and hence they termed the supposed diseased state " arterio-capillary fibrosis," and gave the fibrous substance the name " hyaline-fibroid."

    1
    0
  • Exudates are poured out under inflammatory conditions, while none of the truly dropsical effusions are of inflammatory origin; and hence the class of exudates, as above defined, may be rejected from the category of liquids we are at present considering.

    1
    0
  • Hence the elementary arc divided by the element of time is the rate of change of velocity of the moving-point, or in other words, the velocity in the hodograph is the acceleration in the orbit.

    1
    0
  • Xaas, stone, and Teµeiv, to cut; hence Aaroyia, quarry) of Syracuse, over too ft.

    1
    0
  • It is not, however, defensible in the rear: hence Dionysius's success against the Carthaginians.

    1
    0
  • Hence another generation had to pass away before Germany found herself on the level, in scientific investigation, of France and England.

    1
    0
  • Hence the description of the advance of medicine in western Europe and America may for the latest stage be taken as a whole, without that separate treatment, nation by nation, which in the history of earlier times was necessary.

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  • These figures point to the fact that London is essentially a mart, and neither is itself, nor is the especial outlet for, a large manufacturing centre; hence imports greatly exceed exports.

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  • Hence the Mercian king must then have been the overlord of London.

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  • Hence the impression that the true Zulu are far more numerous north of the Limpopo than has ever been the case.

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  • Hence a number of attempts have been made to do without stop-cocks altogether.

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  • Hence, supposing the crystals immediately after their formation to be in absolute contact with one another all round, then, in the case of Class II., such contact will be maintained on cooling, while in the case of Class I.

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  • Hence tin and lead, though very malleable, are little ductile.

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  • Hence 1000Æ is the elongation in millimetres per metre length per kilo.

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  • Hence the space variation of the pressure in any direction, or the pressure-gradient, is the resolved force per unit volume in that direction.

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  • Hence in any infinitesimal part of the fluid the circulation is zero round every small plane curve passing through the vortex line; and consequently the circulation round any curve drawn on the surface of a vortex filament is zero.

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  • His native home was probably Arabia; hence Eridu (" the good city ") and Ur (" the city ") would have been built in Semitic territory, and their population may have included Semitic elements from the first.

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  • Hence the sudden collapse of Assyria when drained of its fighting population in the age of Assur-bani-pal.

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  • Dampf, steam), and hence moisture.

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  • As a verb, the word means to stifle or check; hence damped vibrations or oscillations are those which have been reduced or stopped, instead of being allowed to die out naturally; the "dampers" of the piano are small pieces of feltcovered wood which fall upon the strings and stop their vibrations as the keys are allowed to rise; and the "damper" of a chimney or flue, by restricting the draught, lessens the rate of combustion.

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  • Hence the prophet prophesies of a definite future arising out of and organically connected with the present.

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  • Hence to harmonize such difficulties with belief in God's righteousness, it had to take account of the role of such empires in the counsels of God, the rise; duration and downfall of each in turn, till finally the lordship of the world passed into the hands of Israel, or the final judgment arrived.

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  • - xc. Hence these chapters are earlier than 166 B.C. Chapters cvi.

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  • Hence we shall not be surprised to find that the two tendencies are fully represented in primitive Christianity, and, still more strange as it may appear, that New Testament apocalyptic found a more ready hearing amid the stress and storm of the 1st century than the prophetic side of Christianity, and that the type of the forerunner on the side of its declared asceticism appealed more readily to primitive Christianity than that of Him who came "eating and drinking," declaring both worlds good and both God's.

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  • The tendril or inflorescence, according to the views above explained, though in reality terminal, is bent to one side; hence it appears to be lateral and opposite to the leaf.

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  • 5, 2 and 3) is produced; hence every care should be taken to collect these and burn them.

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  • A native of Apamea in Syria and a pupil of Panaetius, he spent after his teacher's death many years in travel and scientific researches in Spain (particularly at Gades), Africa, Italy, Gaul, Liguria, Sicily and on the eastern shores of the Adriatic. When he settled as a teacher at Rhodes (hence his surname "the Rhodian") his fame attracted numerous scholars; next to Panaetius he did most, by writings and personal intercourse, to spread Stoicism in the Roman world, and he became well known to many leading men, such as Marius, Rutilius Rufus, Pompey and Cicero.

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  • It is thus not only a general word for a prince or sovereign, but also the common word for a feudal superior, and particularly of a feudal tenant holding directly of the king, a baron (q.v.), hence a peer of the realm, a member of the House of Lords, constituted of the lords temporal and the lords spiritual; this is the chief modern usage.

