Corresponding Sentence Examples

They are violet-red in colour, and on boiling or long standing with dilute acids they pass into the corresponding roseo-salts.

Cremona's reputation had now become European, and in 1879 he was elected a corresponding member of the Royal Society.

After that, most of Europe will be corresponding more or less to international borders, so I'll wait for further comment from Engels before going further.

It is estimated that Sardinia pays, in local and general, direct and indirect taxation of all kinds, 23,000,000 lire (920,000), a sum corresponding to 35.44 lire per head.

The growth of a special " original " jurisdiction at Constantinople, which perhaps developed earlier than the corresponding institution at Rome, may be traced to the fact that bishops from all parts were constantly in Constantinople.

Indicator diagram corresponding to 1 lb.

In a general sense, the word means having two corresponding parts or in duplicate.

This compound gives a blue potassiumand lithium-ultramarine when treated with the corresponding chloride, and an ethyl-ultramarine when treated with ethyl icdide.

Each definition gives rise to a corresponding algebra of higher complex numbers.

Recognizing that ownership by a small payment only, not corresponding to the value of the land, it left the larger part of the income to meet the need which had arisen.

In this way the feudal county, or duchy, formed itself, corresponding in most cases only roughly to the old administrative divisions of the state, for within the bounds of the county there had often formed private feudal possessions too powerful to be forced into dependence upon the count, sometimes the vice-comes had followed the count's example, and often, on the other hand, the count had attached to his county like private possessions of his own lying outside its boundaries.

By the reduction of nitro-phenols, the corresponding aminophenols are obtained, and of these, the metaand para-derivatives are the most important.

After promising fidelity and the abandonment of the Scots marriage scheme, Cecil took him corresponding with Mary and tampering with the Ridolfi plot.

In any case, only the eastern districts would have been affected by invaders from over the Rhine, the chief seat of the Belgae proper being in the west, the country occupied by the Bellovaci, Ambiani and Atrebates, to which it is probable (although the reading is uncertain) that Caesar gives the distinctive name Belgium (corresponding to the old provinces of Picardy and Artois).

A male Pales was sometimes spoken of, corresponding in some respects to Pan; the female Pales was associated with Vesta and Anna Perenna.

Of this the part corresponding to lines 790820 exists also in the original Old Saxon.

The suspicion of some earlier scholars that the Praefatio and the Versus might be a modern forgery is refuted by the occurrence of the word vitteas, which is the Old Saxon fittea, corresponding to the Old English fitt, which means a "canto" of a poem.

The esters of the acid may be obtained by distilling a mixture of the sodium or potassium salts and the corresponding alcohol with hydrochloric or sulphuric acids.

Epsom salts crystallizes in the orthorhombic system, being isomorphous with the corresponding zinc and nickel sulphates, and also with magnesium chromate.

The oxides of type RO are soluble in water, the solution possessing a strongly alkaline reaction and rapidly absorbing carbon dioxide on exposure; they are basic in character and dissolve readily in acids with the formation of the corresponding salts.

This pad varies much; it is morphologically the homologue of the pair of basiventral elements which by their lateral extension give origin to the corresponding ribs.

Mailer introduced the terms Polymyodi and Tracheophones, Huxley that of Oligomyodi; Mailer himself had, moreover, pointed out the more important characters of the mode of insertion, but it was Garrod who invented the corresponding terms of Acro- and Mesomyodi (= Tracheophones+Oligomyodi).

The Copley medal was conferred upon him in 1823, and the Lalande prize in 1817 by the Paris Academy, of which he was a corresponding member.

The corresponding border town on the Syrian side is represented by the picturesque and finely preserved ruins called Salahiya, the Ad-dalie or Dalie (Adalia) of Arabic times, two days below Deir, whose more ancient name is as yet unknown.

The city 1 The state of Panama, with boundaries nearly corresponding to those of the present republic, and including the province of Panama and other provinces, was created in 1855 by legislative enactment.

The coal is here confined to the lower division of the system; the Upper Carboniferous (corresponding with the English Coal-Measures) is exclusively marine, consisting chiefly of Fusulina limestone.

This act liberated the serfs from a yoke which was really terrible, even under the best landlords, and from this point of view it was obviously an immense benefit.2 But it was far from securing corresponding economic results.

In the latest years in which comparisons can be made, the passenger journeys in the United Kingdom amounted to 1500 millions (including season-ticket holders, estimated) and the train n iles to 428.3 millions, while the corresponding figures in the United States were 873.9 millions and 1171.9 millions.

There are two main ways of attaching the rails to the sleepers, corresponding to two main types of rails - the bull-headed rail A B FIG.

The draught corresponding to the smallest rate of combustion shown in Table XX.

The form of the torque curve, or crank effort curve, as it is sometimes called, is discussed in the article Steam Engine, and the torque curve corresponding to actual indicator diagrams taken from an express passenger engine travelling at a speed of 65 m.

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.

The corresponding boiler efficiencies are given in the third column of the table, when they are known, and the combined efficiencies in the fourth column.

From the diagram it will be seen that the corresponding efficiency of the ideal engine is about 0.18.

Lines representing efficiency ratios of o 6, 0.5 and 0.4 are plotted on the diagram, so that the efficiency ratios corresponding to the various experiments plotted may be readily read off.

In a particular case where the boiler pressure was maintained constant at 130 lb per square inch, and the cut-off was approximately 20% of the stroke, the values c =55 and b=o 031 were deduced, from which it will be found that the value of the piston speed corresponding to the maximum horsepower is 887 ft.

The orders actually granted have allowed 50 lb, 56 lb, 60 lb and 70 lb rails, with corresponding axle loads of 10, 12, 14 and 16 tons.

Corresponding to heaven, the abode of the righteous, we have Ge-henna (originally Ge-Hinnom, the scene of the Moloch rites of human sacrifice), the place of punishment after death for apostate Jews.

In February 1845 he received the announcement of his election as corresponding member of the French Institute in place of the Spanish historian Navarrete, and also of the Royal Society of Berlin.

But the heads of the church carried the day, and, more stringent measures being adopted against dissenters, Schwenkfeld left Strasburg for a time, residing in various cities of south Germany and corresponding with many nobles.

This tribe, called Bruttii and Brittii in Latin inscriptions, and Bpirrtot on Greek coins and by Greek authors, occupied the south-western peninsula of Italy in historical times, the ager Bruttius (wrongly called Bruttium) corresponding almost exactly to the modern Calabria.

The supreme governing authority was vested in magistrates called Cosmi, answering in some measure to the Spartan Ephori, but there was nothing corresponding to the two kings at Sparta.

In 1642 Henderson, whose policy was to keep Scotland neutral in the war which had now broken out between the king and the parliament, was engaged in corresponding with England on ecclesiastical topics; and, shortly afterwards, he was sent to Oxford to mediate between the king and his parliament; but his mission proved a failure.

