Constant Sentence Examples
Anything was better than this constant conflict.
Could she be constant in her attachments?
It was dark, but the constant lightning flashes exposed a world of wildly waving branches.
Constant repetition makes it easier to learn how to spell a word.
The enormous study was full of things evidently in constant use.
Constant practice makes the fingers very flexible, and some of my friends spell rapidly--about as fast as an expert writes on a typewriter.
The entire trip took just over an hour with the driver, a volunteer from Amarillo, Texas who never stopping his constant drawl of friendly conversation, little of which Dean heard.
While back-country skiing was also popular, the ever constant danger of killing snow slides made marked trails a safer method of enjoying this vigorous sport.
Alex and Bill had run a water line to the hutches, so they had a constant supply of fresh water.
You've been the one constant in my life since this mess started.
AdvertisementOnly once afterward in fifteen years was their constant companionship broken for more than a few days at a time.
An IV in her arm dripped a constant dose of powerful anesthetic.
Indeed, I feel that the success is hers more than mine; for she is my constant inspiration....
Soldiers were passing in a constant stream along the street blocking it completely, so that Alpatych could not pass out and had to wait.
Thanks for your help, but around here we're waging a constant war against nature.
AdvertisementDuring these years there was constant warfare between the English and the Scots on the border, but in May 1524 Albany was obliged to retire to France.
She learned it gladly when she discovered that she could herself read what she had written; and this still affords her constant pleasure.
Sackler and DeLeo, partners for nearly 12 years, had more in common than their constant arguing would suggest.
Prince Andrew was on duty that day and in constant attendance on the commander-in-chief.
Her make-up was smeared from walking through the Monterey mists, her maid-of-honor dress wrinkled from constant sitting and standing.
AdvertisementYou'd think the plan was to help the survivors, but I'm in a constant battle with others who want to wipe out everything east of the Mississippi and just start over.
Forced to flee by the treachery of the very men whom he had succoured, he lived for a time in constant fear of being captured by Saul, and at length took refuge with Achish king of Gath and established himself in Ziklag.
In a sleigh drawn by two gray trotting-horses that were bespattering the dashboard with snow, Anatole and his constant companion Makarin dashed past.
C. Druce's will; and the case became the subject of constant proceedings in the law-courts without result.
There was no other purr aside from the constant, low hum similar to the hum surrounding electric wires.
AdvertisementFor reasons of health it may be assumed that no system of heating is advisable which does not provide for a constant renewal of the air in the locality warmed.
It is marked by the constant and continuous absorption of a certain quantity of oxygen and bythe exhalation of a certain volume of carbon dioxide and water vapour.
He was in constant fear of assassination and distrusted all around him.
In the article Thermodynamics it is shown that the amount of heat required to raise a given weight of a gas through a certain range of temperature is different according as the gas is maintained at constant pressure, the volume in creasing, or at constant volume, the pressure increasing.
When no external force acts, the case which we shall consider, there are three integrals of the equations of motion (i.) T =constant, x 2 +x 2 +x 2 =F 2, a constant, (iii.) x1y1 +x2y2+x3y3 =n = GF, a constant; and the dynamical equations in (3) express the fact that x, x, xs.
Numbers of Scotch sailors and of English deserters served in the Dutch fleet in this war - the bad administration of the navy and the constant ill-treatment of the crews having caused bitter discontent.
In this country, as in all others they had visited underneath the earth's surface, there was no night, a constant and strong light coming from some unknown source.
Anyone projecting an end to the historical constant of war had better be ready to overcome no small amount of justified skepticism.
Lucy eventually realized that her constant attraction the the casanova of the town could only end in disaster.
When a water jet serves as collector, the pressure under which it issues should be practically constant.
Linss (6) found that an insulated conductor charged either positively or negatively lost its charge in the free atmosphere; the potential V after time t being connected with its initial value Vo by a formula of the type V = Voe - at where a is constant.
His attention to all trade questions was close and constant; he was a member of the council of trade and plantations appointed in 1670, and was its president from 1672 to 1676.
In Ireland the game took root very gradually, but in Ulster, owing doubtless to constant intercourse with Scotland, such clubs as have been founded are strong in numbers and play.
To the saintliness of the cloister he added the wisdom of the man of the world; he was constant in misfortune, not elated by prosperity, never "carrying things to the sweating-point'," but preserving, in a time of universal corruption, unreality and self-indulgence, a nature sweet, pure, self-denying, unaffected.
An electuary of opium, known as Mithradatum, was invented by Mithradates VI., king of Pontus, who lived in constant fear of being poisoned, and tested the effects of poisons on criminals, and is said to have taken poisons and their antidotes every day in the year.
The surface-layer of the body in the massive Fungi differs in character according, to its function, which is not constant throughout the class, as in the Algae, because of the very various conditions of life to which different Fungi are exposed.
The need for a constant supply of water is partly based upon the constitution of protoplasm, so far as we know it.
This system of channels is in communication with the outer atmosphere through numerous small apertures, known as stomata, which are abundant upon the leaves and young twigs, and gaseous interchange between the plant and the air is by their assistance rendered constant and safe.
Finally, within any district of constant or fairly constant climatic conditions, it is possible to distinguish plant communities which are related chiefly to edaphic or soil conditions; and the vegetation units of these definite edaphic areas are the plant formations of some writers, and, in part, the edaphic formations of Schimper.
Many Staphylinidae are constant inmates of ants' nests.
One of the constant features of respirationthe exhalation of carbon dioxide can still be observed.
To obtain a correct idea of this region it must be borne in mind also that the course of the river and the features of the country on both banks are subject to constant fluctuation.
As this led to constant disputes, Henry VII.
To the men of the middle ages, in any case, St Catherine was very real; she was ranked with the fourteen most helpful saints in heaven, and was the constant theme of preachers and of poets.
When the value of dyldx is not very small E is no longer constant, but is rather greater in compression and rather less in extension than -yP. This can be seen by considering that the relation between p and is given by a curve and not by a straight line.
The term Pv/V added up for a complete wave vanishes, for P/V is constant and Zv=o, since on the whole the compression equals the extension.
Or if the conditions along this distance U could be maintained constant, and we could travel back along it uniformly in one second, we should meet all the conditions actually arriving at AB and at the same intervals.
This will go on continually as long as air is supplied to the cylinder, and the velocity of rotation of the upper plate will be accelerated up to a certain maximum, at which it may be maintained by keeping the force of the current constant.
The result is a note whose pitch rises as the velocity of rotation increases, and becomes steady when that velocity reaches its constant value.
C is a constant, equal to the coefficient of viscosity in Helmholtz's theory, but less simple in Kirchhoff's theory.
We shall first investigate the velocity with which a disturbance travels along a string of mass m per unit length when it is stretched with a constant tension T, the same at all points.
