Hence Sentence Examples

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

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

Hence the theorem is established.

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.

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.

Hence there are advantages in employing a very loose coupling.

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

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.

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

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.

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

Hence S may be replaced by (Mv) 3.

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

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

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.

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.

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

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.

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.

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.

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.

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.

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

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

Hence nothing in the whole universe can be annihilated.

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

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.

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

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.

Hence obedience was instinctive and initiative almost undreamt of.

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.

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.

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.

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.

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

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.

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

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

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

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.

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

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.

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

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.

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

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.

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

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

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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

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

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.

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

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.

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.

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.

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

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

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

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.

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."

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

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.

Hence arose a double negotiation between him and Eugenius IV.

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

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.

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

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).

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.

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

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.

Hence zinc can only dissolve when some more easily separable.

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.

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

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.

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

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.

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.

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

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.

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.

Hence this product is the required resultant of the three equations.

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.

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).

Hence the theorem of expressibility enunciated above.

Hence the condition is i+k+...

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

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).

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

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

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.

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.

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

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.

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

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.

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.

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

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.

Hence B =µH and I =KH.

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

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.

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

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.

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.

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.

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.

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

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.

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

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

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

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

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.

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

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 ..

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

Hence, as CA increases, viz.

Hence there is much doubt as to his exact meaning.

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.

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) .

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.

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

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.

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.

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.

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

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

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

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.

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

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.

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.

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.

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."

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.

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.

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

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.

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.

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

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

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

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

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

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.

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.

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.

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.

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.

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.

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

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.

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.

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

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

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.

Hence the centre of attraction was now the city with its interests, not the desert.

Hence it is that the Nubians of this district, fairest of all the race, still claim Arab and Osmanli (Bosnian) descent.

Hence the density v is given by 47rabc (x2/a4+y2/b4-I-z2/c4), and the potential at the centre of the ellipsoid, and therefore its potential as a whole is given by the expression, adS Q dS V f r 47rabc r' (x2/a4-I-y2/b4+z2/c4) Accordingly the capacity C of the ellipsoid is given by the equation 1 I J dS C 47rabc Y (x 2 +y 2 + z2) V (x2/a4+y2/b4+z2/c4) (5) It has been shown by Professor Chrystal that the above integral may also be presented in the form,' foo C 2 J o J { (a2 + X) (b +X) (c 2 + X) } (6).

Hence what should be matter of silent religious meditation must now needs be imperilled by exposition in words."

Here it was that Athena helped Bellerophon to bridle Pegasus; and hence she received the epithet of "the Bridler," Chalinitis.

Hence arise the springs which run perennially, several of which have been collected into the gravitation water supplies of the Vignacourt and Fawara aqueducts.

Hence the regulation of the zerethra or subterranean conduits which drained away the overflow southward was a matter of vital importance both to Tegea and to Mantineia, and a cause of frequent quarrels.

Hence the orders issued overnight on the presumption that the main force of the French was retreating to the north and west were allowed to stand, and the whole II.

Hence he was already aware that the French position extended to Roncourt at least, and had despatched a whole division down the valley of the Orne to outflank them.

Of this fact the Germans were well aware, and hence they decided from the first to reduce the place by hunger, calculating that with the extra 150,000 men thrown back upon the fortress, its food supplies could not last very long.

The spines are variously coloured, white and yellow tints predominating, and from the symmetrical arrangement of the areolae or tufts of spines they are very pretty objects, and are hence frequently kept in drawing-room plant cases.

Hence it has been a practice, very extensively followed, to employ cycles or periods, consisting of a moderate number of years, and to distinguish and reckon the years by their number in the cycle.

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

Hence all the elaborate arguments based on the supposition that Moses probably could not write fall to the ground.

Hence it happens that a consular year, generally speaking, comprehends a part not only of two Julian years, but also of two civil years.

Hence the era of Antioch differed from the original era of Alexandria by ten years; but after the alteration of the latter at the accession of Diocletian, the two eras coincided.

Hence W/(W - W,) is the relative density or specific gravity of the body.

Hence X= 3a.

It forms a colourless vitreous mass, hence its name " glacial phosphoric acid."

The amount radiated out in the form of sound waves is deduced, and hence the energy of the stream at any distance is known.

Hence the second clock will gain or lose on the other.

The changes hence involved little real readjustment of industry.

Hence he could only find expression for himself in forms of this or that earlier philosophy, and hence too the frequent formlessness of his own thought, the tendency to relapse into mere impatient despair of ever finding an adequate vehicle for transmitting thought.