The rapid extension of tobacco culture was accompanied by a corresponding growth in the manufacture of chewing and smoking tobacco and snuff, and some of the brands have a wide reputation.

The vowels play no part in differentiating the roots, for the vowels are practically the same in the corresponding forms of every root.

It would appear probable, however, that the former of these words was derived from an Assyrian or Hebrew root, which signifies the west or setting sun, and the latter from a corresponding root meaning the east or rising sun, and that they were used at one time to imply the west and the east.

This diminution of pressure, which continues as the heat increases till it reaches its maximum in July soon after the solstice, is followed by the corresponding development of the south-west monsoon; and as the barometric pressure is gradually restored, and becomes equalized within the tropics soon after the equinox in October, with the general fall of temperature north of the equator, the south-west winds fall off, and are succeeded by a north-east monsoon, which is developed during the winter months by the relatively greater atmospheric pressure which then occurs over Asia, as compared with the equatorial region.

Such a reduction of temperature is brought about along the greater part of the coasts of India and of the BurmoSiamese peninsula by the interruption of the wind current by continuous ranges of mountains, which force the mass of air to rise over them, whereby the air being rarefied, its specific capacity for heat is increased and its temperature falls, with a corresponding condensation of the vapour originally held in suspension.

There is also a corresponding diffusion o f Japanese and Chinese forms along this zone, these being most numer - ous in the eastern Himalaya, and less frequent in the west.

The latter, corresponding substantially to the present province of West Prussia, remained subject to Poland until 1309, when it was divided between Brandenburg and the Teutonic Order.

They are disposed in two groups on either side, corresponding in the Polychaeta to the parapodia; the two bundles are commonly reduced among the earthworms to two pairs of setae or even to a single seta.

In Hyperiodrilus the whole spermatheca is thus included in a corresponding sac, which is of great extent.

We have thus the replacement of a spermatheca, corresponding to those of the remaining families of Oligochaeta, and derived, as is believed, from the epidermis, by a structure performing the same function, but derived from the mesoblastic tissues, and with a cavity which is coelom.

The sole difference is therefore that in Eudrilus the ovarian sac gives rise to a tube which bifurcates, one branch meeting a corresponding branch of the other ovary of the pair, while the second branch reaches the exterior.

It is an oxide of iron having the formula Fe 3 O 4, corresponding with 72.4% of metal, whence its great value as an ore.

The early divisions of the county were known as wapentakes, five being mentioned in Domesday, while 13th-century documents mention seven wapentakes, corresponding with the six present hundreds, except that Repton and Gresley were then reckoned as separate divisions.

He derives his name Climax (or Climacus) from his work of the same name (KMµa 701i Ilapa5Eivov, ladder to Paradise), in thirty sections, corresponding to the thirty years of the life of Christ.

Corresponding to Proserpine as goddess of the dead is the old Norse goddess Hel (Gothic Halja), whom Saxo Grammaticus calls Proserpine.

The Highland Society having early extended its operations to the whole of Scotland, by and by made a corresponding addition to its title, and as the Highland and Agricultural Society of Scotland gradually extended its operations.

When the shell is sinistral the asymmetry of the organs is usually reversed, and there is a complete situs inversus viscerum, the direction of the spiral of the shell corresponding to the position of the organs of the body.

The siphon is an incompletely tubular outgrowth of the mantle margin on the left side, contained in a corresponding outgrowth of the edge of the shell-mouth, and serving to conduct water to the respiratory cavity.

This is a groove, the edges of which are raised and ciliated, lying near the branchial plume in the genera which possess that organ, whilst in Firoloida, which has no branchial plume, the osphradium occupies a corresponding position.

As happened at every stage of Napoleon's advancement, the states tributary to France underwent changes corresponding to those occurring at Paris.

Here Arsaces and his brother Tiridates are derived from the royal house of the Achaemenids, probably from Artaxerxes II.; the young Tiridates is insulted by the prefect Agathocles or Pherecles; in revenge the brothers with five companions (corresponding to the seven Persians of Darius) slay him, and Arsaces becomes king.

The demiurge of the Mandaeans, and corresponding to the Ialdabaoth of the Ophites, he at the instance of his father frames the earth and men - according to some passages in conjunction with the seven bad planetary spirits.

The legs, wings and other organs of the trunk receive their nerves from the thoracic and abdominal ganglia, and the fusion of several pairs of these ganglia may be regarded as corresponding to a centralization of individuality.

Moreover, in many insects with imperfect metamorphosis the change from larva or (as the later stage of the larva is called in these cases) nymph to imago is about as great as the corresponding change in the Holometabola, as the student will recognize if he recalls the histories of Ephemeridae, Odonata and male Coccidae.

In 1828 James Wilson (author of the article Ornithology in the 7th and Wilson 8th editions of the present work) began, under the title of Illustrations of Zoology, the publication of a series of his own drawings (which he did not, however, himself engrave) with corresponding letterpress.

But, relieved as it may be by reflections of this kind - dreams some may perhaps still call them - the study of ornithology has unquestionably become harder and more serious; and a corresponding change in the style of investigation, followed in the works that remain to be considered, will be immediately perceptible.

Thus the Mintra of the Malay Peninsula have a demon corresponding to every kind of disease known to them; the Tasmanian ascribed a gnawing pain to the presence within him of the soul of a dead man, whom he had unwittingly summoned by mentioning his name and who was `devouring his liver; the Samoan held that the violation of a food tabu would result in the animal being formed within the body of the offender and cause his death.

Corresponding to the animal guardian of the ordinary man, we have the familiar of the witch or wizard.

In modern spiritualism the familiar is represented by the "guide," corresponding to which we have the theosophical "guru."

A new form had therefore to be invented for the genuine b in Slavonic, to which there was, at the period when the alphabet was adopted, no corresponding sound in Greek.

Potassium cyanide reacts with this acid to form the corresponding dinitrile, which is converted by hydrochloric acid into citric acid.

The instrument can be provided with a curve or table showing the current corresponding to each angular displacement of the torsion head.

Each instrument is accompanied by a pair of weights and by a square root table, so that the product of the square root of the number corresponding to the position of the sliding weight and the ascertained constant for each weight, gives at once the value of the current in amperes.

Of remains of the Roman period, however, there are none above ground, though various discoveries have been made from time to time within the city walls, the modern streets corresponding more or less, as it seems, with the ancient lines.

The corresponding decomposition of a glyceride into an acid and glycerin takes place when the glyceride is distilled in superheated steam, or by boiling in water mixed with a suitable proportion of caustic potash or soda.

All the bones of the limbs are separate, and those of the carpus and tarsus do not alternate; that is to say, each one in the upper row is placed immediately above the corresponding one in the row below.

Towards the end of the 8th century they aided Charlemagne in putting an end to the Avar kingdom, and were rewarded by receiving part of it, corresponding to North Hungary, as a fief of the German emperor, whose supremacy they also acknowledged more or less for their other possessions.