Keeping the same tension, it may be shown that nl is constant by finding n for various lengths.
The material between A and B, though continually changing, is always in the same condition, and therefore the momentum within AB is constant.
Let us suppose that with constant excess of pressure, p, in the wind-chest, the amplitude produced is proportional to the pressure, so that the two tones issuing may be represented by pa sin 27-nit and pb sin 21rn 2 t.
The westerly wind is almost constant and, in conjunction with the elevation of the land, greatly modifies the climatic conditions.
He had been the target of constant attack during his life, and his personal foibles, careless dress and mental eccentricities were the theme of endless ridicule.
He was in constant demand as a lecturer from 1843, when he made his first appearance on the platform, always drew large audiences, and, in spite of his bad management in money matters, received considerable sums, sometimes $600o or $7000 for a single winter's lecturing.
The digressions are indeed constant, and sometimes have the appearance of being absolutely wilful.
During the century which followed the death of Hermann Billung, there had been constant warfare with the Slays, but although the emperors had often taken the field, the Saxons had been driven back to the Elbe, which was at this time their eastern boundary.
A particular tendency to arrange history according to a mechanical rule appears in the constant endeavour to show that recompense and retribution followed immediately on good or bad conduct, and especially on obedience or disobedience to prophetic advice.
Every point is equidistant from a fixed point within the surface; this point is the "centre," the constant distance the "radius," and any line through the centre and intersecting the sphere is a "diameter."
Two spheres intersect in a plane, and the equation to a system of spheres which intersect in a common circle is x 2 + y 2 + z 2 +2Ax -fD = o, in which A varies from sphere to sphere, and D is constant for all the spheres, the plane yz being the plane of intersection, and the axis of x the line of centres.
Then w 3 = (w l +w 2)1 2 /(Cds-1 2) = (w i -Fw 2)lr/ (Cs -lr), where C is a constant for any type of girder.
That is, G = a1 2, where a is a constant.
It is usually accurate enough in deflection calculations to take for I the moment of inertia at the centre of the beam and to consider it constant for the length of the beam.
Let measurements along the beam be represented according to any convenient scale, so that calling L 1 and 1 1 the lengths to be drawn on paper, we have L = aL i; now let r1, r 2, r 3 be a series of radii such that r 1 = R i /ab, r 2 = R 2 /ab, &c., where b is any convenient constant chosen of such magnitude as will allow arcs with the radii, r 1, &c., to be drawn with the means at the draughtsman's disposal.
Those who enjoyed his closest intimacy were the physiologist Cabanis (Madame de Condorcet's brother-in-law), the poet 1Vlanzoni, the publicist Benjamin Constant, and Guizot.
Benjamin Constant's letters (1802-1823) were published by Victor Glachant in 1906.
But in spite of the constant renewal of negotiations for a compromise it was impossible to arrive at any agreement, until the outbreak of war left all the projects for a Ruthenian university at Lemberg, a Slovene one in Laibach, and a second Czech one in Moravia, unrealized.
Hence there appear constant traces of study of the Apostolic writings, so far as these were accessible in the locality of each writer at his date of writing (for the details of this subject, and its bearing on the history of the Canonical Scriptures of the New Testament, see The New Testament in the Apostolic Fathers, Oxford, 1 9 05).
A report by Sir James Clark led to the queen's visiting Balmoral in 1848, and to the purchase of the Balmoral estate in 1852, and the queen's diary of her journeys in Scotland shows what constant enjoyment she derived from her Highland home.
People noticed meanwhile that the queen had taken a great affection for her Scottish man-servant, John Brown, who had been in her service since 1849; she made him her constant personal attendant, and looked on him more as a friend than as servant.
The Thanet beds resting on chalk form a narrow outcrop rising into cliffs at Pegwell Bay and Reculver, and consist (1) of a constant base bed of clayey greenish sand, seldom more than 5 ft.
In the Domes day Survey only five lay tenants-in-chief are mentioned, all the chief estates being held by the church, and the fact that the Kentish gentry are less ancient than in some remoter shires is further explained by the constant implantation of new stocks from London.
There seems to be a constant tendency to increase the requirements.
Meters intended to measure electric quantity are called coulomb meters and also ampere-hour meters; they are employed for the measurement of public electric supply on the assumption that the electromotive force or pressure is constant.
Electrolytic Meters are exclusively ampere-hour meters, measuring electric quantity directly and electric energy only indirectly, on the assumption that the pressure of the supply is constant.
In its improved form this meter consists of a single horseshoe permanent magnet formed of tungsten-steel having a strong and constant field.
The current to be measured passes through the fixed field-coils, whilst through the armature passes a shunt current obtained by connecting the brushes across the supply mains through a constant resistance.
The latter chemist was led by his doctrine of mass-action to deny that substances always combine in constant and definite proportions.
He wrote many books, and countless articles for reviews, newspapers and other publications, and was a constant contributor to the Saturday Review until 1878, when he ceased to write for it for political reasons.
For his constant journeys he required two horses, one for himself and one for his attendant.
In the simplest case, that of uniform translation, these components of the gradient will each be constant throughout the region; at a distant place in free aether where there is no motion, they must thus be equal to -u,-v,-w, as they refer to axes moving with the matter.
The polarization itself is determined from the electric force (P,Q,R) by the usual statical formula of linear type which becomes tor an isotropic medium (.f',g',h') = c2(P,Q,R), because any change of the dielectric constant K arising from the convection of the material through the aether must be independent of the sign of v and therefore be of the second order.
Meanwhile in the Western Church the subject of sin and grace, and the relation of divine and human activity in salvation, received especial attention; and finally, at the second council of Orange in 529, after both Pelagianism and semi-Pelagianism had been repudiated, a moderate form of Augustinianism was adopted,, involving the theory that every man as a result of the fall is in such a condition that he can take no steps in the direction of salvation until he has been renewed by the divine grace given in baptism, and that he cannot continue in the good thus begun except by the constant assistance of that grace, which is mediated only by the Catholic Church.
In fact, the Persian religion throughout all its multitude of purifications, observances and expiations was a constant warfare against impurity, death and the devil.
The chief spokesman of the new movement was Henry Clay, who remained throughout his life the constant advocate of this so-called " American system."
Kiejstut ruled the western portion of the land where the Teutonic Knights were a constant menace, while Olgierd drove the Tatar hordes out of the southeastern steppes, and compelled them to seek a refuge in the Crimea.
Their predominant and constant characteristic is a sober sagacity which instinctively judges aright and imperturbably realized its inspirations.
Every year the senate was to appoint sixteen of its number to be in constant attendance upon the king in rotas of four, which sedecimvirs were to supervise all his actions.
Their daring grew with their numbers, and at last they came to be a constant annoyance to all their neighbours, both Christian and Mussulman, frequently involving Poland in dangerous and unprofitable wars with the Ottoman Empire.