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

Hence the name of Gallican is loosely given to all its modern upholders, whether of French nationality or not.

Hence, between hills crowned by frequent feudal castles, it runs by Wimpfen and by Hornberg, where Gdtz von Berlichingen lived, to Eberbach, where it enters the sandstone formation of the Odenwald.

Hence on the one hand it is unreal to lay stress on coincidences with Romans, as if these necessarily implied that both epistles must have been composed shortly after one another, while again the further stage of thought on Christ and the Church, which is evident in Colossians, does not prove that the latter must have followed the former.

The roots are dug up in Mexico throughout the year, and are suspended to dry in a net over the hearth of the Indians' huts, and hence acquire a smoky odour.

In modern political history the expression "cave of Adullam" (hence "Adullamites") came into common use (being first employed in a speech by John Bright on the 13th of March 1866) with regard to the independent attitude of Robert Lowe (Lord Sherbrooke), Edward Horsman and their Liberal supporters in opposition to the Reform Bill of 1866.

It generally happens that much of the mercury column is outside the flask and consequently at a lower temperature than the bulb, hence a correction of the observed temperature is necessary.

P 1 greater than P2, if the molecular weight of A be much less than that of B, then it is obvious that the ratio M 1 P 1 /M 2 P 2 need not be very great, and hence the less volatile liquid B would come over in fair amount.

The great variety in the apparent motions of meteors proves that they are not directed from the plane of the ecliptic; hence their orbits are not like the orbits of planets and short-period comets, which are little inclined, but like the orbits of parabolic comets, which often have great inclinations.

They are flattened organisms provided with two or more suckers, hence their name (7 rpThµarc,8rls, pierced with holes), and are exclusively parasitic both in their earlier and mature stages of life.

Hence the battle has been explained as the necklace myth in epic form.

Hence, if a prism is placed in front of the eye with its base towards the nose, a ray of light falling upon it will be bent inwards, and seem to come from a point farther out from the axis of vision.

Hence in its condition of repose such an eye cannot distinctly see parallel rays from a distance and, still less, divergent rays from a near object.

Hence it is suggested that the attack on Rome was merely an incident of the march of the Etruscans, driven southward by the invasion of upper Italy by the Celts, through Latium on their way to Campania.

Hence the mountain has served as a type for the general popular conception of a volcano, and its history has supplied a large part of the information on which geological theories of volcanic action have been based.

The sub-aquatic habits of the present species probably render such a function impossible, hence the absence of the glands.

Hence, among all the English poets, it is Tennyson who presents the least percentage of entirely unattractive poetry.

Hence it took a prominent part in the Peloponnesian War until the crushing defeat at Idomene (426) crippled its resources.

Hence came his " conversion," and the sense of vocation for the ministry which impelled him in 1822 to enter Manchester College, then lodged at York.

Hence the beliefs he preached were never to him mere speculative ideas, but rather the ultimate realities of being and thought, the final truths as to the character and ways of God interpreted into a law for the government of conscience and the regulation of life.

Hence throughout this season the prevailing winds are light breezes from the west and south.

Hence the skill undoubtedly possessed by several graduates of the defunct art school has to be devoted chiefly to a subordinate purpose, namely, the fashioning of models for metal-casters.

Hence the ware came to be known to Japanese and foreigners alike as Imari-yaki (yaki = anything baked; hence ware).

In a more particular sense, "a liberty" is the term for a franchise, a privilege or branch of the crown's prerogative granted to a subject, as, for example, that of executing legal process; hence the district over which the privilege extends.

Hence both science and religion must come to recognize as the" most certain of all facts that the Power which the Universe manifests to us is utterly inscrutable."Thus to be buried side by side in the Unknowable constitutes their final reconciliation, as it is the refutation of irreligion which consists of" a lurking doubt whether the Incomprehensible is really incomprehensible."Such are the foundations of Spencer's metaphysic of the Unknowable, to which he resorts in all the fundamental difficulties which he subsequently encounters.

Hence the Persistence of Force is the ultimate basis of knowledge.

Hence pleasure is, on the whole, good, and asceticism reprehensible, although in man's case there has arisen (owing to the rapidity of evolution) a certain derangement and divergence between the pleasant and the salutary (§ 39).

Hence the fear with which the political, religious and social controls were regarded came to be associated also with the specifically moral control of lower by higher feelings, and engendered the coercive element in the feeling of obligation.

Hence Spencer concludes that the sense of duty is transitory and must diminish as moralization increases.

Hence the numerous bleachers dwell in the country with their assistants and machinery.

