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magnitude

magnitude

magnitude Sentence Examples

  • If the magnitude and increasing complexity of these creations fails to impress you, the sheer quantity should suffice.

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  • The magnitude of that what-if scenario was downright scary.

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  • She listened, unable to fathom the magnitude of chaos he spoke of.

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  • The chief characteristic of the Amazonian forest, aside from its magnitude, is the great diversity of genera and species.

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  • The new technology that the lab is using can measure the magnitude of even the smallest earthquakes.

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  • First, in the magnitude of what it claims, and second, in the degree to which it differs from what pessimists predict.

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  • It does so in orders of magnitude better than what came before it—libraries—but only better, not differently.

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  • When I reflected on the magnitude of the disaster, I was greatly troubled. How could we help all those people?

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  • During his absence were manifested the beginnings of the troubles in the order that were to attain to such magnitude after his death.

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  • The children did not understand the magnitude of the fires, so an adult had to explain how important it was to be prepared to leave home quickly.

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  • Using lines in mathematics and physics helps us to understand direction, but using vectors also tells us the magnitude.

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  • But among archaeologists the word is usually restricted in its technical modern application to a sepulchral mound of greater or less magnitude.

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  • The general term in a solution involves the product ao°ai 1 a2 2 ...an" wherein Tr =0, Zs7r s =w; the number of such products that may appear depends upon the number of partitions of w into B or fewer parts limited not to exceed n in magnitude.

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  • Finally, experiments were made to ascertain the effect of ' The loads were successively applied in decreasing order of magnitude.

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  • y Orionis or Bellatrix, and x Orionis are stars of the 2nd magnitude.

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  • The development is based on the necessity of being able to represent geometrical magnitude by arithmetical magnitude; and it may be regarded as consisting of three stages.

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  • Hermann Hankel has pointed out the readiness with which the Hindus passed from number to magnitude and vice versa.

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  • 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.

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  • Further, it is evident that account must be taken of the variation of phase in estimating the magnitude of the effect at P of the first zone.

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  • If, on the other hand, the point be well immersed in the geometrical shadow, the earlier zones are altogether missing, and, instead of a series of terms beginning with finite numerical magnitude and gradually diminishing to zero, we have now to deal with one of which the terms diminish to zero at both ends.

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  • (It is easy to see that the radius of the bright spot is of the same order of magnitude.) The experiment succeeds in a dark room of the length above mentioned, with a threepenny bit (supported by three threads) as obstacle, the origin of light being a small needle hole in a plate of tin, through which the sun's rays shine horizontally after reflection from an external mirror.

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  • " Thus the magnitude of the central spot is diminished, and the brightness of the rings increased, by covering the central parts of the object-glass."

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  • Under these conditions there is no doubt that the star would appear to be fairly resolved, since the brightness of its external ring system is too small to produce any material confusion, unless indeed the components are of very unequal magnitude.

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  • 5) is QQ'- QS = BD sec 4:,(I - cos SQQ') = BD sec cI)(1 +cos 20) = 2BD cos 4); from which it follows that an error of given magnitude in the figure of a surface is less important in oblique than in perpendicular reflection.

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  • the distance from the centre of one wire or line to the centre of the next, and not otherwise upon the thickness of the wire and the magnitude of the interspace.

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  • This kind of irregularity may clearly be present in a ' It must not be supposed that errors of this order of magnitude are unobjectionable in all cases.

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  • The aperture and the number of bands being both fixed, the condition of blackness determines the angular magnitude of a band and of the spectrum.

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  • If w be the apparent magnitude of the source seen from A, wb should be much smaller than the above quantity, or w

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  • For a disturbing force of given integral magnitude it is seen to be everywhere about an axis perpendicular to r and the direction of the force, and in magnitude dependent only upon the angle (43) between these two directions and upon the distance (r).

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  • (16), secondary disturbance corresponding to the element dS of the plane may be supposed to be that caused by a force of the above magnitude acting over dS and vanishing elsewhere; and it only remains to examine what the result of such a force would be.