The Polish exiles who filled Europe after 1830 intrigued from abroad, and maintained a constant agitation.
They had recourse to the so-called "unarmed agitation," which was in effect a policy of constant provocation designed to bring on measures of repression to be represented to Europe as examples of Russian brutality.
Owing to the famine and the disturbed state of the country, which demanded his attention as a large landowner and lieutenant of King's County (from 1831), the instrument remained unused for nearly three years, but since 1848 it has been in constant use, chiefly for observations of nebulae, for which it was particularly suited on account of its immense optical power, nominally 6000.
There they are represented as spending their time in constant fighting and feasting in his service.
For spherical shot is not constant, and a separate ballistic table must be constructed; but may be taken as 1.7 on the average.
Denoting the value of T at any velocity v by T (v), then (8) T(v) = sum of all the preceding values of AT plus an arbitrary constant, expressed by the notation (9) T(v) =Z(Av)/gp+ a constant, or fdv/gp+ a constant, in which p is supposed known as a function of v.
The constant may be any arbitrary number, as in using the table the difference only is required of two tabular values for an initial velocity V and final velocity v; and thus (to) T(V) - T(v) = Ev Ov/gp or fvdv/gp; and for a shot whose ballistic coefficient is C (II) t=C[T(V) - T(v)].
Denoting by S(v) the sum of all the values of AS up to any assigned velocity v, (is) S(v) =E(OS)+ a constant, by which S(v) is calculated from AS, and then between two assigned velocities V and v, V AT, = vAv or rvvdv vgp gp' and if s feet is the advance of a shot whose ballistic coefficient is C, (17) s=C[S(V) - S(v)].
To facilitate the reading of Latin texts, the favourite method was the use of interlinear translations, originally proposed by Locke, first popularized in France by Dumarsais (1722), and in constant vogue down to the time of the Revolution.
A fortnight later the same manoeuvres, combined with constant "tapping" at the Confederate defences, caused him to fall back again.
Hitherto neither leader had offered a weak spot to his opponent, though the constant skirmishing had caused a loss of 9000 men to Sherman and about two-thirds of that number to the Confederates.
The ends of this wire are connected to one or more secondary cells of constant electromotive force, a variable resistance being interposed so as to regulate the current flowing through the fine wire.
Instead of adjusting in this manner the electromotive force of any form of cell, if we pass any constant current through a known resistance and bring wires from the extremities of that resistance into connexion with the slider and the galvanometer terminal, we can in the same way determine the fall of potential down the above resistance in terms of the electromotive force of the standard cell and thus measure the current flowing through the standard resistance.
In the Marquesas group the trade-wind is constant.
In the ensuing account a constant repetition of the names of the main archipelagoes will be found; it may of course be assumed that each successive voyager added something to the knowledge of them, but on the other hand, as has been said, islands were often rediscovered and renamed in cases where later voyagers took no account of the work of their predecessors, or where the earlier voyagers were unable clearly to define the positions of their discoveries.
McClellan lingered north of Richmond, despite President Lincoln's constant demand that he should "strike a blow" with the force he had organized and taken to the Yorktown peninsula in April, until General Lee had concentrated 73,000 infantry in his front; then the Federal commander, fearing to await the issue of a decisive battle, ended his campaign of invasion in the endeavour to "save his army"; and he so far succeeded that on July 3 he had established himself on the north bank of the James in a position to which reinforcements and supplies could be brought from the north by water without fear of molestation by the enemy.
Poas (8895), the scene of a violent eruption in 1834, begins a fresh series of igneous peaks, some with flooded craters, some with a constant escape of smoke and vapour.
The cause was the constant raids made by the tribes on villages in British territory, culminating in an attack on a small British detachment, in which two English officers were killed.
A constant difficulty in studying works on metrology is the need of distinguishing the absolute facts of the case from the web of theory into which each writer has woven them -- often the names used, and sometimes the very existence of the units in question, being entirely an assumption of the writer.
And coins have long been recognized as one of the great sources of metrology -- valuable for their wide and detailed range of information, though most unsatisfactory on account of the constant temptation to diminish their weight, a weakness which seldom allows us to reckon them as of the full standard.
The second of these relations is an important one, as it shows that from a table of logarithms to base a, the corresponding table of logarithms to base b may be deduced by multiplying all the logarithms in the former by the constant multiplier i/logab, which is called the modulus of the system whose base is b with respect to the system whose base is a.
The two systems of logarithms for which extensive tables have been calculated are the Napierian, or hyperbolic, or natural system, of which the base is e, and the Briggian, or decimal, or common system, of which the base is io; and we see that the logarithms in the latter system may be deduced from those in the former by multiplication by the constant multiplier /loge io, which is called the modulus of the common system of logarithms.
Logistic or Proportional Logarithms. - The old name for what are now called ratios or fractions are logistic numbers, so that a table of log (a/x) where x is the argument and a a constant is called a table of logistic or proportional logarithms; and since log (a/x) =log a-log x it is clear that the tabular results differ from those given in an ordinary table of logarithms only by the subtraction of a constant and a change of sign.
In this capacity he exercised a wide influence on local opinion, and the revolt of the Newcastle electorate in later years against doctrinaire Radicalism was largely due to his constant preaching of a broader outlook on national affairs.
Constant use, increased friction (m o r e especially at high speeds), and damage to the rotator will alter an ascertained log error; head or following seas, strong winds, currents and tidal streams also FIG.
The fundamental uniform fact in nature is constant change (lravra Xwpei Kai ovSiv Ova); everything both is and is not at the same time.
The best way of deducing r„ is to select portions of the dynamometer record where the speed is constant.
The lead is variable in the Stephenson link motion, whilst in the Walschaert and the Joy gears it is constant.
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.
It is necessary that the voltage of the current shall be constant whatever be the increase of the speed of the train, and therefore of the dynamo.
In most of the systems that have been proposed this result is attained by electrical regulation; in one, however, a mechanical method is adopted, the dynamo being so' hung that it allows the driving belt to slip when the speed of the axle exceeds a certain limit, the armature thus being rotated at an approximately constant speed.
It is with a full knowledge of these difficulties in the way of investigation that they maintain that unmistakably genuine phenomena are of constant occurrence.
Among the Jews the preaching of the prophets had been a constant protest against the grosser forms of sacrifice, and there are indications that when Christianity arose bloody sacrifices were already beginning to fall into disuse; a saying which was attributed by the Ebionites to Christ repeats this protest in a strong form, "I.
Of this invocation, which is constant in all Eastern rituals, there are few, though sufficient, surviving traces in Western rituals.'
Traces remain of the circuit wall, and of a sanctuary with copious terra-cotta offerings; the large necropolis yields constant loot to illicit excavation.