The current, by endosmosis, favours the passage of the solution into the hide-substance, and at the same time appears to assist the chemical combinations there occurring; hence a great reduction in the time required for the completion of the process.

Hence to represent D, Greek has now to resort to the clumsy device of writing NT instead.

Buddhism is a wide departure in doctrine and practice from Brahmanism, and hence after a swift unfolding and quick spread it was driven out of India and had to find a home in other lands.

And if he is the sea-god, we must remember that there is a heavenly as well as an earthly ocean; hence the clouds are sometimes called Tangaloa's ships.

Hence his mistakes though easy to understand are by no means so pardonable as were, for example, those of the Georges, who had been absolute monarchs in their own country.

The smooth, black and brown scales of the back are highly iridescent, hence the generic name of this peculiar snake, which reaches the length of one yard.

In another, probably also egg-eating snake, the Indian teeth, hence the term "proteroglypha," which is intended to mean that the anterior teeth are grooved.

During such periods of excitement it is even able, by the pressure of the muscles on the poison-duct, to eject the fluid to some distance; hence it shares with the cobra a third Dutch name, that of "spuw slang" (spitting snake).

All mixtures whose temperature lies above the line ACB are wholly liquid, hence this line is often called the "liquidus "; all mixtures at temperatures below that of the horizontal line through C are wholly solid, hence this line is sometimes called the " solidus," but in more complex cases the solidus is often curved.

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

Hence the two great forms of prose literature which drew their nourishment from the struggles of political life, oratory and contemporary history, were arrested in their development.

Hence 'the insects may more conveniently be regarded as constituting the single family Phryganeidae.

Hence the immediately beneficial effect produced in the cases of "fainting" or syncope.

Hence the diminished oxidation of the tissues, which leads to the accumulation of unused fat and so to the obesity which is so often seen in those who habitually take much alcohol.

It follows that the drug is an antipyretic, and it is hence largely used in fevers as a means of reducing the temperature.

Hence if the electrified sealing-wax rod makes the leaves collapse, the electroscopic charge is positive, but if the glass rod does the same, the electroscopic charge is negative.

Hence the charge on the conductor can be measured by the number of unit electric tubes springing from it.

Hence when a body is charged positively its potential is raised above that of the earth, and when negatively it is lowered beneath that of the earth.

Hence the total solid angle round any point is 47r.

Hence the forces due to the two areas at opposite ends of the chord are equal and opposed.

Hence we see that if the whole surface of the sphere is divided into pairs of elements by cones described through any interior point, the resultant force at that point must consist of the sum of pairs of equal and opposite forces, and is therefore zero.

Hence if the force is zero the potential V must be constant.

Hence if we distribute electricity.

The above expressions for the capacity of an ellipsoid of three unequal axes are in general elliptic integrals, but they can be evaluated for the reduced cases when the ellipsoid is one of revolution, and hence in the limit either takes the form of a long rod or of a circular disk.

Hence the electric force E in the interspace 1dRccor the potential V at any point in the interspace is given by varies inversely E = as - the distance distance =A/R from or V the - axis.

Hence we have (V 1 - V 2) d=47rQ/S or C= Q/(V i - V 2) = S/47rd (13).

Hence the potential V at the centre of the inner sphere is given by V =Q/R1 - Q/R2+Q/R3.

Hence Qi /CI =Q2/C2 or Q I /Q 2 =C I /C 2.

This unit is too small for practical purposes, and hence a unit of capacity 900,000 greater, called a microfarad, is generally employed.

Hence the flux through dS is qdw.

Hence the total electric flux due to a charge Q through an enclosing surface is 41rQ, and therefore is zero through one enclosing no electricity.

Hence, multiplying these normal forces by the areas of the corresponding faces, we have the total flux parallel to the x-axis given by - (d 2 V/dx 2)dxdydz, and similar expressions for the other sides.

Hence the total flux is - (+ d2V d 2 V d2V dye + dz2) dy dz, dx2 and by the previous theorem this must be equal to 4'rrp dxdydz.

Hence if dS and dS' are the areas of the ends, and +E and - E' the oppositely directed electric forces at the ends of the tube, the surface integral of normal force on the flux over the tube is EdS - E'dS' (20), and this by the theorem already given is equal to zero, since the tube includes no electricity.

Hence the characteristic quality of a tube of electric force is that its section is everywhere inversely as the electric force at that point.

Hence we have - dV /dn = 4lra or a = - (1 /47r) dV /dn = E/42r.

If a is the surface density and dS an element of surface, then fadS is the whole charge, and hence afV adS is the expression for the energy of charge of a conductor.