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  • The magnitude of the risk was sufficiently shown at Langensalza.

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  • The plague was scarcely stayed before the whole city was in flames, a calamity of the first magnitude, but one which in the end caused much good, as the seeds of disease were destroyed, and London has never since been visited by such an epidemic. On the 2nd of September 1666 the fire broke out at one o'clock in the morning at a house in Pudding Lane.

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  • He remarked that the flow of water from an orifice depends not only on the magnitude of the orifice itself, but also on the height of the water in the reservoir; and that a pipe employed to carry off a portion of water from an aqueduct should, as circumstances required, have a position more or less inclined to the original direction of the current.

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  • Every solid substance is found to be plastic more or less, as exemplified by punching, shearing and cutting; but the plastic solid is distinguished from the viscous fluid in that a plastic solid requires a certain magnitude of stress to be exceeded to make it flow, whereas the viscous liquid will yield to the slightest stress, but requires a certain length of time for the effect to be appreciable.

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  • 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.

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  • Uniplanar motion alone is so far amenable to analysis; the velocity function 4 and stream function 1G are given as conjugate functions of the coordinates x, y by w=f(z), where z= x +yi, w=4-Plg, and then dw dod,y az = dx + i ax - -u+vi; so that, with u = q cos B, v = q sin B, the function - Q dw u_vi=g22(u-}-vi) = Q(cos 8+i sin 8), gives f' as a vector representing the reciprocal of the velocity in direction and magnitude, in terms of some standard velocity Q.

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  • well as of the body from the vector OF to O'F' requires an impulse couple, tending to increase the angle F00', of magnitude, in sec. foot-pounds F.00'.sin FOO'=FVt sin (0-0), (4) equivalent to an incessant couple N=FV sin (0-0) = (F sin 0 cos 0-F cos 0 sin ¢)V = (c 2 -c i) (V /g) sin 0 cos 4) =W'(13-a)uv/g (5) This N is the couple in foot-pounds changing the momentum of the medium, the momentum of the body alone remaining the same; the medium reacts on the body with the same couple N in the opposite direction, tending when c 2 -c 1 is positive to set the body broadside to the advance.

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  • will have moved from 0 to 0', where 00' = Vt; and at 0' the momentum is the same in magnitude as before, but its vector is displaced from OF to O'F'.

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  • 00 ab2dX °0 ab2dX (22) L (I JS)' (18) (t9) This impulse will remain of constant magnitude, and fixed relatively to the body, which thus experiences an additional reaction from the circulation which is the opposite of the force required to change the position in space of the circulation impulse; and these extra forces must be taken into account in the dynamical equations.

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  • He sought to determine the distance and magnitude of the sun, to calculate the diameter of the earth and the influence of the moon on the tides.

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  • The industries of Elberfeld are on a scale of great magnitude.

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  • Faulting, however, is by no means absent, and some of the faults are of considerable magnitude.

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  • They range from the 7th magnitude to the smallest object perceptible in large telescopes.

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  • The general effect is impressive, not by any virtues of style, for we do not discern one, but by reason of the magnitude and importance of the undertaking, and the visible conscientiousness and the grasp with which it is executed.

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  • The island of Shikoku has no mountains of notable MO,Ukn~1ins of magnitude.

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  • But while every one appreciates the magnitude of the relief that would thus be afforded, there has as yet been little substantial progress A language which has been adapted from its infancy to ideographi transmission cannot easily be fitted to phonetic uses.

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  • Much more memorable, however, was a library formed by Iyeyasus grandson the feudal chief of Mito (1662I 700), who not only collected a vast quantity of books hitherto scattered among Shinto and Buddhist monasteries and private houses, but also employed a number of scholars to compile a history unprecedented in magnitude, the Dai-Nihon-shi.

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  • The magnitude of the sum, and his acquiescence in the grant of pensions by the Shelburne ministry, convinced the country that his zeal for economy was hypocritical.