He constructed a map of as many as 576 of these lines, the principal of which he denoted by the letters of the alphabet from A to G; and by ascertaining their refractive indices he determined that their relative positions are constant, whether in spectra produced by the direct rays of the sun, or by the reflected light of the moon and planets.
This affords an example of a principle which had been stated by Hess in a very general form under the name of the Law of Constant Heat Sums - namely, that the thermal effect of a given chemical action is the same, independently of the character and number of the stages in which it takes place.
The total thermal effect, too, which is associated with the transformation, must be the same, whether the transformation is conducted directly or indirectly (Hess's Law of Constant Heat Sums), since the thermal effect depends only on the intrinsic energies of the initial and final systems.
If now it is required to find the heat of formation of the compound CO, which cannot be directly ascertained, we have merely to subtract the second equation from the first, each symbol representing constant intrinsic energy, and thus we obtain C+0 - 00= 26300 cal., or C+0=C0+26300 cal., that is, the heat of formation of a gramme-molecule of carbon monoxide is 26300 cal.
It has already been stated that the heats of neutralization of acids and bases in aqueous solution are additively composed of two terms, one being constant for a given base, the other constant for a given acid.
Canaan (Palestine and the south Phoenician coast land) and Amor (Lebanon district and beyond) were under the constant supervision of Egypt, and Egyptian officials journeyed round to collect tribute, to attend to complaints, and to assure themselves of the allegiance of the vassals.
This involved constant contact with officials of the warring countries, especially those of Germany, but he soon showed that the work was entirely neutral.
The political history during the royal period is, like that of the other colonies, the story of a constant struggle between the representatives of the people and the representatives of the crown.
Their position varies, but is constant for the species, and they are rarely found behind the gonads.
Taylor did not vacate his fellowship at Cambridge before 1636, but he spent, apparently, much of his time in London, for Laud desired that his "mighty parts should be afforded better opportunities of study and improvement than a course of constant preaching would allow of."
Here he became private chaplain to Richard Vaughan, 2nd earl of Carbery (1600-1686), whose hospitable mansion, Golden Grove, is immortalized in the title of Taylor's still popular manual of devotion, and whose first wife was a constant friend of Taylor.
Throughout his life, and to the very end, "work" was his constant inspiration.
A year or two later field trials were begun in England, with the final result that basic slag has become recognized as a valuable source of phosphorus for growing crops, and is now in constant demand for application to the soil as a fertilizer.
Meantime hostilities more car less constant continued with England, but, though in 1322 Edward made an incursion as far as Edinburgh, the internal weakness of his government prevented his gaining any real success, while in October of this year Bruce again ravaged Yorkshire, defeated the English near Byland, and almost captured their king.
His general formula for getting at the number of units in any sensation is S = C log R, where s stands for the sensation, R for the stimulus numerically estimated, and c for a constant that must be separately determined by experiment in each particular order of sensibility.
His words to Benjamin Constant - "I am growing old.
That work was carried out by Benjamin Constant in concert with the emperor.
The secret of this character lies evidently in a constant attempt to express an ideal in forms more and more closely approaching to realities.
Nevertheless, the constant increase of our knowledge of insect forms renders classification increasingly difficult, for gaps in the series become filled, and while the number of genera and families increases, the distinctions between these groups become dependent on characters that must seem trivial to the naturalist who is not a specialist.
In so large and so homogeneous a group as that of the true Passerines, a constant 1 An abstract is contained in the Minute-book of the Scientific Meetings of the Zoological Society, 26th June and 10th July 1838.
The two authors were in constant communication, and the classifications they adopted had much in common.
The channel required constant dredging and was altogether inconvenient; yet for many years it remained the main sea approach to Venice.
There was a constant feud between the chief of Bobbili and the raja of Vizianagram; and when Bussy marched to restore order the raja persuaded him that the fault lay with the chief of Bobbili and joined the French with 11,000 men against his rival.
The lemniscate of Bernoulli may be defined as the locus of a point which moves so that the product of its distances from two fixed points is constant and is equal to the square of half the distance between these points.
Several facts point to the conclusion that the primary use of this secretion was the formation of egg-cases or cocoons by the female, for this is the only constant use for which the silk is employed, without exception, by all species.
In this table measurements of price movements stated both absolutely and as percentages of price levels are given, because authorities have expressed doubts as to whether the former or the latter might be expected to remain constant, other things being equal, when price rose.
Before the accession of Zengi, there had been constant fighting, which had led, however, to no definite result, between the various Mahommedan princes and the Franks of northern Syria.
The constant pressure of Tancred of Antioch and Baldwin de Burgh of Edessa led to a series of retaliations between 11 io and 1115; Edessa was attacked in 1110, 1111, 1112 and 1114; and in 1113 Maudud of Mosul had even penetrated as far as the vicinity of Acre and Jerusalem.
But it is important to bear in mind the continuity of the Crusades - the constant flow of new forces eastward and back again westward; for this alone explains why the Crusades formed a great epoch in civilization, familiarizing, as they did, the West with the East.
The haemoglobin would, by its pre-eminent properties of fixing oxygen, serve to furnish the nerve system, which more than any other requires a constant supply, with the necessary oxygen.
With respect to the sense organs of the Nemertines, we find that eyes are of rather constant occurrence, although many Heteronemertines living in the mud appear to be blind.
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.
When the English colonies of the Carolinas and Georgia were founded, there was constant friction with Florida.
The Spanish were accused of inciting the Indians to make depredations on the English settlements and of interfering with English commerce and the Spanish were in constant fear of the encroachments of the British.
But there is some evidence that, in accordance with the strong and constant tradition among the alchemists, the idea of transmutation did originate in Egypt with the Greeks of Alexandria.
Thus, in the treatise known as Physica et Mystica and falsely ascribed to Democritus (such false attributions are a constant feature of the literature of alchemy), various receipts are given for colouring and gilding metals, but the conception of transmutation does not occur.
The museums, enriched by a constant inflow of works of art and inscriptions, have been carefully and scientifically arranged, and afford opportunities for systematic study denied to scholars of the past generation.
But his whole official career was a constant struggle with narrow routine and personal jealousy on the part of the boyars and clerks of the council.
Lavoisier appears to have assumed that the composition of every chemical compound was constant, and the same opinion was the basis of much experimental inquiry at the hands of Joseph Louis Proust during 1801 to 1809, who vigorously combated the doctrine of Claude Louis Berthollet (Essai de statique chimique, 1803), viz.
When the same two elements combine together to form more than one compound, the different masses of one of the elements which unite with a constant mass of the other, bear a simple ratio to one another.
This formula, notwithstanding many attempts at both disproving and modifying it, has well stood the test of time; the subject has been the basis of constant discussion, many variations have been proposed, but the original conception of Kekule remains quite as convenient as any of the newer forms, especially when considering the syntheses and decompositions of the benzene complex.