When very young he showed his interest in the past history of his native land, and in 1617, at the age of twenty-three, he had set to work looking through archives, copying charters, and corresponding with the principal men of learning of his time, the brothers Dupuy, Andre Duchesne and Jean Besly, whom he visited in Poitou.

As the immediate result of this change the offices of heads of departments in Berar, except the j udicial commissionership and the conservatorship of forests, were amalgamated with the corresponding appointments in the Central Provinces, and Berar is now treated as one of the divisions of that province for purposes of revenue administration, with a divisional commissioner as its immediate head.

This acid gives with silver nitrite the corresponding nitromalonic acid, which readily yielded the third nitromethane, CHaHb(N02),Hd, also identical with the first.

Moreover, while methylamine, dimethylamine, and trimethylamine increase in basicity corresponding to the introduction of successive methyl groups, phenylamine or aniline, diphenylamine, and triphenylamine are in decreasing order of basicity, the salts of diphenylamine being decomposed by water.

This latter compound may be chlorinated to perchloracetoacrylic chloride (9), from which the corresponding acid (to) is obtained by treatment with water; alkalis hydrolyse the acid to chloroform and dichlormaleic acid (I I).

A doubly linked pair of atoms is denoted by the sign A with the index corresponding to the side; if there are two pairs of double links, then indices corresponding to both sides are employed.

But, at the same time, the constants in the above relation are not identical with those in the corresponding relation empirically deduced from observations on fatty hydrocarbons; and we are therefore led to conclude that a benzene union is considerably more stable than an ethylene union.

Thelfirst four substances are readily formed from, and converted into, the corresponding dihydroxy open-chain compound; these substances are truly aliphatic in character.

H C corresponding to paroxazine (para-oxazine).

The specific heat of indium is o 057; and the atomic heats corresponding to the atomic weights 38, 76 and 114 are 3.2, 4.3, 6.5.

Certain regularities attend the corresponding property of the melting-point.

This is true of the fatty acid series, and the corresponding ketones and alcohols, and also of the succinic acid series.

Obviously equimolecular surfaces are given by (Mv) 3, where M is the molecular weight of the substance, for equimolecular volumes are Mv, and corresponding surfaces the two-thirds power of this.

If the crystal structure be regarded as composed of 0 three interpenetrating point systems, one consisting of sulphur atoms, the second of four times as many oxygen atoms, and the third of twice as many potassium atoms, the systems being so arranged that the sulphur system is always centrally situated with respect to the other two, and the potassium system so that it would affect the vertical axis, then it is obvious that the replacement of potassium by an element of greater atomic weight would specially increase the length of w (corresponding to the vertical axis), and cause a smaller increase in the horizontal parameters (x and 1/ '); moreover, the increments would advance with the atomic weight of the replacing metal.

If, on the other hand, the sulphur system be replaced by a corresponding selenium system, an element of higher atomic weight, it would be expected that a slight increase would be observed in the vertical parameter, and a greater increase recorded equally in the horizontal parameters.

There is a ladies' branch of the Kennel Club, and the corresponding clubs in America are the Ladies' Kennel Association of America and the Ladies' Kennel Association of Massachusetts.

At Montevecchio he lived contentedly among his books, in the neighbourhood of his two friends, Pico at Querceto, and Poliziano at Fiesole, cheering his solitude by playing on the lute, and corresponding with the most illustrious men of Italy.

In the more recent hymns of the Rig-Veda and in later India, on the other hand, only evil spirits are understood by asuras, while in Iran the corresponding word ahura was, and ever has continued to be, the designation of God the Lord.

There has been no agricultural advance corresponding to that which has taken place in Orkney, mainly owing to the poverty and insufficiency of the soil.

When a number of specimens have to be submitted to pressure, ventilation is secured by means of frames corresponding in size to the drying paper, and composed of strips of wood or wires.

When adjacent burial areas belonged to members of the same Christian confraternity, or by gift or purchase fell into the same hands, communications were opened between the respective cemeteries, which thus spread laterally, and gradually acquired that enormous extent which, " even when their fabulous dimensions are reduced to their right measure, form an immense work."' This could only be executed by a large and powerful Christian community unimpeded by legal enactments or police regulations, " a living witness of its immense development corresponding to the importance of the capital."

Owen for that division of ungulate mammals in which the toe corresponding to the middle (third) digit of the human hand and foot is symmetrical in itself, and larger than those on either side (when such are present).

During the American military occupation of the island in 1899-1902, of the total imports 45.9% were from the United States, 14 from other American countries, 15 from Spain, 14 from the United Kingdom, 6 from France and 4 from Germany; of the exports the corresponding percentages for the same countries were 70.7, 2, 3, To, 4 and 7.

The corresponding figures for Spain were $7,265,142 and $20,035,183; and for the United Kingdom, $714,837 and $11,971,129, the trade with other countries being of much less amount.

This position he founded on the law of wages formulated by Ricardo, and accepted by all the leading economists, that wages are controlled by the ordinary relations of supply and demand, that a rise in wages leads to an increase in the labouring population, which, by increasing the supply of labour, is followed by a corresponding fall of wages.

Its salts may be obtained in some cases by heating the corresponding nitrates, but the method does not give good results.

This relation-number is the ordinal number corresponding to n; let it be symbolized by it.

Thus, corresponding to the cardinal numbers 2, 3, 4.

The definitions of the finite ordinals can be expressed without use of the corresponding cardinals, so there is no essential priority of cardinals to ordinals.

Similarly, a class of serial relations, called well-ordered serial relations, can be defined, such that their corresponding relation-numbers include the ordinary finite ordinals, but also include relation-numbers which have many properties like those of the finite ordinals, though the fields of the relations belonging to them are not finite.

Similarly, the other rational integers must be distinguished from the corresponding cardinals.

Similarly, any rational real number is distinct from the corresponding rational number.

In exchange for the subsistence of the French troops of occupation, a corresponding number of these new levies were moved to the south of France, where they commenced to arrive at.

On the morrow after the sabbath a wave offering and also a burnt offering of the he-lamb (with the corresponding meal and drink offering).

These were presented in the month Rajab, corresponding to Nisan (Smith, Religion of Semites, p. 210).

The first three form together a progressive introduction to Christianity corresponding to the stages through which the Aim7ns passed at Eleusis - purification, initiation, revelation.

The climate of the east coast is on the whole considerably more arctic than that of the west coast on corresponding latitudes; the land is much more completely snowcovered, and the snow-line goes considerably lower.

What Cardiff lacks is a corresponding import trade, for its imports in 1906 amounted to only 2,108,133 tons, of which the chief items were iron ore (8 9 5,610 tons), pit-wood (303,407), grain and flour (298,197).

They are separated from the minerals by converting them into oxalates, which by ignition give the corresponding oxides.

When they are arranged in uniserial or biserial rows the genital ducts open into or near the branchial grooves in the region of the pharynx and in a corresponding position in the post-branchial region.

