Dispersion Sentence Examples

The dispersion from Arabia is easy to imagine.

At the same time the Jews of the Dispersion had to some extent shaken off the exclusiveness of their old political relations and were prepared to compare and contrast their old territorial theology with cosmopolitan culture.

Even if first trained in the Hellenistic synagogues of the Dispersion, as was often the case, they apprehended the Law on its more helpful and less exacting side, and had not been brought "by the Law to die unto the Law," that they might "live unto God."

Through them the experience of the dispersion was brought to bear upon the Palestinian Jews.

The tuft of hairs at the base facilitates rapid dispersion of the seed, early germination of which is rendered desirable owing to its tenuity.

The structure of the dispersion was examined by small-angle synchrotron X-ray scattering on beamline 8.2.

Disp A three character code indicating the dispersion used to determine the mk spectral type, or a quality for the spectral type.

Cross disperser a low dispersion prism or grating separating the various orders of spectra typically in an echelle spectrograph.

The simple theory of the dispersion of light by small particles suffices to explain not only the blue of the zenith, but the comparative absence of small wave-lengths from the direct solar rays, and the brilliant orange and red coloration of the setting sun and of the clouds illuminated by his rays.

Once translated into Greek, the Scriptures became a bond of union for the Jews of the dispersion and were at least capable of being used as an instrument for the conversion of the world to Judaism.

The phrase "to bring again the captivity" would not alone suffice to prove this, for it is used in a wide sense, and perhaps means rather to "reverse the calamity," 4 but the dispersion of Israel among the nations, and the allotment of the Holy Land to new occupants, cannot fairly be referred to any calamity less than that of the captivity.

Improving his advantage, Bolivar pressed forward, and on the 6th of August defeated Canterac on the plains of Junin, after which he returned to Lima, leaving Sucre to follow the royalists in their retreat to Upper Peru - an exploit which the latter executed with equal ability and success, gaining a decisive victory at Ayacucho, and thus completing the dispersion of the Spanish force.

On the dispersion of the Jesuits the Bollandists were authorized to continue their work, and remained at Antwerp until 1778, when they were transferred to Brussels, to the monastery of canons regular of Coudenberg._ Here they published vol.

The simplest way of showing dispersion is to refract a narrow beam of sunlight through a prism of glass or prismatic vessel =containing water or other clear liquid.

The explanation of the colours of the rainbow, which are also due to dispersion, was given by Newton, although it was known previously to be due to refraction in the drops of rain (see Rainbow).

He concluded that there could be no refraction without dispersion, and hence that achromatism was impossible of attainment (see Aberration).

Since the index of refraction varies with the colour or wave length of the light (see Dispersion), it follows that a system of lenses (uncorrected) projects images of different colours in somewhat different places and sizes and with different aberrations; i.e.

The examination of dispersion of the optic axes in biaxal crystals (see Refraction, § Double) may be conveniently made with a plate perpendicular to the acute bisectrix placed in the diagonal position for light of mean period between a crossed polarizer and analyser.

Disp A three character code indicating the dispersion used to determine the MK spectral type, or a quality for the spectral type.

Secular Zionists relied more on the argument that Palestine alone could solve the problem of Jewish dispersion and virulent anti-Semitism.

The ultra-fine mineral content is responsible for deflecting attention away from lines and imperfections through light dispersion, which results in a softened skin tone.

Since soybean oil lowers the melting point of the candle, the candle burns cooler and has a faster scent dispersion.

This allows for faster scent dispersion.

Both natural and lab-created stones have the same hardness, specific gravity, refractive index and dispersion factor."

Therefore, while every other religion which was purely national was extinguished in the nation's overthrow, the religion of Israel survived even amid exile and dispersion.

If Jerusalem has been chosen as His sanctuary and Israel as His own people, it is only that Israel may diffuse God's blessings in the world even at the cost of Israel's own humiliation, exile and dispersion.

He was also ready and able to protect the Jews of the dispersion.

The extinction of the western caliphate and the dispersion of the once noble heritage of the Ommayads into numerous petty independent states, had taken place some thirty years previously, so that Castilian and Moslem were once again upon equal terms, the country being almost equally divided between them.