The next advance was made by Joseph Louis Proust, whose investigations led to a clear grasp of the law of constant proportions.
Experiment, however, showed that while the quotient on the left hand of this equation was fairly constant for a great number of substances, yet its value was not gR but 7 R; this means that the critical density is, as a general rule, 3.7 times the theoretical density.
Recent researches have shown that the law originally proposed by Kopp - " That the specific volume of a liquid compound (molecular volume) at its boiling-point is equal to the sum of the specific volumes of its constituents (atomic volumes), and that every element has a definite atomic value in its compounds " - is by no means exact, for isomers have different specific volumes, and the volume for an increment of CH 2 in different homologous series is by no means constant; for example, the difference among the esters of the fatty acids is about 57, whereas for the aliphatic aldehydes it is 49.
This states that " the atomic heat (the product of the atomic weight and specific heat) of all elements is a constant quantity."
The value of this constant when 11= i is about 6.4; Dulong and Petit, using 0=1, gave the value.
Nilson and Pettersson's observations on beryllium and germanium have shown that the atomic heats of these metals increase with rise of temperature, finally becoming constant with a value 5.6.
In the article Thermo Chemistry a general account of heats of formation of chemical compounds is given, and it is there shown that this constant measures the stability of the compound.
The identity of the four valencies of the carbon atom follows from the fact that the heats of combustion of methane, ethane, propane, trimethyl methane, and tetramethyl methane, have a constant difference in the order given, viz.
It therefore appears that the difference between the heats of combustion of two adjacent members of a series of homologous compounds is practically a constant, and that this constant has two average values, viz.
It is remarkable that the difference in the heats of formation of ketones and the paraffin containing one carbon atom less is 67.94 calories, which is the heat of formation of carbon monoxide at constant volume.
P. Dale; the more simple formula (n - i)/d, which remained constant for gases and vapours, but exhibited slight discrepancies when liquids were examined over a wide range of temperature, being adopted.
Although establishing certain general relations between atomic and molecular refractions, the results were somewhat vitiated by the inadequacy of the empirical function which he employed, since it was by no means a constant which depended only on the actual composition of the substance and was independent of its physical condition.
Mossotti found a relation between the dielectric constant and the space actually occupied by the molecules, viz.
K= (I +2a)/(I -a), or a=(K-I)/(K+2), where K is the dielectric constant and a the fraction of the total volume actually occupied by matter.
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 relation they suspected to be of the form -yS = KT, where K is a constant analogous to R, and S the surface containing one gramme-molecule, y and T being the surface tension and temperature respectively.
This is of constant occurrence in classical pianoforte music, in which thick chords are subjected to polyphonic laws only in their top and bottom notes, while the inner notes make a solid mass of sound in which numerous consecutive fifths and octaves are not only harmless but essential to the balance of tone.
At the end of each twig is a membrane pierced by pores, and a number of cilia depend into the lumen of the tube; these cilia maintain a constant motion.
Constant punitive measures were carried on by the military police; but in December 1892 a police column proceeding to establish a post at Sima was heavily attacked, and simultaneously the town of Myitkyina was raided by Kachins.
All the well-known breeds of dogs are highly artificial and their maintenance requires the constant care of the breeder in mating, and in rejecting aberrant progeny.
As regards domestic morality, the system offered constant facilities for libertinism, and tended to subvert domestic peace by compromising the dignity and ruining the happiness of the wife.
Though the Roman slaves were not, like the Spartan Helots, kept obedient by systematic terrorism, their large numbers were a constant source of danger.
He had constant encounters with the mob, but his tact and courage never failed.
During the 14th century there were constant quarrels between the citizens and the abbey of St Mary's about the suburb of Bootham, which the citizens claimed as within the jurisdiction of the city, and the abbey as a separate borough.
The favouring bionomic conditions are those of a relatively constant environment under which relatively stereotyped responses are advantage ous.
Natural selection which, under a uniform and constant environment, leads to the survival of relatively fixed and definite modes of response, under an environment presenting a wider range of varying possibilities leads to the survival of plastic accommodation through intelligence.
Its ten Sephiroth are made up of the grosser elements of the former three worlds; they consist of material substance limited by space and perceptible to the senses in a multiplicity of forms. This world is subject to constant changes and corruption, and is the dwelling of the evil spirits.
The heading "Measurement of Dynamical Quantities" includes the topics units, measurements, and the constant of gravitation.
On the 12th of July 1444 a ten years' peace was signed with Hungary, whereby Walachia was placed under the suzerainty of that country; and, wearied by constant warfare and afflicted by the death of his eldest son, Prince Ala-ud-din, Murad abdicated in favour of his son Mahommed, then only fourteen years of age, and retired to Magnesia (1444).
The Kurds, the constant oppressors of that people, had received official recognition and almost complete immunity from the control o f the civil law by being formed into a Y g eo Y manry frontier-guard known as the Hamidian cavalry.
Crete being thus removed from the scope of her action, Turkey found ample occupation in the almost constant turbulence of the Yemen, of Albania and of Macedonia.
With horses only just recovering from an epidemic, they proved quite unequal to the task of catching the Cossacks, who swarmed round them in every direction, never accepting an engagement but compelling a constant watchfulness for which nothing in their previous experience had sufficiently prepared the French.
Narbonne's place had been supplied by Benjamin Constant, whom she first met at Coppet in 1794, and who had a very great influence over her, as in return she had over him.
She journeyed, in company with Constant, by Metz and Frankfort to Weimar, and arrived there in December.
She was again at Coppet in the summer of 1808 (in which year Constant broke with her, subsequently marrying a German lady) and set to work at her book, De l'Allemagne.
There is no direct evidence of it, but the conduct of her close ally Constant may be quoted in its support, and it is certain that she had no affection for the Bourbons.
Take away her assiduous frequentation of society, from the later philosophe coteries to the age of Byron - take away the influence of Constant and Schlegel and her other literary friends - and probably little of her will remain.
Since the beginning of the 19th century they have been bigoted Wahhabis, though previously regarded by their neighbours as very lax Mahommedans; during Mehemet Ali's occupation of Nejd their constant raids on the Egyptian communications compelled him to send several punitive expeditions into the district, which, however, met with little success.
It would seem that, on the whole, nitrogen compounds in the ocean (whether existing in the organic or inorganic forms) remain constant in amount.
The quantities of oxygen and carbonic acid in the sea are nearly constant so far as we can determine.
The bed of the great river maintains a fairly constant position between its extreme banks, but the channels within that bed are so constantly shifting as to require close supervision on the part of the navigation authorities; so much detritus is carried down as to form a perpetually changing series of obstructions to steamer traffic.
In batteries which use acids as the electrolyte, a film of hydrogen tends to be deposited on the copper or platinum electrode; but, to obtain a constant electromotive force, several means were soon devised of preventing the formation of the film.