Hence that distribution of potential which is neces 1 See Maxwell, Electricity and Magnetism, vol.

Hence this charge is the electrical image of the charge +q at A in the spherical surface.

Hence there is no need to reject the tradition as to the existence of a written Targum on Job in the time of Gamaliel I.

Hence we find various expedients adopted in the Targums for avoiding any reference to the Deity, which might be misunderstood by the people, or which involved apparent irreverence.

But the authority enjoyed by the latter rendered it secure against any encroachments; hence any later expansions, especially those of a popular Haggadic character, naturally found their way into the less stereotyped Targum Jerushalmi.

Hence it is proper to separate emigration from immigration.

Hence, probably, the wide popularity which his works enjoyed in the 18th century; and hence the agreeable feeling with which, notwithstanding all their false taste and their tiresome digressions, they impress the modern reader.

Hence any impurity which diminishes the surface tension of the water will diminish the size of the drop (unless the density is proportionately diminished).

Hence the conflict which made Trajan appear in the eyes of Christians like Tertullian the most infamous of monsters.

Hence the association of Christmas with "Santa Claus," an American corruption of the Dutch form "San Nicolaas," the custom being brought to America by the early Dutch colonists.

Small quantities are occasionally met with in iron pyrites, and hence tellurium is found with selenium in the flue dust, or chamber deposits of sulphuric acid works.

One of its companies carried a number of gamecocks said to have been the brood of a blue hen; hence the soldiers, and later the people of the state, have been popularly known as the " Blue Hen's Chickens."

Hence "to cash" means to convert cheques and other negotiable instruments into coin.

Hence any writer who would appeal to them was obliged to do so in the name of some great figure of the past.

Hence we conclude that the grounds are lacking which would entitle our assuming a priori that the Apocalypse is pseudonymous.

Hence their tidal conditions are quite oceanic, though their salinity is usually rather lower than that of ocean water.

Hence the geoid or figure of the sea-surface is not part of an ellipsoid of rotation but is irregular.

During the rapid formation of ice the still unfrozen brine is often imprisoned between the little plates of frozen water; hence without some special treatment sea-ice is not suitable as a source of drinking water.

Ice is a very poor conductor of heat and accordingly protects the surface of the water beneath from rapid cooling; hence new-formed pancake ice does not increase excessively in thickness in one winter, and even in the centre of the Arctic Basin the ice-covering only amounts to 6 or at most 9 ft.

One of the indirect methods of investigating currents is by taking account of the initial temperature of the current and following it by the thermometer throughout its course; hence the familiar contrast between warm and cold currents, of which the Gulf Stream and the Labrador current are types.

We must remember that the ocean is a continuous sheet of water of a certain depth, and the conditions of continuity which hold good for all fluids require that there should be no vacant space within it; hence if a single water particle is set in motion, the whole ocean must respond, as Varenius pointed out in 1650.

This deflecting force is directly proportional to the velocity and the mass of the particle and also to the sine of the latitude; hence it is zero at the equator and comes to a maximum at the poles.

For this reason the up-welling coastal water is coldest close to the shore, and hence it only appears on the Somali coast during the south-west monsoon.

Hence a strong surface current sets inwards through the Straits of Bab-el-Mandeb and Gibraltar, while an undercurrent flows outwards, raising the temperature and salinity of the ocean for a long distance beyond the straits.

Hence he began to study the New Testament.

Oaths and the taking of life were absolutely forbidden; hence the magistracy and the army were for the Mennonite unlawful callings; but magistrates were to be obeyed in all things not prohibited by Scripture.

Hence arose the famous secret correspondence of Mercy-Argenteau, an invaluable record of all the details of Marie Antoinette's life from her marriage in 1770 till the death of Maria Theresa in 1780.

It follows that the average distance apart of the molecules in the gaseous state is roughly ten times as great as in the solid or liquid state, and hence that in the gaseous state the molecules are at distances apart which are large compared with their linear dimensions.

The ruined city of Kherla formed the seat of government under the Gonds and preceding rulers, and hence the district was, until the time of its annexation to the British dominions, known as the "Kherla Sarkar."

The town of Multai contains an artificial tank, from the centre of which the Tapti is said to take its rise; hence the reputed sanctity of the spot, and the accumulation of temples in its honour.

The land molluscs show relationship with the Indian and the Malayan sub-regions; but many forms have here their centre, and have spread hence into Australia and the Pacific islands.

Hence so long as the consuls were the only higher magistrates their frequent absence often rendered the appointment of a praefect necessary, but after the institution of the praetorship (367 B.C.) the necessity only arose exceptionally, as it rarely happened that both the consuls and the praetor were absent simultaneously.