Some rabbis interpreted Israel's dispersion as divinely designed for the very purpose of proselytizing (Pesahim 87b.).

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.

There will be destruction by interference of the first, third and odd spectra generally; while the advantage gained in the spectra of even order is not in dispersion, nor in resolving power, but simply in brilliancy, which is increased four times.

If we now suppose half the grating cut away, so as to leave 1000 lines in half an inch, the dispersion will not be altered, while the brightness and resolving power are halved.

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

According to this view the chromatic effects depend entirely upon atmospheric dispersion.

The use of a grating is very convenient, for not only are there several spectra in view at the same time, but the dispersion can be varied continuously by sloping the grating.

In the former case the function of the telescope is simply to increase the dispersion, and the formation of the bands is of course independent of the particular manner in which the dispersion arises.

If, however, the half-covered aperture be in front of the object-glass, the phenomenon is magnified as a whole, and the desirable relation between the (unmagnified) dispersion and the aperture is the same as without the telescope.

The Jews in Jerusalem could not ignore the Jews of Galilee or even of the Dispersion.

The dispersion of Greek science and intellectual activity through the world by the conquests of Alexander and his successors led to the formation of more than one learned centre, in which medicine among other sciences was represented.

But, here again a disembarkation in face of opposition would have to be risked and a dispersion of resources would arise, while there were strong objections from the point of view of ship transport to conveying troops to a point so distant from the island of Imbros as Bulair; for Imbros was to be utilized as the principal concentration point for the reinforcements from England.

Their object was to pursue the inquiry begun by Fraunhofer as to the effect of chemical composition on the distribution of dispersion.

In this table n is the refractive index of the glass for sodium light (the D line of the solar spectrum), while the letters C, F and G' refer to lines in the hydrogen spectrum by which dispersion is now generally specified.

Still this partial divorce of himself from the record of the social and scientific activity of his time, though it may save a thinker from the deplorable evils of dispersion, moral and intellectual, accounts in no small measure for the exaggerated egoism, and the absence of all feeling for reality, which marked Comte's later days.

In this way the diversity of human speech and the dispersion of mankind were accounted for; and in Gen.

Trains of waves nearly but not quite homogeneous as regards wave-length will as usual be propagated as wave-groups travelling with the slightly different velocity d(VX-1)/dX-', the value of K occurring in V being a function of X determined by the law of optical dispersion of the medium.

Meanwhile the new movement spread quite naturally beyond the confines of Palestine and found adherents among the Jews of the dispersion, and at an early day among the Gentiles as well.

The fundamental type of the Arabic sanctuary can be traced through all the Semitic lands, and so appears to be older than the Semitic dispersion; even the technical terms are mainly the same, so that we may justly assume that the more developed ritual and priesthoods of the settled Semites sprang from a state of things not very remote from what we find among the heathen Arabs.

That the interval which elapsed before the Prophets and the Hagiographa were also translated was no great one is shown by the prologue to Sirach which speaks of " the Law, the Prophets and the rest of the books," as already current in a translation by 132 B.C. The date at which the various books were combined into a single work is not known, but the existence of the Septuagint as a whole may be assumed for the 1st century A.D., at which period the Greek version was universally accepted by the Jews of the Dispersion as Scripture, and from them passed on to the Christian Church.

But as it is quite inconceivable that the Jews of the Dispersion should not have known beforehand at what full moon they were to present themselves at Jerusalem for the Passover, it must be assumed as true in fact, whether or no it was true in theory, that the old empirical methods must have been qualified, at least partially, by permanent, that is in effect by astronomical rules.

Still indeed the New-Testament idea of a purely spiritual kingdom of God, in this world but not of it, is beyond the prophet's horizon, and he can think of no other vindication of the divine purpose than that the true Israel shall be gathered again from its dispersion.

Dispersion is therefore due to the fact that rays of different colours possess different refrangibilities.

The simplest way of showing dispersion is to refract a narrow beam of sunlight through a prism of glass or prismatic vessel containing water or other clear liquid.