Constant cells may be divided into two groups, according as their action is chemical (as in the bichromate cell, where the hydrogen is converted into water by an oxidizing agent placed in a porous pot round the carbon plate) or electrochemical (as in Daniell's cell, where a copper plate is surrounded by a solution of copper sulphate, and the hydrogen, instead of being liberated, replaces copper, which is deposited on the plate from the solution).
Hence it is probable that in cases where the transport number keeps constant with 00000 0 0.
Again, water, the best electrolytic solvent known, is also the body of the highest specific inductive capacity (dielectric constant), and this property, to whatever cause it may be due, will reduce the forces between electric charges in the neighbourhood, and may therefore enable two ions to separate.
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.
The value of k, however, does not keep constant so satisfactorily in the case of highly dissociated substances, and empirical formulae have been constructed to represent the effect of dilution on them.
This is fully borne out by the experiments of Julius Thomsen, who found that the heat of neutralization of one gramme-molecule of a strong base by an equivalent quantity of a strong acid was nearly constant, and equal to 13,700 or 13,800 calories.
In the case of weaker acids, the dissociation of which is less complete, divergences from this constant value will occur, for some of the molecules have to be separated into their ions.
In order that the current should be maintained, and the electromotive force of the cell remain constant during action, it is necessary to ensure that the changes in the cell, chemical or other, which produce the current, should neither destroy the difference between the electrodes, nor coat either electrode with a non-conducting layer through which the current cannot pass.
As an example of a fairly constant cell we may take that of Daniell, which consists of the electrical arrangement - zinc zinc sulphate solution copper sulphate solution copper, - the two solutions being usually separated by a pot of porous earthenware.
In spite of this appearance, however, while the supply of copper is maintained, copper, being more easily separated from the solution than zinc, is deposited alone at the cathode, and the cell remains constant.
When the solutions may be taken as effectively dilute, so that the gas laws apply to the osmotic pressure, this relation reduces to E _ nrRT to c1 ey gE c2 where n is the number of ions given by one molecule of the salt, r the transport ratio of the anion, R the gas constant, T the absolute temperature, y the total valency of the anions obtained from one molecule, and c i and c 2 the concentrations of the two solutions.
To pass a steady current in the direction opposite to this electromotive force of polarization, the applied electromotive force E must exceed that of polarization E', and the excess E - E' is the effective electromotive force of the circuit, the current being, in accordance with Ohm's law, proportional to the applied electromotive force and represented by (E - E')/ R, where R is a constant called the resistance of the circuit.
Planck 2 enables us to calculate the diffusion constant of dissolved electrolytes.
In this manner the diffusion constant can be calculated in absolute units (HC1= 2.49, HN03 = 2.27, NaC1=1.12), the unit of time being the day.
By experiments on diffusion this constant has been found by Scheffer, and the numbers observed agree with those calculated (HC1= 2.30, HNO 3 = 2 22, NaCI = I II).
This dual government was a constant cause of friction between the Servians and the Turks, and on the occasion of one conflict between the two parties the Turkish commander of the fortress bombarded the Servian part of the town (June 1862).
But the government and the people displayed a memorable and exemplary energy, under the constant supervision of the king, the queen, and burgomaster Nansen.
Block rubber is considered to possess certain advantages in securing a constant proportion of water, and in being satisfactory for transport.
The probabilities are that in the end the production of a rubber as nearly as possible free from water and impurities and of constant composition will be realized as best meeting the requirements of the modern manufacturer.
As soon as the output of plantation rubber of constant composition has reached much larger dimensions it is probable that the manufacturer will be able to dispense with washing.
These require constant shifting because the objects are in contact at many points, and because the top ones shield those below from the depositing action of the current.
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.
The necessity of a constant protest against polytheism led to a tenacious insistence on the divine unity, and the task was to reconcile this unity with the deity of Jesus Christ.
The two methods have been conducted so as to be in constant touch, though the nature of the results obtained by the one differs much from those which flow naturally from the other.
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).
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.
By means of the Grand Junction and Oxford canals especially, constant communication is maintained between the Thames and the great industrial centres of England.
It forms gigantic deposits of almost constant thickness, embedded between a floor of limestone and a roof of porphyry.
The indirect method is based upon the observed constant of aberration or the displacement of the stars due to the earth's motion.
If V denote the potential, F the resultant force, X, Y, Z, its components parallel to the co-ordinate axes and n the line along which the force is directed, then - sn = F, b?= X, - Sy = Y, -s Surfaces for which the potential is constant are called equipotential surfaces.
The potential due to a thin magnet at a point whose distance from the two poles respectively is r and r' is V =m(l/r=l/r') (8) When V is constant, this equation represents an equipotential surface.
If r and r' make angles 0 and 0 with the axis, it is easily shown that the equation to a line of force is cos 0 - cos B'= constant.
A thin sheet of magnetic matter magnetized normally to its surface in such a manner that the magnetization at any place is inversely proportional to the thickness h of the sheet at that place is called a magnetic shell; the constant product hI is the strength of the shell and is generally denoted by 4, or 4.
Moreover, it is not constant, being an apparently arbitrary function of H or of B; in the same specimen its value may, under different conditions, vary from less than 2 to upwards of 5000.
The principal points of difference are that (I) the magnetic permeability, unlike the electric conductivity, which is independent of the strength of the current, is not in general constant; (2) there is no perfect insulator for magnetic induction, which will pass more or less freely through all known substances.
Therefore and m = v I - 'm of d22 (47) constant cell B21 its object is to produce inside the tube a magnetic field equal and opposite to that due to the earth's magnetism.
For a series of experiments made with the same coil this fraction is constant, and we may write SB = kD.
Denoting by W the work in ergs done upon a cubic centimetre of the metal (=_fHdB or f HdI), he finds W =nips approximately, where n 47r is a number, called the hysteretic constant, depending upon the metal, and B is the maximum induction.
The value of the constant / 7 ranges in different metals from about o ooI to 0.04; in soft iron and steel it is said to be generally not far from 0.002.
The effective number of turns in the coil surrounding the test rod can be varied by means of three dial switches (for hundreds, tens and units), which also introduce compensating resistances as the number of effective turns in the coil is reduced, thus keeping the total resistance of the circuit constant.
If the field is uniform, H=O/wd, where 0 is the rotation, d the thickness of the substance arranged as a plate at right angles to the direction of the field, and w Verdet's constant for the substance.
Since Verdet's constant is somewhat uncertain for different batches of glass even of the same quality, each plate should be standardized in a field of known intensity.
Ann., 18 95, 54,655), who found the limiting values of to be 7.5 to 9.5 for iron, and 11.2 to 13.5 for steel, remaining constant up to H = 06; by P. Culmann (Elekt.