Corresponding with this result we find that the freezing point of dilute solutions indicates that two pressure-producing particles per molecule are present.

In order that this should hold, we have seen that a considerable quantity of acetic acid must be present, so that a corresponding amount of the salt will be decomposed, the quantity being greater the less the acid is dissociated.

Now a well-known relation connects the available energy of a reversible system with the corresponding change in its total internal energy.

Thus, if L denote the heat corresponding with the chemical changes associated with unit electric transfer, Le will be the heat corresponding with an electric transfer e, and will also be equal to the change in internal energy of the cell.

In 1753 he was elected a corresponding member of the Paris Academy of Sciences, and shortly afterwards he became professor of philosophy in the Barnabite College of St Alexander at Milan.

An Orthodox bishop, vested for the holy liturgy, wears over his cassock - (i) the rnxcipcov, or alb (q.v.); the E7nrpay,Acov, or stole (q.v.); (3) the a narrow stuff girdle clasped behind, which holds together the two vestments above named; (4) the E7 n, uaviexa, liturgical cuffs, corresponding, possibly, to the pontifical gloves of the West;' (5) the i 7rtyovarcov, a stiff lozengeshaped piece of stuff hanging at the right side by a piece of riband from the girdle or attached to the o-AKKos, the equivalent of the Western maniple (q.v.); (6) the like the Western dalmatic (q.v.), worn instead of the 4acv6Acov, or chasuble; (7) the c?µocp6pcov, the equivalent of the Western pallium (q.v.).

In the Protestant Churches 2 the custom as to vestments differs widely, corresponding to a similar divergence in tradition and teaching.

Two such folds maybe distinguished, corresponding on a smaller scale to the belt of alpine tracts which fringe the plateau on the north-west.

The ventral valve in many of the genera is provided with two curved hinge-teeth, which fit into corresponding sockets in the opposite valve, so that the valves cannot be separated without breaking one of the teeth.

This determinant and that associated with Aik are termed corresponding determinants.

Let the determinant of the b's be Ab and B rs, the minor corresponding to b rs .

It will be a useful exercise for the reader to interpret the corresponding covariants of the general quantic, to show that some of them are simple powers or products of other covariants of lower degrees and order.

Putting n equal to co, in a generating function obtained above, we find that the function, which enumerates the asyzvgetic seminvariants of degree 0, is 1 1-z2.1-z3.1-z4....1-z0 that is to say, of the weight w, we have one form corresponding to each non-unitary partition of w into the parts 2, 3, 4,...0.

In General It Is A Seminvariant Of Degrees 0, 0', And Weight 0 0' S; To This There Is An Exception, Viz., When 0=O, Or When 0'=O, The Corresponding Partial Degrees Are 1 And 1.

The linear transformation replaces points on lines through the origin by corresponding points on projectively corresponding lines through the origin; it therefore replaces a pencil of lines by another pencil, which corresponds projectively, and harmonic and other properties of pencils which are unaltered by linear transformation we may expect to find indicated in the invariant system.

Or, instead of looking upon a linear substitution as replacing a pencil of lines by a projectively corresponding pencil retaining the same axes of co-ordinates, we may look upon the substitution as changing the axes of co-ordinates retaining the same pencil.

As new axes of co-ordinates we may take any other pair of lines through the origin, and for the X, Y corresponding to x, y any new constant multiples of the sines of the angles which the line makes with the new axes.

The uppermost lock is St John's, below Lechlade; the lowest is Richmond, but this is a half-tide lock, keeping the water above at a level corresponding to half that of flood tide.

The corresponding hydrate, Pb(OH)2, is obtained as a white crystalline precipitate by adding ammonia to a solution of lead nitrate or acetate.

This salt gives the corresponding chloride and fluoride with hydrochloric and hydrofluoric acids, and the phosphate, Pb(HP04)2, with phosphoric acid.

Sulphurous acid reduces it to the corresponding dihydroxy compound.

The corresponding value of the solar parallax is 8.782".

The sum of the corresponding numbers multiplied by 332600 gives Log.

In practice it is usual to standardize or " calibrate " the galvanometer by causing a known change of induction to take place within a standard coil connected with it, and noting the corresponding deflection on the galvanometer scale.

Let s be the area of a single turn of the standard coil, n the number of its turns, and r the resistance of the circuit of which the coil forms part; and let S, N and R be the corresponding constants for a coil which is to be used in an experiment.

Then if a known change of induction SB a inside the standard coil is found to cause a throw of d scale-divisions, any change of induction SB through the experimental coil will be numerically equal to the corresponding throw D multiplied by snRBa/SNrd.

The closed figure a c d e a is variously called a hysteresis curve or diagram or loop. The area f HdB enclosed by it represents the work done in carrying a cubic centimetre of the iron through the corresponding magnetic cycle; expressed in ergs this work is I HdB.

Steinmetz's formula may be tested by taking a series of hysteresis curves between different limits of B,' measuring their areas by a pianimeter, and plotting the logarithms of these divided by 47r as ordinates against logarithms of the corresponding maximum values of B as abscissae.

The actual experiment to which it relates was carried only as the point marked X, corresponding to a magnetizing force of 65, and an induction of nearly 17,000.

Rowland, believing that the curve would continue to fall in a straight line meeting the horizontal axis, inferred that the induction corresponding to the point B-about 17,500-was the highest I Phil.

The greatest weight supported in the experiments was 14,600 grammes per square cm., and the corresponding induction 18, Soo units.

Thus any desired number of corresponding values of H and B can be easily and quickly found.

But this " critical value " of the force is found to depend in an unexpected manner upon the hardness of the steel; the critical value diminishes as the hardness becomes greater up to a certain point, corresponding to a yellow temper, after which it increases and with the hardest steel becomes very high.

Heydweiller, 2 which appeared to indicate a reversal in weak fields (corresponding to I= 5, or thereabouts), have been shown by Honda and Shimizu to be vitiated by the fact that his specimen was not initially in a magnetically neutral state; they found that when the applied field had the same direction as that of the permanent magnetization, Heydweiller's fallacious results were easily obtained; but if the field were applied in the direction opposite to that of the permanent magnetization, or if, as should rightly be the case, there were no permanent magnetization at all, then there was no indication of any Villari reversal.

The anticipated reversal was duly found by Chree, the critical point corresponding, under the moderate stress employed, to a field of about 120 units.

When the curve after its steep descent has almost reached the axis, it bends aside sharply and becomes a nearly horizontal straight line; the authors suggest that the critical temperature should be defined as that corresponding to the point of maximum curvature.

After this operation had been repeated a few times the iron was found to have acquired a stable condition, and the curves corresponding to the two temperatures became perfectly definite.

The values of the permeability corresponding to the highest and lowest temperatures are given in the following table.

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

The corresponding appendages are marked with the same Roman numeral.

The entosternite was probably in origin part of the fibrous connective tissue lying close to the integument of the sternal surface - giving attachment to muscles corresponding more or less to those at present attached to it.