As the light is twice refracted, the dispersion is increased, and the rays, after transmission through the prism, form a divergent system, which may be allowed to fall on a sheet of white paper, forming the wellknown solar spectrum.

Newton also made use of the method of crossed prisms, which has been found of great use in studying dispersion.

The coloured borders seen in the images produced by simple lenses are due to dispersion.

The phenomenon of dispersion shows that in dispersive media the velocity is different for lights of different wave-lengths.

In air and other gases, at ordinary pressures, the dispersion is very small, because the refractivity is small.

In order to find the amount of dispersion caused by any given prism, the deviations produced by it on two rays of any definite pure colours may be measured.

The angle of difference between these deviations is called the dispersion for those rays.

If 6 F and Sc are the angular deviations of these rays, then S F - Sc is called the mean dispersion of the prism.

If the refracting angleof the prism is small, then the ratio of the dispersion to the mean deviation of the two rays is the dispersive power of the material of the prism.

By studying the dispersion of colours in water, turpentine and crown glass Newton was led to suppose that dispersion is proportional to refraction.

He concluded that there could be no refraction without dispersion, and hence that achromatism was impossible of attainment.

This property is referred to as the "irrationality of dispersion."

The irrationality of dispersion is well illustrated by C.Christiansen's experiments on the dispersive properties of white powders.

The name given to this phenomenon, - "anomalous dispersion" - is an unfortunate one, as it has been found to obey a regular law.

In studying the dispersion of the aniline dyes, a prism with a very small refracting angle is made of two glass plates slightly inclined to each other and enclosing a very thin wedge of the dye, which is either melted between the plates, or is in the form of a solution retained in position by surface-tension.

Only very thin layers are sufficiently transparent to show the dispersion near or within an absorption band, and a large refracting angle is not required, the dispersion usually being very considerable.

Becquerel, however, investigated the character of the dispersion by using prism-shaped flames strongly coloured with sodium.

If suitable values are chosen for these constants, the formula can be made to represent the dispersion of ordinary transparent media within the visible spectrum very well, but when extended to the infra-red region it often departs considerably from the truth, and it fails altogether in cases of anomalous dispersion.

This is exactly in accordance with the observed facts in the case of substances showing anomalous dispersion.

Sellmeier's theory did not take account of absorption, and cannot be applied to calculate the dispersion within a broad absorption band.

Ketteler and known as the Ketteler-Helmholtz formula, has been much used in calculating dispersion, and expresses the facts with remarkable accuracy.

P. Drude has obtained a similar formula based on the electromagnetic theory, thus placing the theory of dispersion on a much more satisfactory basis.

Such stones have been occasionally cut as lenses for microscopes, being recommended for such use by their high refractivity, weak dispersion and great hardness.

It is evident that by the use of a spectroheliograph of sufficiently high dispersion, photographs may be taken of vapours in the sun represented by lines narrower than those of calcium and hydrogen.

This law cannot be maintained in its generality, but nevertheless highly dispersive substances like carbon bisulphide are always found to produce a greater shift than liquids of smaller dispersion like water and alcohol.

In Browning's form the setting is automatic. The dispersion may be further increased by causing the rays to pass more than once through the prism or prisms. Thus, by means of a system of reflecting prisms, Hilger passed the dispersed rays six times through one prism, and, by similar means, Browning passed the rays first through the upper part of a train and then back through the lower part.

To save his flock from extinction or dispersion, Ulfilas decided to withdraw both himself and his people.

The common style of the epistles forbids any dispersion of them over a term of years.

As the popular use of Aramaic was gradually restricted by the spread of Arabic as the vernacular (from the 7th century onwards), while the dispersion of the Jews became wider, biblical Hebrew again came to be the natural standard both of East and West.

The dispersion among the nations is to return home.

The calcium flocculi, on account of the brilliant reversals of the H and K lines to which they give rise, and the protection to the plate afforded by the diffuse dark bands in which these bright lines occur, are easily photographed with a spectroheliograph of low dispersion.

In the case of narrower lines, however, higher dispersion is required to prevent the light of the continuous spectrum on either side of the dark line from blotting out the monochromatic image.