While therefore the initial susceptibility of nickel is less than that of iron and steel, the range of magnetic force within which it is approximately constant is about one hundred times greater.
On the application of a small magnetizing force to a bar of soft annealed iron, a certain intensity of magnetization is instantly produced; this, however, does not remain constant, but slowly increases for some seconds or even minutes, and may ultimately attain a value nearly twice as great as that observed immediately after the force was applied.'
Honda subjected tubes of iron, steel and nickel to the simultaneous action of circular and longitudinal fields, and observed the changes of length when one of the fields was varied while the other remained constant at different successive values from zero upwards.
They consider, however, that Kirchhoff's theory, which assumes change of magnetization to be simply proportional to strain, is still in its infancy, the present stage of its evolution being perhaps comparable with that reached by the theory of magnetization at the time when the ratio I/H was supposed to be constant.
For strong magnetizing forces (which in these experiments did not exceed II= 48.9) the permeability remains almost constant at its initial value (about 400), until the temperature is within nearly i oo of the critical point; then the permeability diminishes more and more rapidly until the critical point is reached and the magnetization vanishes.
Experiments were made at several constant temperatures with varying magnetic fields, and also at constant fields with rising and falling temperatures.
Experiments with the sample of unannealed iron failed to give satisfactory results, owing to the fact that no constant magnetic condition could be obtained.
It is suggested that a permanent magnet might conveniently be " aged " (or brought into a constant condition) by dipping it several times into liquid air.
The tranverse electromotive force is equal to KCH/D, where C is the current, H the strength of the field, D the thickness of the metal, and K a constant which has been termed the rotatory power, or rotational coefficient.
Wills found that the suceptibility was constant in fields ranging from 4200 to 15,000.
Du Bois believes this to be an important general law, applicable to the case of every paramagnetic substance, and suggests that the product KB should be known as " Curie's constant " for the substance.
In the course of constant efforts to secure the mark the brothers Frederick and Dietrich defeated the troops of King Albert at Lucka in May 1307 and secured partial possession of their lands.
In strong contrast to the ungainly toucan is the tiny humming-bird, whose beautiful plumage, swiftness of flight and power of wing are sources of constant wonder and admiration.
Even where settlements have been located, constant effort is required to keep the vegetation down.
His extreme liberalism prevented his opposing the spread of Socialist doctrines preached far and wide by Benjamin Constant.
Building and the allied trades are chronically brisk, owing to the constant development of the city.
Of the king's sons Robert, though titular count of Maine, was kept in leading strings; and even William Rufus, who was in constant attendance on his father, never held a public office.
The constant practice has been to reordain unconditionally Anglican priests and deacons.
As the grandson of St Ladislaus, Manuel had Hungarian blood in his veins; his court was the ready and constant refuge of the numerous Magyar malcontents, and he aimed not so much at the conquest as at the suzerainty of Hungary, by placing one of his Magyar kinsmen on the throne of St Stephen.
His care for the common people was sincere and constant, but his beneficial efforts in this direction were thwarted by the curious interaction of two totally dissimilar social factors, feudalism and Hussitism.
Immediately after this proclamation Gdrgei disappeared with his army among the hills of Upper Hungary, and, despite the difficulties of a phenomenally severe winter and the constant pursuit of vastly superior forces, fought his way down to the valley of Hernad - and safety.
Thus, while of German periodicals ap p earing in Hungary there were in 1871 only 85, they increased in 1880 to 114, in 1885 to 141; and they were, at the beginning of 1895, still 128, in spite of the constant spread of that process of Magyarization which has, since 1880, considerably changed the linguistic habits of the people of Hungary.
We know that log l oN(I+9) = log l oN+log 10 (I+0), and inspection of a table of logarithms shows that, when 0 is small, log 10 (I+B);s approximately equal to X0, where X is a certain constant, whose value is.
There is no doubt that there was a constant traffic between Greece and India, and it is more than probable that an exchange of produce would be accompanied by a transference of ideas.
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.
In the applications with which we are concerned, t, n are very small quantities; and we may take P = x yn - At the same time dS may be identified with dxdy, and in the de nominator p may be treated as constant and equal to f.
B) - f S,u ds (along The new wave-surface is formed in such a position that the optical distance is constant; and therefore the dispersion, or the angle through which the wave-surface is turned by the change of refrangibility, is found simply by dividing (5) by the distance AB.
In the present application 4' is not necessarily equal to; but if P correspond to a line upon the grating, the difference of retardations for consecutive positions of P, so far as expressed by the term of the first order, will be equal to mX (m integral), and therefore without influence, provided v (sin 0-sin0') = nzX (11), where a denotes the constant interval between the planes containing the lines.
The constant care bestowed by his father on his education resulted in an honourable but not particularly distinguished career for young Stanhope.
His tastes were those of a student, and he did not disguise his dislike of public functions and the constant little journeys which take up so much of a bishop's time.
His nose is not only the flattest, but also the smallest among the IndoChinese; his eyes are rarely oblique; his mouth is large and his lips thick; his teeth are blackened and his gums destroyed by the constant use of the betel-nut, the areca-nut and lime.
His works were studied and _learned by heart by the great Latin writers of the Renaissance, such as Erasmus and Melanchthon; and Casaubon, in his anxiety that his son should write a pure Latin style, inculcates on him the constant study of Terence.
He found by patient inquiry that several physical features and the dimensions of certain bones or bony structures in the body remain practically constant during adult life.
The importance of Crispi in Italian public life depended less upon the many reforms accomplished under his administrations than upon his intense patriotism, remarkable fibre, and capacity for administering to his fellow-countrymen the political tonic of which they stood in constant need.
Upon the fall of his cabinet Antonelli created for himself the governorship of the sacred palaces in order to retain constant access to and influence over the pope.
The " Albertine " system plays a comparatively insignificant part in the annual flood rise of the White Nile, but to its waters are due the maintenance of a constant supply to this river throughout the year.
In the military history of all these centuries constant allusion is made to the Rhine, its passages and its fortresses.
Once prime minister, his personal popularity proved to be a powerful unifying influence in a somewhat heterogeneous party; and though the illness and death (August 30, 1906) of his wife (daughter of General Sir Charles Bruce), whom he had married in 1860, made his constant attendance in the House of Commons impossible, his domestic sorrow excited widespread sympathy and appealed afresh to the affection of his political followers.
The best-known accounts of Cirey life, those of Madame de Grafigny, date from the winter of 1738-39; they are somewhat spiteful but very amusing, depicting the frequent quarrels between Madame du Chatelet and Voltaire, his intense suffering under criticism, his constant dread of the surreptitious publication of the Pucelle (which nevertheless he could not keep his hands from writing or his tongue from reciting to his visitors), and so forth.