In 1912 in the corresponding area there were 98 secondary schools with 22,600 pupils, one per 26,000 inhabitants (in Germany one per 54,000).

Darzens (Comptes Rendus, 1904, 139, p. 1214) prepares esters of disubstituted glycidic acids, by condensing the corresponding ketone with monochloracetic ester, in the presence of sodium ethylate.

They are easily oxidized to the corresponding fatty acid, in many cases simply by exposure to air.

Unsaturated aldehydes are also known, corresponding to the olefine alcohols; they show the characteristic properties of the saturated aldehydes and can form additive compounds in virtue of their unsaturated nature.

The head of the divine hierarchy of Mithras was Infinite Time - Cronus, Saturn; Heaven and Earth were his offspring, and begat Ocean, who formed with them a trinity corresponding to Jupiter, Juno, and Neptune.

The year is usually divided into a winter (inverno) and summer (verao), corresponding approximately to a dry and wet season.

In 1852 the revenue was £27,158 and the expenditure £ 24,296, and in 1862 the corresponding figures were £98,799 and £85,928.

Its investigations pointed to the loosening of tribal ties and to the corresponding growth of a spirit of individual independence.

One of the first of these attacks was made by Berengarius of Tours (999-1088) upon the doctrine of transubstantiation; he denied the possibility of a change of substance in the bread and wine without some corresponding change in the accidents.

Nitrosohydrocarbons have been prepared in the aliphatic series by the oxidation of the corresponding hydroxylamino compounds.

Ruff (Ber., 18 9 8, 3 1, p. 457) from nitro-di-isobutyl by reducing it to the corresponding hydroxylamino compound with aluminium amalgam and oxidizing this with chromic acid mixture.

Five subdivisions may be recognised in the Miocene deposits, corresponding with five different stages in the evolution of southern Europe.

The corolla is generally funnelshaped, more rarely bell-shaped or tubular; the outer face is often marked out in longitudinal areas, five well-defined areas tapering from base to apex, and marked with longitudinal striae corresponding to the middle of the petals, and alternating with five non-striated weaker triangular areas; in the bud the latter are folded inwards, the stronger areas being exposed and showing a twist to the right.

We find that fractions follow certain laws corresponding exactly with those of integral multipliers, and we are therefore able to deal with the fractional numbers as if they were integers.

When, by practice with logarithms, we become familiar with the correspondence between additions of length on the logarithmic scale (on a slide-rule) and multiplication of numbers in the natural scale (including fractional numbers), A /5 acquires a definite meaning as the number corresponding to the extremity of a length x, on the logarithmic scale, such that 5 corresponds to the extremity of 2X.

We take a fixed line OX, usually drawn horizontally; for each value of X we measure a length or abscissa ON equal to x.L, and draw an ordinate NP at right angles to OX and equal to the corresponding value of y .

This insertion of irrational numbers (with corresponding negative numbers) requires for its exact treatment certain special methods, which form part of the algebraic theory of number, and are dealt with under Number.

These works possess considerable originality, and contain many new improvements in algebraic notation; the unknown (res) is denoted by a small circle, in which he places an integer corresponding to the power.

Special linguistic and other privileges were assured to the Italian minority in the Dalmatian towns, but no corresponding charter was granted to the four to five hundred thousand Slovenes and Croats annexed to Italy.

It is to be noted that, whilst the zoological system took the form of a genealogical tree, with main stem and numerous diverging branches, the actual form of that tree, its limitation to a certain number of branches corresponding to a limited number of divergences in structure, came to be regarded as the necessary consequence of the operation of the physico-chemical laws of the universe, and it was recognized that the ultimate explanation of that limitation is to be found only in the constitution of matter itself.

The component vibrations at P due to the successive zones are thus nearly equal in amplitude and opposite in phase (the phase of each corresponding to that of the infinitesimal circle midway between the boundaries), and the series which we have to sum is one in which the terms are alternately opposite in sign and, while at first nearly constant in numerical magnitude, gradually diminish to zero.

Now as to the phase of the secondary wave, it might appear natural to suppose that it starts from any point Q with the phase of the primary wave, so that on arrival at P, it is retarded by the amount corresponding to QP. But a little consideration will prove that in that case the series of secondary waves could not reconstitute the primary wave.

The first root after zero is thus in the third quadrant, corresponding to m =1.

The part corresponding to negative values of u is similar, OA being a line of symmetry.

The brightness (corresponding to B) midway between the two central points AA' is 8106 of the brightness at the central points themselves.

The obliquity, corresponding to u =7, is such that the phases of the secondary waves range over a complete period, i.e.

The accompanying table is given by Lommel, in which the first column gives the roots of J2(z) =o, and the second and third columns the corresponding values of the functions specified.

This is necessarily a question of degree; but it does not require detailed calculations in order to show that the discrepancy first becomes conspicuous when the phases corresponding to the various secondary waves which travel from P to B range over a complete period.

At other parts of the field the effect is the same, in accordance with the principle known as Babinet's, whether the imaginary screen in front of the object-glass is generally transparent but studded with a number of opaque circular disks, or is generally opaque but perforated with corresponding apertures.

Let AoBo be a plane wave-surface of the light before it falls upon the prisms, AB the corresponding wave-surface for a particular part of the spectrum after the light has passed the prisms, or after it has passed the eye-piece of the observing telescope.

The directions of the lateral spectra are such that the passage from one element of the grating to the corresponding point of the next implies a retardation of an integral number of wave-lengths.

The vibrations corresponding to the two parts are precisely antagonistic, since if both were operative the resultant would be zero.

Then the relative retardation of the extreme rays (corresponding to the edges A, B of the grating) is mnX.

According to the principle already laid down it can make but little difference in the principal direction corresponding to the first spectrum, provided each line lie within a quarter of an interval (a+d) from its theoretical position.

The latter found that certain gratings exercised a converging power upon the spectra formed upon one side, and a corresponding diverging power upon the spectra on the other side.

Previously to the introduction of the plate we have an effect corresponding to wave-lengths closely grouped around the principal wave-length, viz.

If V be the value of v corresponding to CA, viz.

The position of Q corresponding to a given value of V, that is, to a band of given order, is by (19) BQ= aa b AD=V?

The utility of the curve depends upon the fact that the elements of arc represent, in amplitude and phase, the component vibrations due to the corresponding portions of the primary wave-front.

The only assumption here involved is the evidently legitimate one that, when two systems of variously distributed motion at the lamina are superposed, the corresponding motions in front are superposed also.

If, instead of supposing the motion at dS to be that of the primary wave, and to be zero elsewhere, we suppose the force operative over the element dS of the lamina to be that corresponding to the primary wave, and to vanish elsewhere, we obtain a secondary wave following quite a different law.

In the north portico a square hole in the floor, with a corresponding hole in the roof above it, must have given access to another sacred object, the mark of Poseidon's trident in the rock.