The very high dispersion (index for red light = 2.402, for blue light = 2.460) gives it the wonderful " fire " or display of spectral colours.

But more than this, it throws a remarkable light upon the solidarity of the Hellenic Dispersion.

His army, however, under Fiki Adam, fought a fierce battle close to El Fasher on the 22nd, which resulted in its defeat and dispersion, and Abu Gemaiza himself dying the following day, the movement collapsed.

It is difficult to imagine how the dispersion of such a pack could have come about in such a sporting country, but in 1827 Sir Arthur Chichester got a pack together again.

But it is possible that Palestinian Jews accompanied the expedition as guides or exerted their influence with Jews of the Dispersion on behalf of Alexander.

Adopting a hypothetical law of the dispersion of differently coloured rays of light, he proved analytically the possibility of constructing an achromatic object-glass composed of lenses of glass and water.

This want of proportion in the dispersion for different regions of the spectrum is called the "irrationality of dispersion"; and it is as a direct consequence of this irrationality, that there exists a secondary spectrum or residual colour dispersion, showing itself at the focus of all such telescopes, and roughly in proportion to their size.

These glasses, however, still hold the field, although glasses are now produced whose irrationality of dispersion has been reduced to a very slight amount.

Moreover the greater depths of the curves (or "curvature powers") in itself neutralize more or less the advantages obtained from the reduced irrationality of dispersion.

Let it be supposed that two positive lenses of equal curvature powers are made out of these two glasses, then in order to represent the combined dispersion of the two together the two 0µ's for each spectral region may be added together to form 0'µ as in the line below, and then, on again expressing the partial z'µ in terms of L'µ (C to F) we get the new figures in the bottom row beneath the asterisks.

We find that we have now got a course of dispersion or degree of rationality which very closely corresponds to that of an ordinary light flint glass, styled o.

This case well illustrates the much closer approach to strict rationality of dispersion which is obtainable by using two different sorts of glass for the two positive lenses, even when one of them has a higher dispersive power than the glass used for the negative lens.

Fraunhofer, who defined the colours by means of the dark lines in the solar spectrum; and showed that the ratio of the dispersion of two glasses varied about 20% from the red to the violet (the variation for glass and water is about 50%).

In using glasses not having proportional dispersion, the deviation of a third colour can be eliminated by two lenses, if an interval be allowed between them; or by three lenses in contact, which may not all consist of the old glasses.

If a collective system be corrected for the axis point for a definite wave-length, then, on account of the greater dispersion in the negative components - the flint glasses; - over-correction will arise for the shorter wavelengths (this being the error of the negative components), and under-correction for the longer wave-lengths (the error of crown glass lenses preponderating in the red).

The optical characters are interesting, because of the striking crossed dispersion of the optic axes, of which phenomenon borax affords the best example.

The dispersion of a large part of her army and notably of her reserves in Asia Minor, where rail communications were few, and roads ill-developed, made any reinforcement of the European theatres a matter of time and difficulty; in the case of Macedonia, such reenforcement was practically impossible save by sea.

On the walls of the grand marble staircase, which rises to the full height of the building, Kaulbach's cyclus of stereochromic pictures is painted, representing the six great epochs of human progress, from the confusion of tongues at the Tower of Babel and the dispersion of the nations to the Reformation.

The author was in all probability a Jew by race, and he would seem to have addressed himself especially to Jewish readers; but they were Jews of the Dispersion.

There is another coefficient of absorption (K) which occurs in Helmholtz's theory of dispersion (see Dispersion).

The possible applications of anomalous dispersion are varied and interesting, and have recently had much attention given to them.

Though few follow him so far, an explanation of the principle will make it clear that there are numerous possible opportunities for anomalous dispersion to qualify inferences from the spectrum.

Theoretically anomalous dispersion is inseparable from absorption.

These bands Julius calls dispersion bands, and then, assuming that a species of tubular structure prevails within a large part of the sun (such as the filaments of the corona suggest for that region), he applies the weakening of the light to explain, for instance, the broad dark H and K calcium lines, and the sun-spots, besides many remoter applications.