The resident, Freytag, was not a very wise person (though he probably did not, as Voltaire would have it, spell "poesie" "poeshie"); constant references to Frederick were necessary; and the affair was prolonged so that Madame Denis had time to join her uncle.
In the 17th and 18th centuries it was a favourite duellingground, and in the present day it is not infrequently the scene of political and other popular demonstrations (as is also Trafalgar Square), while the neighbourhood of Marble Arch is the constant resort of orators on social and religious topics.
The police have powers of control over vehicles and exercise them admirably; their work in this respect is a constant source of wonder to foreign visitors.
A constant supply is maintained generally throughout " Water London," although a suspension between certain hours has been occasionally necessitated, as in 1895 and 1898, when, during summer droughts, the East London supply was so affected.
The estimated cost was between three and four millions sterling, to be met by a toll, and it was urged that a uniform depth, independent of tides, would be ensured above the dam, that delay of large vessels wishing to proceed up river would thus be obviated, that the river would be relieved of pollution by the tides, and the necessity for constant dredging would be abolished.
This constant burning of large portions of the city is a marked feature of its early history, and we must remember that, although stone buildings were rising on all sides, these were churches, monasteries, and other public edifices; the ordinary houses remained as before, small wooden structures.
The dedications of many of the churches indicate their great age, but the constant fires in London destroyed these buildings.
In the middle ages there was a constant succession of pageants, processions and tournaments.
Fleet Street was the show-place of London, in which were exhibited a constant succession of puppets, naked Indians and strange fishes.
There were really constant disagreements, and sometimes the king degraded the mayor and appointed a custos or warden in his place.
About this time Dingiswayo was captured and put to death by Zwide, chief of the Undwandwe clan, with whom he had waged constant war.
Their first cost is great and they are dangerous for new men, as they require constant alertness, presence of mind, and a certain knack in using them.
In spite of the discouraging conditions in which they found themselves, and of the constant annoyance suffered from hostile artillery fire, the troops were in fair heart, while the tactical efficiency of the recently created divisions, which had not been of a high standard when they arrived in the theatre of war, had appreciably progressed.
Taxes and land revenue are light; markets for the disposal of produce are constant and prices good; while fresh land is still available in most districts.
The purple-blue of cobalt, the chrome green or yellow of chromium, the dichroic canarycolour of uranium and the violet of manganese, are constant.
The desired result is obtained either by moving the manufactured goods gradually away from a constant source of heat, or by placing them in a heated kiln and allowing t he heat gradually to die out.
Constancy of composition of the raw materials and their careful and thorough admixture in constant proportions are therefore essential to the production of the required glasses.
The stages of the process so far described generallyoccupy from 36 to 60 hours, and during this time the constant care and watchfulness of those attending the furnace is required.
The manufactured goods are either removed gradually from a constant source of heat by means of a train of small iron trucks drawn along a tramway by an endless chain, or are placed in a heated kiln in which the fire is allowed gradually to die out.
The demand constantly increases, and, owing to constant improvements in material in the moulds and in the methods of working, the supply fully keeps pace with the demand.
The bottles are stacked in iron trucks, which, when full, are moved slowly away from a constant source of heat.
It would appear not improbable that the former was the case, for it must be remembered that articles formed of glass were in the later days of Roman civilization in constant daily use, and that the making of glass was carried on, not as now in large establishments, but by artisans working on a small scale.
The coefficient of expansion is constant for such metals only as crystallize in the regular system; the others expand differently in the directions of the different axes.
The general colour of the upper parts and sides of the adult is a tawny yellowish brown, sometimes having a grey or silvery shade, but in some cases dark or inclining to red; and upon these and other differences, which are probably constant locally, a number of sub-species have been named.
These equations can be made to represent the state of convective equilibrium of the atmosphere, depending on the gas-equation p = pk =RA (6) where 0 denotes the absolute temperature; and then d9 d p R dz - dz (p) n+ 1' so that the temperature-gradient deldz is constant, as in convective equilibrium in (I I).
With uniform temperature, taking h constant in the gas-equation, dp / dz= =p / k, p=poet/ k, (9) so that in ascending in the atmosphere of thermal equilibrium the pressure and density diminish at compound discount, and for pressures p 1 and 1, 2 at heights z 1 and z2 (z1-z2)11?
Taking the axis of x for an instant in the normal through a point on the surface H = constant, this makes u = o, = o; and in steady motion the equations reduce to dH/dv=2q-2wn = 2gco sin e, (4) where B is the angle between the stream line and vortex line; and this holds for their projection on any plane to which dv is drawn perpendicular.
Calling the sum of the pressure and potential head the statical head, surfaces of constant statical and dynamical head intersect in lines on H, and the three surfaces touch where the velocity is stationary.
The curves 0 = constant and 4, = constant form an orthogonal system; and the interchange of 0 and 4, will give a new state of uniplanar motion, in which the velocity at every point is turned through a right angle without alteration of magnitude.
If other vortices are present, any one may be supposed to move with the velocity due to the others, the resultant stream function being = gy m log r =log IIrm; (9) the path of a vortex is obtained by equating the value of 1P at the vortex to a constant, omitting the rm of the vortex itself.
Uniplanar Motion of a Liquid due to the Passage of a Cylinder through it.-A stream-function 4, must be determined to satisfy the conditions v24 =o, throughout the liquid; (I) I =constant, over any fixed boundary; (2) d,t/ds = normal velocity reversed over a solid boundary, (3) so that, if the solid is moving with velocity U in the direction Ox, d4y1ds=-Udy/ds, or 0 +Uy =constant over the moving cylinder; and 4,+Uy=41' is the stream function of the relative motion of the liquid past the cylinder, and similarly 4,-Vx for the component velocity V along Oy; and generally 1,1'= +Uy -Vx (4) is the relative stream-function, constant over a solid boundary moving with components U and V of velocity.
If the liquid is stirred up by the rotation R of a cylindrical body, d4lds = normal velocity reversed dy = - Rx- Ry ds (5) ds 4' + 2 R (x2 + y2) = Y, (6) a constant over the boundary; and 4,' is the current-function of the relative motion past the cylinder, but now V 2 4,'+2R =o, (7) throughout the liquid.
Then 4, =o over the cylinder r = a, which may be considered a fixed post; and a stream line past it along which 4, = Uc, a constant, is the curve (r - ยข2) sin 0=c, (x2 + y2) (y - c) - a 2 y = o, (3) a cubic curve (C3).
An angular velocity R, which gives components - Ry, Ix of velocity to a body, can be resolved into two shearing velocities, -R parallel to Ox, and R parallel to Oy; and then ik is resolved into 4'1+1'2, such that 4/ 1 -R-Rx 2 and 1//2+IRy2 is constant over the boundary.
The circulation being always zero round a small plane curve passing through the axis of spin in vortical motion, it follows conversely that a vortex filament is composed always of the same fl