A papal diploma, still extant, shows that Count Borel and Bishop Octo or Otho of Ausona were at Rome in January 971, and, as all the other indications point to a corresponding year, enables us to fix the chronology of Gerbert's later life.

The Transvaal revenue (apart from railway receipts) in 1908-1909 was £5,735,000, the corresponding expenditure £4,524,000.

Taking the refractive index of water for the red rays as 0;, and for the violet rays as 1 r, we can calculate the following values for the minimum deviations corresponding to certain assigned values of n.

Details of the morphology of plants will be found in the articles relating to the chief groups of plants, those of animals in the corresponding articles on groups of animals, while the classification of animals adopted in this work will be found in the article ZOOLOGY.

Piperonal (q.v.) is the corresponding aldehyde.

The male head-dress was the galerus, a hat of leather, said to have been worn by the Lucumos in early times, or the apex, a pointed hat corresponding to the tutulus worn by females.

In Annam the rainy season begins during September and lasts for three or four months, corresponding with the northeast monsoon and also with a period of typhoons.

There are six species of monkey corresponding to those of Guiana and the Amazon valley, the sloth and ant-eater, 12 known genera of rodents, including many species of Mures, the cavy, the capybara, the paca, the nutria, the agouti, the tree porcupine, Loncheres cristata, Echimys cayen and the Brazilian hare.

The New English Dictionary points out that whereas the old Teutonic type of the word is neuter, corresponding to the Latin numen, in the Christian applications it becomes masculine, and that even where the earlier neuter form is still kept, as in Gothic and Old Norwegian, the construction is masculine.

Hansemann's "anaplasia " hypothesis seeks to find an explanation of the formation of new growths in the absence of the histological differentiation of the cell associated with a corresponding increase in its proliferative power and a suspension, or loss, of its functional activity.

The ancient commote of Senghenydd (corresponding to the modern hundred of Caerphilly) comprised the mountainous district extending from the ridge of Cefn Onn on the south to Breconshire on the north, being bounded by the rivers Taff and Rumney on the west and east.

Every orbit must clearly have a hodograph, and, conversely, every hodograph a corresponding orbit; and, theoretically speaking, it is possible to deduce the one from the other, having given the other circumstances of the motion.

The number of students of medicine must at one time have been considerable, and in a corresponding degree the number of teachers.

Not that the spirit of the science, or of its corresponding practice, was at once changed.

These remedies were arcana - a word corresponding partly to what we now call specific remedies, but implying a mysterious connexion between the remedy and the "essence" of the disease.

Sometimes acid sometimes alkaline properties predominated in the juices and secretions of the body, and produced corresponding disturbances.

Haller occupied in the new university of Gottingen (founded 1737) a position corresponding to that of Boerhaave at Leiden, and in like manner influenced a very large circle of pupils, The appreciation of his work in physiology belongs to the history of that science; we are only concerned here with its influence on medicine.

In Italy, on the other hand, it received enthusiastic support, and, naturally, a corresponding degree of opposition.

The practical difference in the corresponding treatment was very great, as Rasori advocated a copious use of bleeding and of depressing remedies, such as antimony.

By chemical warnings the defensive processes seem to be awakened, or summoned; and when we think of the infinite variety of such possible phases, and of the multitude of corresponding defensive agents, we may form some dim notion of the complexity of the animal blood and tissues, and within them of the organic molecules.

Toxins may thus become so closely keyed into their corresponding atom groups, as for instance in tetanus, that they are no longer free to combine with the antitoxin; or, again, an antitoxin injected before a toxin may anticipate it and, preventing its mischievous adhesion, dismiss it for excretion.

With this broader and more accurate knowledge of the conditions of the health of the circulation a corresponding efficiency has been gained in the manipulation of certain remedies and new methods of treatment of heart diseases, especially by baths and exercises.

In acoustics he invented, about 1819, the improved siren which is known by his name, using it for ascertaining the number of vibrations corresponding to a sound of any particular pitch, and he also made experiments on the mechanism of voice-production.

The working out of each floor is conducted much as if it were a bed of corresponding thickness.

At the end of the stroke, when his platform comes opposite to a corresponding platform on the other rod, he steps over on to the latter during the instant of rest prior to the reversal of the stroke, descends with the second rod on this down stroke, steps again at the proper time to a platform of the first rod and so on to the bottom.

To decrease the velocity, when large volumes of air are required, the air passages are made larger, and the mine is divided into sections and the air current subdivided into a corresponding number of independent circuits.

Many sections, however, contained in the corresponding part of Mark have no parallel in Luke, while the parallel to one of them is placed later and differs considerably in form.

Koerner (Ber., 1884, 17, p. 203) by condensing ortho-nitrobenzaldehyde with aniline, the resulting ortho-nitro-para-diamino-triphenylmethane being reduced to the corresponding orthoamino compound, which on oxidation yields chrysaniline.

For the special supervision and encouragement of indigenous primary education in monastic and in lay schools, each circle of inspection is divided into sub-circles corresponding with one or more of the civil districts, and each sub-circle is placed under a deputyinspector or a sub-inspector of schools.

When heated with the alkali and alkaline earth metals it yields silicon and the corresponding metallic chlorides.

The hexachloride, Si 2 C1 61 is formed when silicon chloride vapour is passed over strongly heated silicon; by the action of chlorine on the corresponding iodocompound, or by heating the iodo-compound with mercuric chloride (C. Friedel, Comptes rendus, 18 7 1, 73, P. 497).

The organic derivatives of silicon resemble the corresponding carbon compounds except in so far that the silicon atom is not capable of combining with itself to form a complex chain in the same manner as the carbon atom, the limit at present being a chain of three silicon atoms. Many of the earlier-known silicon alkyl compounds were isolated by Friedel and Crafts and by Ladenburg, the method adopted consisting in the interaction of the zinc alkyl compounds with silicon halides or esters of silicic acids.

The carbonates are decomposed by mineral acids, with formation of the corresponding salt of the acid, and liberation of carbon dioxide.

For example, a pair of equal opposite vortices, moving on a line parallel to a plane boundary, will have a corresponding pair of images, forming a rectangle of vortices, and the path of a vortex will be the Cotes' spiral r sin 20 = 2a, or x-2+y-2=a-2; (io) this is therefore the path of a single vortex in a right-angled corner; and generally.

If there are more B corners than one, either on xA or x'A', the expression for i is the product of corresponding factors, such as in (5) Restricting the attention to a single corner B, a = n(cos no +i sin 110) _ (b-a'.0-a) +1!

Thus if T is expressed as a quadratic function of U, V, W, P, Q, R, the components of momentum corresponding are dT dT dT (I) = dU + x2=dV, x3 =dW, dT dT dT Yi dp' dQ' y3=dR; but when it is expressed as a quadratic function of xi, 'x2, x3, yi, Y2, Y3, U = d, V= dx, ' w= ax dT Q_ dT dT dy 1 dy2 dy The second system of expression was chosen by Clebsch and adopted by Halphen in his Fonctions elliptiques; and thence the dynamical equations follow X = dt x2 dy +x3 d Y = ..., Z ..., (3) = dt1 -y2?y - '2dx3+x3 ' M =..