But it should be noted that the bands of his experiment are not due to anomalous dispersion in a strict sense.

They are formed now on one side, now on the other, of the absorption line; but the rapid increase of refractive index which accompanies true anomalous dispersion, and might be expected to produce similar bands by scattering the light, appears both from theory and experiment to belong to the side of greater wave-length exclusively.

In calcium, for instance, the g line shows in the laboratory much stronger anomalous dispersion than H and K; but in the solar spectrum H and K are broad out of all comparison to g.

While abroad the great vassals of the crown generally held their property in compact blocks, in England their power was weakened by the dispersion of their lands.

The dispersion of these state papers is due to the fact that they were in those days treated not as the property of the state, but as the private property of individual secretaries.

The actual distinction of the Druses, as a racial unity, despite their dispersion, depends so exclusively on the peculiarity of their common religion, that it will be well at once to give an account of Druse creed and practice as they are understood to stand at the present day.

When mature, the sporangia are raised above the margin of the indusium by the elongation of the receptacle, thus facilitating the dispersion of the spores.

In October Leopold ordered the dispersion of the emigres who had mustered in arms in the Austrian Netherlands.

In January 1799 the French occupied Naples and set up the Parthenopean republic. But the consequent dispersion of their weak forces only exposed them to greater peril.

In strictness the angle is dependent upon the frequency, but if the dispersion be weak relatively to the double refraction, the product sin 24 - a)sin 2Ni - (3) has sensibly the same value for all terms of the summation, and we may write I=cos 2 (1 3 - a)/a 2 - sin 2 (1 ' - a) sin 2 (t ' - a 2 sin 2 2 This formula contains the whole theory of the colours of crystalline plates in polarized light.

The isochromatic lines, unless the dispersion be excessive, follow in the main the course of the curves of constant retardation, and the principal lines of like polarization are with a crossed polarizer and analyser dark brushes, that in certain cases are fringed with colour.

Crossed, inclined and horizontal dispersion are characterized respectively by a distribution of colour that is symmetrical with respect to the centre alone, the plane of the optic axes, and the perpendicular plane.

He further showed that except in the cases of copper, lead and gold the dispersion is abnormal - the index for red light being greater than that for sodium light.

Soleil's saccharimeter, as its name implies, is designed for the study of solutions of sugar, and it is clear that it will only work satisfactorily with active media that have nearly the same rotary dispersion as quartz.

But the dispersion of Louis of Anjou's troops and his carelessness, together with the lack of success which attended the preaching of a crusade in Germany, France and England, finally decided John XXIII.

The Armenians are essentially an Oriental people, possessing, like the Jews, whom they resemble 'in their exclusiveness and widespread dispersion, a remarkable tenacity of race and faculty of adaptation to circumstances.

To reduce the aberrations Sir David Brewster proposed to employ in the place of glass transparent minerals of high refractive index and low dispersion.

With powerful systems, object-points lying quite near the plane focused for would be represented by such large dispersion circles that practically only the points lying in one plane appear simultaneously sharp; and it is only by varying the focus that the object-points lying in other planes can be observed.

As the pencils used in the representations are of wide aperture on the object-side, only such points as are proportionately very near the focal plane can produce such small dispersion circles on the plane focused for, that they, so far as the objectiveand eyepiece-magnification permit, appear as points to the eye.

Schott succeeded, however, in producing glasses which with a comparatively low refraction have a high dispersion, and with a high refraction a low dispersion.

So long as the object is not sharply focused two separate dispersion figures will be seen.

Though the Ornitholepas australis (Targioni Tozzetti, 1872), found on the tail feathers of a bird, represents only the cypris-larva of a cirripede, it still shows one of the many facilities for dispersion which these creatures enjoy.

In optics, he developed the wave theory, and his name is associated with the simple dispersion formula.

Dispersion Stability Ensuring that the dispersion stability is controlled can prevent agglomeration leading to voids within the green body.

Most noticeable has always been the high-frequency roll-off that resulted from limited speaker dispersion characteristics.

AtmDCC An atmospheric dispersion compensator and field corrector (AtmDCC) is required to correct for atmospheric refraction and field curvature.