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  • It is probable that if bulk, rapidity of production, variety of matter, originality of design, and excellence of style be taken together, hardly any author can show a work of equal magnitude.

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  • 1918, the magnitude of Germany's defeat being no longer in doubt, the Taryba, or Council of State, promulgated a provisional constitution under which it became the Lithuanian Parliament.

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  • In the United Kingdom the excise duty is eleven shillings per proof gallon of alcohol, while the customs duty is eleven shillings and 5' g fivepence; the magnitude of these imposts may be more readily understood when one remembers that the proof gallon costs only about sevenpence to manufacture.

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  • In the next place we must notice that electrification is a measurable magnitude and in electrostatics is estimated in terms of a unit called the electrostatic unit of electric quantity.

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  • The magnitude of the defeat, unprecedented in American history, was generally considered as due in part to the unwarranted character of the charges made by Cox himself during the campaign, but chiefly to a widespread revolt against the recent course of President Wilson, whose policies Cox upheld.

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  • Trans., 1854, 1862) found that the cooling effect, do, was of the same order of magnitude as the deviations from Boyle's law in each case, and that it was proportional to the difference of pressure, dp, so that d0/dp was nearly constant for each gas over a range of pressure of five or six atmospheres.

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  • Despite the strong and graphic touches here and there, exhibiting the impression which the beauty of sea and land, the splendour of Constantinople, the magnitude of the effete but still imposing Greek power, made on him, there is not only an entire absence of dilation on such subjects as a modern would have dilated on (that was to be expected), but an absence likewise of the elaborate and painful description of detail in which contemporary trouveres would have indulged.

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  • The fisheries are extensive, and though there are no ports of the first magnitude on the firth, a considerable shipping trade is carried on at Whitehaven, Harrington, Workington, Maryport and Silloth in Cumberland, and at Annan, Kirkcudbright, Creetown and Wigtown on the Scottish side.

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  • From an early period of his life in London the condition of the poor pressed upon him with consuming force; the enormous magnitude of the social questions involved was a burden which he could hardly bear.

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  • This movement is characterized firstly by its magnitude; secondly, by the fact that the emigrant changes his political allegiance, for by far the greater part of modern emigration is to independent countries, and even where it is to colonies the colonies are largely self-governing and self-regarding; and thirdly, it is a movement of individuals seeking their own good, without state direction or aid.

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  • Friendly inhabitants kept Bazaine well informed as to the magnitude of the danger threatening him from the south, and a special telegram from Paris, the true origin of which has never been traced, led him to believe that the I.

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  • He had to face the dominant fact of the situation - the aggressive pressure of Germany at a time when Russia was drifting into an internal crisis of the first magnitude and was unable to concentrate the material and moral forces required in the coming conflict.

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  • The administration of the navy, called upon as it was to deal with a war of unprecedented magnitude, was overtaxed by the obligation to refit ships, raise crews, and provide for the numerous sick or wounded.

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  • Interesting stars are: a Aurigae or Capella (the goat), one of the brightest stars in the heavens, determined by Newall and Campbell to be a spectroscopic binary; [3 Aurigae, a star of the second magnitude also a spectroscopic binary; e Aurigae, an irregularly variable star; and Nova Aurigae, a "new" star discovered by Anderson in 1892, and afterwards found on a photographic plate exposed at Harvard in December 1891.

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  • But obstacles of no small magnitude arose.

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  • Nevertheless, the greatest depths of the ocean below sea-level and the greatest heights of the land above it are of the same order of magnitude, the summit of Mount Everest rising to 29,000 ft.

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  • The essential part of many transmission dynamometers is a spring whose deformation indirectly measures the magnitude of the force transmitted through it.

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  • " In modern times the study of nature has brought to light many properties of bodies which appear to depend on the magnitude and motions of their ultimate constituents, and the question of the existence of atoms has once more become conspicuous among scientific inquiries.