This " bank " or kisad, together with the corresponding western bank of the Tigris (according to Hommel the modern Shatt el-Hai), gave its name to the land of Chesed, whence the Kasdim of the Old Testament.

From such names it is only a step to names of one element, a characteristic feature of which is the frequent addition of an ending -turn (feminine), an, a, um, atum, atija, sha, &c., most of these being " hypocoristic affixes," corresponding in a measure to modern pet-names.

Each gild numbered various classes of members, ranging from beginners, or Schiller (corresponding to trade-apprentices), and Schulfreunde (who were equivalent to Gesellen or journeymen), to Meister, a Meister being a poet who was not merely able to write new verses to existing melodies but had himself invented a new melody.

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.

Since both d-glucose and d-gulose yield the same active (d) saccharic acid on oxidation, the configuration of this and the corresponding /-acid must be sought from among those numbered 5-10 in the above table.

Sometimes the cells are erected in a circle, so that the spout below the slicing machine revolving above them with a corresponding radius can discharge the slices into the centre of any of the cells.

The use of sulphurous acid gas is entirely abandoned, and instead of three carbonatations with corresponding labour and plant only one is required.

These are set in a kiln or oven, and are kept at as even a temperature as possible, corresponding to a dull cherry-red.

Radii are drawn from the centre of the quadrant to the points of division of the arc, and these radii are intersected by the lines drawn parallel to BC and through the corresponding points on the radius AB.

For the best qualities the leaves are primed, aircured, and then subjected to a lengthy treatment corresponding to mild fermentation.

After four days' heating the provisional front wall is removed piecemeal, and the retorts, after having been heated to redness, are inserted in corresponding sets.

The pure substances are best obtained by fusion of the corresponding toluene sulphonic acids with potash.

The furnace used by Henri Moissan in his experiments on reactions at high temperatures, on the fusion and volatilization of refractory materials, and on the formation of carbides, suicides and borides of various metals, consisted, in its simplest form, of two superposed blocks of lime or of limestone with a central cavity cut in the lower block, and with a corresponding but much shallower inverted cavity in the upper block, which thus formed the lid of the furnace.

Sulphides are known corresponding to the bestknown oxides.

The residue crystallizes slowly, and the crystalline product is almost wholly d-benzyl-allyl-phenyl-ammonium-d-sulphonate, the corresponding /-compound remaining as a syrupy residue.

The corresponding iodides are obtained by the addition of potassium iodide to solutions of the sulphonates, and are optically active antipodes.

It had an active membership of 163 in 1906, besides 172 honorary and corresponding members.

Generally the components of a mixture will be vaporized in the order of their boiling-points; consequently if the condensates or "fractions" corresponding to definite ranges of temperature be separately collected, it is obvious that a more or less partial separation of the components will be effected.

The vapour pressure-composition curve will now be concave to the axis of composition, the minima corresponding to the pure components.

He has also the privilege of corresponding direct with the caliph; but otherwise is regarded as rather opposed to the Osmanli administration, and has no real power.

It is terminated by a well-developed structure (fg) corresponding with the apical sense-organ of ordinary Trochospheres, and an excretory organ (nph) of the type familiar in these larvae occurs on the ventral side of the stomach.

The principal differences are the complication of the ciliated band, the absence of the excretory organ, the great lateral compression of the body, the possession of a pair of shells protecting the sides, the presence of an organ known as the "pyriform organ," and the occurrence of a sucker in a position corresponding with the depression seen between (m) and (a) in fig.

There is a nexus between each leading group of social phenomena and other leading groups; if there is a change in one of them, that change is accompanied by a corresponding modification of all the rest.

As it was composed in rather less than six months, and as the author honestly warns us that he has given all his attention to a more profound co-ordination, instead of working out the special explanations more fully, as he had promised, we need not be surprised if the result is disappointing to those who had mastered the corresponding portion of the Positive Philosophy.

Herder's works may be arranged in an ascending series, corresponding to the way in which the genetic or historical idea was developed and extended.

One steadily exercised influence is constantly at work, for the shores bordering the Pacific Ocean are slowly though appreciably rising, while on the side of the Japan Sea a corresponding subsidence is taking place.

The equatorial currents produce conditions differing from those existing at corresponding latitudes on the neighboring continent.

Whereas in Tokyo the number of frosty nights during a year does not average much over 60, the corresponding number in Sapporo on the north-west of Yezo is 145.

Aston devoted much study to the former question, but although he proved that in construction the two have a striking similarity, he could not find any corresponding likeness in their vocabularies.

Her artists and artisans alike aim at symmetry, not by an equal division of parts, as we do, but rather by a certain balance of corresponding parts, each different from the other, and not numerically even, with an effect of variety and freedom from formality.

The difference between this process and ordinary inlaying is that for sumi-zogan the design to be inlaid is fully chiselled out of an independent block of metal with sides sloping so as to be broader at the base than at the top. The object which is to receive the decoration is then channelled in dimensions corresponding to those of the design block, and the latter having been fixed in the channels, the surface is ground and polished until an intimate union is obtained between the inlaid design and the metal forming its field.

Above these ties are the cornice brackets and beams, corresponding in general design to the cornice of the walls, and the intermediate space is filled with open carvings of dragons or other characteristic designs.

When the temple is of very large dimensions an interior peristyle of pillars is introduced tc assist in supporting the roof, and in such cases each pillar carrim profuse bracketing corresponding to that of the cornice.

Having little to guide them, they often interpreted Western taste incorrectly, and impaired their own reputation in a corresponding degree.

Village roads, being for the convenience of local districts alone, are maintained at the expense of such districts under the general supervision of the corresponding prefecture.

Queen Ulrica elevated him and his family to the rank of nobility, by which his name was changed from Swedberg to Swedenborg, the "en" corresponding to the German "von."

In God there are three infinite and uncreated "degrees" of being, and in man and all things corresponding three degrees, finite and created.

At first the identity of Styria is lost in the great duchy of Carinthia, corresponding more or less closely to the Upper Carinthian mark.

Their organs of locomotion are the ribs, the number of which is very great, nearly corresponding to that of the vertebrae of the trunk.

The integuments of the head are divided into non-imbricate shields or plates, symmetrically arranged, but not corresponding in size or shape with the underlying cranial bones or having any relation to them.

The corresponding changes in the case of the mixture Tuvw are easily understood - the first halt at U, due to the crystallization of pure B, will probably occur at a different temperature, but the second halt, due to the simultaneous crystallization of A and B, will always occur at the same temperature whatever the composition of the mixture.

The summit C of the branch BCD occurs at a percentage exactly corresponding to the formula Hg 2 T1.