This dispersion was accentuated in the presence of acute left ventricular dilatation.

The program has includes " Anomalous dispersion " corrections for the correction of resonance effects in the absorption of x-rays.

Subsequent acid oxidation of the type used on the original material again yielded an aqueous dispersion.

The models for atmospheric dispersion are based on the Gaussian plume model.

First there is the problem of geographical dispersion for potential clients.

It demonstrates that economic progress is not inevitably tied to geographic dispersion.

The main analysis developments will be to develop methods to extract information about phonon dispersion curves.

The velocity dispersion of the cluster galaxies can be measured from optical spectra.

Accurate prediction of pollutant dispersion is an important area of environmental research.

Air pollution dispersion modeling was carried out to predict ground level pollution concentrations in the boro in 2004.

Only bodies 1km diameter actually impact, and the dispersion of secondary ejecta is suppressed.

Pigment dispersion glaucoma affects 1-2% of glaucoma sufferers.

If all the particles have a mutual repulsion then the dispersion will remain stable.

In light Kundt's name is widely known for his inquiries in anomalous dispersion, not only in liquids and vapours, but even in metals, which he obtained in very thin films by means of a laborious process of electrolytic deposition upon platinized glass.

Certainly the asceticism and ritualism might so be interpreted, for there was among the Jews of the Dispersion an increasing tendency to asceticism, by way of protest against the excesses of the Gentiles.

Crassus, who succeeded him, plundered the Temple of its gold and the treasure (54 B.C.) which the Jews of the dispersion had contributed for its maintenance.

These services, which incidentally illustrate the solidarity and unity of the Jewish nation and the respect of the communities of the dispersion for the metropolis, were recognized and rewarded.

Already the Jews of the Dispersion had learned to supplement the Temple by the synagogue, and even the Jews of Jerusalem had not been free to spend their lives in the worship of the Temple.

Some attempt was apparently made to rebuild the Temple; and the Jews of the Dispersion, who had perhaps been won over by Aqiba, supported the rebellion.

But the dispersion of the Jews was proceeding in directions which carried masses from the Asiatic inland to the Mediterranean coasts and to Europe.

But long before this period the Jews of the Dispersion had become as important as the inhabitants of Palestine.

The conditions which he imposed - the obligation to restore the temple funds, and the dispersion of the population into open villages - were soon disregarded.

The first cause of variation may be at present ignored; its significance will become apparent when we consider dispersion (vide infra).

To determine N recourse must be made to Cauchy's formula of dispersion (q.v.), n =A+B/X2+C/A4+...

In the case of substances possessing anomalous dispersion, the direct measurement of the refractive index for Hertzian waves of very long wave-length may be employed.

He also showed how changes in constitution effected dispersions to a far greater extent than they did refractions; thus, while the atomic dispersion of carbon is 0.039, the dispersions due to a double and treble linkage is 0.23 and 0.19 respectively.

Charles was asked to state his case to the committee, and so forcibly did he impress them, that it was there and then decided to move in the matter of a general dispersion of the bible.

The execution of the surplus of the general reform of the church in its head and members was left in the hands of the future pope, who had to proceed conjointly with the council, or rather with a commission appointed by the nations - in other words, once the new pope was elected, the fathers, conscious of their impotence, were disinclined to postpone their dispersion until the laborious achievement of the reform.

Fraunhofer further initiated the specification of refraction and dispersion in terms of certain lines of the spectrum, and even attempted an investigation of the effect of chemical composition on the relative dispersion produced by glasses in different parts of the spectrum.

On the other hand, while in the older crown and flint glasses the relation between refraction and dispersion had been practically fixed, dispersion and refraction increasing regularly with the density of the glass, in some of the new glasses introduced by Abbe and Schott this relation is altered and a relatively low refractive index is accompanied by a relatively high dispersion, while in others a high refractive index is associated with low dispersive power.

The process of dispersion is the inverse of that of absorption, and exhibits similar features.

After their dispersion the Jews were constrained to have recourse to the astronomical rules and cycles of the more enlightened heathen, in order that their religious festivals might be observed on the same days in all the countries through which they were scattered.