Further, the praetorian praefect acquired, in addition to his military functions, a criminal jurisdiction, which he exercised not as the delegate but as the representative of the emperor, and hence it was decreed by Constantine (331) that from the sentence of the praetorian praefect there should be no appeal.

In early life he was a weaver, hence the punning description of him as Weevir, rex philosophorum.

Hence, whatever we begin by saying, we must ultimately say ` mind ' " (Caird, Kant, 1.443) While the form in which these doctrines were stated proved fatal to them in the country of their birth, they took deep root in the next generation in English philosophy.

Hence, when in 1850 a hydraulic installation was required for a new ferry station at New Holland, on the Humber estuary, the absence of water mains of any kind, coupled with the prohibitive cost of a special reservoir owing to the character of the soil, impelled him to invent a fresh piece of apparatus, the "accumulator," which consists of a large cylinder containing a piston that can be loaded to give any desired pressure, the water being pumped in below it by a steam-engine or other prime mover.

Hence he spoke of the "Indies," and "las Indies" continued to be the official name given to their American possessions by the Spaniards for many generations.

As the tangent sight was placed in the line of metal, hence directly over the cascable, very little movement could be given to it, so that a second sight was required for long ranges.

There was a danger of admitting Gentile converts to the church on too easy moral terms; hence the need of such insistence on the ideal as in The Two Ways and the Mandates.

Hence in Chrismann (who is in other respects the most definite of the three) we have a view of dogma almost as clear-cut as that of the Protestant schoolmen.

Hence Catholic, and scientific or historical, definitions of dogma are on different planes.

Hence they and other authorities wish to see " History of Dogma " supplemented by " Histories of Theology."

Hence an important form of literary activity came to be the translation of the homilies approved by the church into the vernacular.

Hence Plato in the Sophist describes the Megarians as "the friends of ideas."

They spent their energy in attacking Plato and Aristotle, and hence earned the opprobrious epithet of Eristic. They used their dialectic subtlety to disprove the possibility of motion and decay; unity is the negation of change, increase and decrease, birth and death.

Hence he never attained to that perfect idiomatic purity of style, which was the special glory of the early writers of comedy, Naevius and Plautus.

Hence his ability to concentrate hung on the mere good luck of obtaining timely information of Napoleon's plans, which in fact he failed to obtain.

Hence the first orders he issued were for his divisions to concentrate at their respective alarm-posts, intending later to send them further orders when the situation had somewhat cleared up. For whatever reasons, Wellington thought Napoleon would attempt to turn his right and cut his line of communications.

Ideas or notions are never true, but only probable; nevertheless, there are degrees of probability, and hence degrees of belief, leading to action.

There were special privileges surrounding tenancies of these lands, such as freedom from tolls and duties, exemption from danegeld and amercement, from sitting on juries, &c. Hence, the phrase "ancient demesne" came to be applied to the tenure by which the lands were held.

Hence there is confusion on every side; it is difficult to distinguish between various sects and to determine their exact opinions or the circumstances under which they came into being.

Like St Francis, Waldo adopted a life of poverty that he might be free to preach, but with this difference that the Waldenses preached the doctrine of Christ while the Franciscans preached the person of Christ, Waldo reformed teaching while Francis kindled love; hence the one awakened antagonisms which the other escaped.

Hence the new phenomenon of written prophecies.

Hence the name of lustrum came to denote the intercensal term, or a period of five years.

Hence the protests of those who believed that the figures for population were too small swelled into a general chorus of dissatisfaction.

Hence a complaint that the population is overstated is seldom heard, and hence, also, popular charges of an undercount afford little evidence that the population was really larger than stated by the census.

Hence there is no such basis as exists in nearly every other civilized state for a national system of registration, and the country depends upon the crude method of enumerators' returns for its information on vital statistics, except in the states and cities which have established a trustworthy registration system of their own.

Hence, by (i) and (ii), the formula holds for this figure.

Hence the required area is double the area of the remainder of the triangle, and therefore it is two-thirds of the area of the triangle.

Hence the area of an ellipse whose axes are 2a and 2b is Trab; and the volume of an ellipsoid whose axes are 2a, 2b and 2c is t rabc. The area of a strip of an ellipse between two lines parallel to an axis, or the volume of the portion (frustum) of an ellipsoid between two planes parallel to a principal section, may be found in the same way.

Hence the volume of each element of the solid figure is to be found by multiplying the area of the corresponding element of the trapezette by 1, and therefore the total volume is 1 X area of trapezette.