If now we wish to represent the variations in some property, such as fusibility, we determine the freezing-points of a number of alloys distributed fairly uniformly over the area of the triangle, and, at each point corresponding to an alloy, we erect an ordinate at right angles to the plane of the paper and proportional in length to the freezing temperature of that alloy.

The tragic writers had occasionally taken their subjects from Roman life (fabulae praetextae), and in comedy we find the corresponding togatae of Lucius Afranius and others, in which comedy, while assuming a Roman dress, did not assume the virtue of a Roman matron.

Propertius is a less accomplished artist and a less equably pleasing writer than either Tibullus or Ovid, but he shows more power of dealing gravely with a great or tragic situation than either of them, and his diction and rhythm give frequent proof of a concentrated force of conception and a corresponding movement of imaginative feeling which remind us of Lucretius.

The phosphorous haloids give the corresponding ethyl haloid.

Thus if Q is the surface density, S the thickness of the shell at any point, and p the assumed volume density of the matter of the shell, we have v =Abp. Then the quantity of electricity on any element of surface dS is A times the mass of the corresponding element of the shell; and if Q is the whole quantity of electricity on the ellipsoid, Q =A times the whole mass of the shell.

To every proposition in electrostatics there is thus a corresponding one in the hydrokinetic theory of incompressible liquids.

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.

He therefore employed the corresponding expression for a cycle of infinitesimal range dt at the temperature t in which the work dW obtainable from a quantity of heat H would be represented by the equation dW =HF'(t)dt, where F'(t) is the derived function of F(t), or dF(t)/dt, and represents the work obtainable per unit of heat per degree fall of temperature at a temperature t.

Assuming the function G to be expressed in terms of p and 0, this condition represents the relation between p and 0 corresponding to equilibrium between the two states, which is the solution of the relation (v" - v')dp/dO=L/D, (5).

The values of the corresponding functions for the liquid or solid cannot be accurately expressed, as the theoretical variation of the specific heat is unknown, but if we take the specific heat at constant pressure s to be approximately constant, and observe the small residual variation dh of the total heat, we may write F'=s'D+dh+B'.

This simple result is generally true, and the corresponding expressions for G" and J" are valid, provided that c - b in formula (17) is a function of the temperature only.

In view of these conditions, the prophet's message is to reassert the true relation of Israel to Yahweh, and to call for a corresponding holiness, especially in regard to questions of ritual and of marriage.

In this period, then, we find first a legitimate extension of cults corresponding to the needs of the growing community, and secondly a religious restlessness and a consequent tendency to more dramatic forms of worship.

Meanwhile a corresponding change was taking place in the attitude of the educated classes owing to the spread of Greek literature.

Corresponding to this acid, a series of salts, named chloraurates or aurichlorides, are known.

The investment of Metz had lasted 54 days, and the deathroll of the civil population had risen to 3587 against 1200 in the corresponding period of a normal year.

As to the exact dates of early Egyptian history there is rather more of vagueness than for the corresponding periods of Mesopotamia.

The acute interest which they excited when George Smith deciphered their contents in 1872 has to some extent abated, but this is only because scholars are now pretty generally agreed as to their bearing on the corresponding parts of Genesis.

These elements will enable us to convert, by a simple arithmetical operation, any historical date, of which the chronological characters are given according to any era whatever, into the corresponding date in the Christian era.

If the year is after Christ, and the event took place in one of the first six months of the Olympic year, that is to say, between July and January, we must subtract 776 from the number of the Olympic year to find the corresponding year of our era; but if it took place in one of the last six months of the Olympic year, or between January and July, we must deduct 777.

As the Syrian year began in autumn, the year of Christ corresponding to any year in the mundane era of Antioch is found by subtracting 5492 or 5493 according as the event falls between January and September or from September to January.

The Chinese divide the time of a complete revolution of the sun with regard to the solstitial points into twelve equal portions, each corresponding to thirty days, ten hours, thirty minutes.

According to this method of dating the years a new era commences with every reign; and the year corresponding to a Chinese date can only be found when we have before us a catalogue of the Nien-hao, with their relation to the years of our era.

These outer defences consisted of two strongly fortified lines, the first of which had been the German outpost line in the spring of 1917 and the British main line of resistance before March 1918, and the second the British outpost line corresponding to this main line - a less formidable obstacle about a mile farther east.

A Dutch fleet of corresponding strength was sent to sea, under command of Baron Opdam van Wassenaer.

The pipette having been carefully dried, the process is repeated with pure alcohol or with proof spirits, and the strength of any admixture of water and spirits is determined from the corresponding number of drops, but the formula generally given is not based upon sound data.

The greater part of 1506 and 1507 was spent in organizing the new militia, corresponding on the subject, and scouring the country on enlistment service.

Jupiter was measured on eleven nights in the months of June and July 1794; from these measures Schur derives the values 35"39 and 37".94 for the polar and equatorial diameter respectively, at mean distance, corresponding with a compression 1/14.44.

It enables the observer to compare any division-interval on one half of either scale with any corresponding interval on the other scale.

During Nansen's expedition on the " Fram " in 1894-1895, Scott Hansen made observations with a Sterneck's half-seconds pendulum on the ice where the sea was more than 1600 fathoms deep and found only an insignificant deviation from the number of swings corresponding to a normal ellipsoid.

Of course the area at great heights is very much less than the area at corresponding depths.

The alkalinity of North Atlantic water of 35 per mille salinity is 26.86 cc. per litre, corresponding to a total amount of carbonic acid of 49 07 cc. According to the researches of August Krogh,' the alkalinity is greatly increased by the admixture of land water.

On the continent of Europe it is customary to consider coal as divisible into two great classes, depending upon differences of colour, namely, brown coal, corresponding to the term "lignite" used in England and France, and black or stone coal, which is equivalent to coal as understood in England.

This word is supposed to be derived from the Walloon hoie, corresponding to the medieval Latin hullae.

These variations in composition are attended with corresponding differences in qualities, which are distinguished by special names.

For flat ropes the drum or bobbin consists of a solid disk, of the width of the rope fixed upon the shaft, with numerous parallel pairs of arms or horns, arranged radially on both sides, the space between being just sufficient to allow the rope to enter and coil regularly upon the preceding lap. This method has the advantage of equalizing the work of the engine throughout the journey, for when the load is greatest, with the full cage at the bottom and the whole length of rope out, the duty required in the first revolution of the engine is measured by the length of the smallest circumference; while the assistance derived from gravitating action of the descending cage in the same period is equal to the weight of the falling mass through a height corresponding to the length of the largest lap, and so on, the speed being increased as the weight diminishes, and vice versa.

An arrangement of this kind for shifting the load from a large cage at one operation was introduced by Fowler at Hucknall, in Leicestershire, where the trains are received into a framework with a number of platforms corresponding to those of the cage, carried on the head of a plunger movable by hydraulic pressure in a vertical cylinder.

The empty tubs are carried by a corresponding arrangement on the opposite side.