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  • He prepared the cyanhydrins of glucose and fructose, hydrolysed them to the corresponding oxy-acids, from which the hydroxy groups were split out by reduction; it was found that glucose yielded normal heptylic acid and fructose methylbutylacetic acid; hence glucose is an aldehyde alcohol, CH 2 OH (CH OH) 4 CHO, whilst fructose is a ketone alcohol CH 2 OH (CH OH) 3 CO.

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  • Hence it follows that the " optical " formulae of the acids derived from two pentoses having the configuration given above will be C02H - 0 - C02H CO 2 H + 0 - C02H, and that consequently only one of the acids will be optically active.

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  • It can be shown that d-galactose is CH 2 (OH) + - + - COH, and hence d-talose is CH 2 (OH) + - + + COH.

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  • Hence in the latest designs for large factories it has been proposed that as much normal juice as can be extracted by double crushing only shall be treated by itself, and that the megass shall then be soused with twice as much water as there is juice remaining in it; after which, on being subjected to a third crushing, it will yield a degraded juice, which would also be treated by itself.

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  • Hence they are called phyllidia (fig.

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  • Where the soil grains are quite free from each other the smaller grains tend to fill up the spaces between the larger ones; hence it might be concluded that in clays the amount of pore-space would be less than in coarser sands.

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  • The space between the parts of such substances is too large to admit of capillary action; hence the water conveyed to the surface of the soil is prevented from passing upwards any further except by slow evaporation through the mulching layer.

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  • The organisms do not carry on their work in soils deficient in air; hence the process is checked in water-logged soils.

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  • Lime also assists in the decomposition of the organic matter or humus in the soil and promotes nitrification; hence it is of great value after green manuring or where the land contains much humus from the addition of bulky manures such as farm-yard dung.

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  • The foster-brotherhood seems to have been unknown to the Franks and the Anglo-Saxons, the nations in which medieval gilds first appear; and hence Dr Pappenheim's conclusions, if tenable at all, apply only to Denmark or Scandinavia.

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  • Hence they should not be confused with the old gild merchant, which originally comprised both merchants and artisans, and had the whole monopoly of the trade of the town.

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  • In some towns all the crafts were thus consolidated into a single fraternity; in this case a body was reproduced which regulated the whole trade monopoly of the borough, and hence bore some resemblance to the old gild merchant.

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  • It forms colourless, transparent rhombohedra, like those of Iceland spar; the angles are nearly equal to right angles, being 73° 30', so that the crystals look like cubes: hence the name of "cubic saltpetre."

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  • Hence only in exceptional circumstances is it possible to utilize a large class of widely distributed ores, carrying from Io to 35 per cent.

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  • At a boiling heat, zinc chloride dissolves in any proportion of water, and highly concentrated solutions, of course, boil at high temperatures; hence they afford a convenient medium for the maintenance of high temperatures.

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  • A solution of the oxide in the chloride has the property of dissolving silk, and hence is employed for removing this fibre from wool.

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

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  • STEARIC ACID, n-Octodecylic acid CH 3 (CH 2) 16 CO 2 H, an organic acid found as its glyceride stearin, mixed with palmitin and olefin, in most tallows (hence its name, from Gr.

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  • The conductor of the cable is practically insulated, as the condensers in the bridge have a very high resistance; hence no appreciable current ever flows into or out of the line.

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  • Hence, by inserting a break-and-make key in the circuit of the battery, coil or dynamo, the uniform noise or hum in the telephone can be cut up into periods of long and short noises, which can be made to yield the signals of the Morse alphabet.

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  • Hence, when the coil at one fixed station was in action it generated high frequency alternating currents, which were propagated across the air gap between the ordinary telegraph wires and the metallic surfaces attached to one secondary terminal of the induction coil, and conveyed along the ordinary telegraph wires between station and moving train.

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  • Hence devices for detecting the oscillations in the antenna are merely very sensitive forms of ammeter and voltmeter.

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  • In one of these ways the oscillations can be created or stopped at pleasure in the radiating antenna, and hence groups of electric waves thrown off at will.

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  • Hence the following appliance was worked out by Lieutenant Solari and officers in the Italian navy.

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  • Hence it will be seen that the difference between various forms of the so-called spark systems of wireless telegraphy is not very great.

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  • Many herbs have had the power of curing all diseases attributed to them, and have hence had the name of "all-heal"; such have been, among others, the mistletoe, the woundwort (Stachys palustris), the yarrow or milfoil, and the great valerian.

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