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  • The most ancient philosophers whose speculations are known to us seem to have discussed the ideas of number and of continuous magnitude, of space and time, of matter and motion, with a native power of thought which has probably never been surpassed.

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  • From this point of view the atomic doctrine might be regarded as a relic of the old numerical way of conceiving magnitude, and the opposite doctrine of the infinite divisibility of matter might appear for a time the most scientific. The atomists, on the other hand, asserted very strongly the distinction between matter and space.

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  • Some industries which have since become dead or of relatively slight magnitude were once of much greater significance, economically or socially: such as the rum-distilling connected with the colonial slave trade, and various interests concerned with shipbuilding and navigation.

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  • But in 1907 Boston was the second port of the United States in the magnitude of its foreign commerce.

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  • In the same period the mediation of the Board settled disputes affecting 5560 establishments; and in the latter half of this period labour disputes involving hostilities and of the magnitude contemplatedby the statute governing the Board of Conciliation and Arbitration had almost disappeared.

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  • However, looking over the whole field of North American achievement, architectural and non-architectural, composite and monolithic, the palm for boldness, magnitude of proportions and infinity of labour, must go to the sculptured mosaics of Yucatan.

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  • Business interests of this magnitude were constantly expanding, and he became interested in numerous subsidiary enterprises, such as tramways and the supply of electric power and light.

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  • The corresponding solid figure, in its most general form, is such as would be constructed to represent the relation of a magnitude E to two magnitudes F and G of which it is a function; it would stand on a plane base, and be comprised within a cylindrical boundary whose cross-section might be of any shape.

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  • It arises mainly in statistics, when the ordinate of the trapezette represents the relative frequency of occurrence of the magnitude represented by the abscissa x; the magnitude of the abscissa corresponding to the median ordinate is then the " median value of x."

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  • ALGOL, the Arabic name (signifying "the Demon") of, 6 Persei, a star of the second magnitude, noticed by G.

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  • The amplitude of the phase is 1�1 magnitude; and the absence of any stationary interval at minimum proves the eclipse to be partial, not annular.

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  • The refining of sugar was begun in New York City late in the 18th century, but the growth of the industry to its present magnitude has been comparatively recent; the value of the sugar and molasses refined in 1905 was $116,438,838.

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  • Tammany and Hoffman were again victorious in 1870; but in 1871 the New York Times disclosed the magnitude of Tammany's thefts, amounting in the erection of the New York county court house alone to almost $8,000,000, and Tweed and his " Ring " were crushed in consequence.

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  • It is remarkable that, as Lord Rayleigh says, " the streams of energy required to influence the eye and the ear are of the same order of magnitude."

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  • (5) Speed of train produces no effect on the mean deflection, but only on the magnitude of the vibrations.

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  • In the present day engineers are in accord as to the principles of estimating the magnitude of the stresses on the members of a structure, but not so in proportioning the members to resist those stresses.

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  • If the loads are very unequal in magnitude or distance this condition may be satisfied for more than one position of the loads, but it is not 0 difficult to ascertain which position gives the maximum moment.

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  • But very great accuracy in drawing this curve is unnecessary, because the rolling stock of railways varies so much that the precise magnitude and distribution of the loads which will pass over a bridge cannot be known.

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  • 56) represent in magnitude and position a load W, at x from the left abutment, on a girder AB of span 1.

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  • 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.

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  • The fusion of law and equity, the reorganization of the whole judicial system of England, and the association of all the supreme tribunals in one common home were works of no ordinary magnitude or importance, and give a character of unusual importance to his chancellorship. That Lord Selborne was a truly religious man it is impossible to doubt: his whole life was regulated and inspired by a sense of his duty towards God and his fellowmen, and a long life spent amid the temptations of legal and public life left not the faintest stain on his memory.

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  • le Blanc has shown, however, that the effect of ammonium amalgam on the magnitude of polarization of a battery is comparable with that of the amalgams of the alkali metals.

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  • It appears to be a rule that the rivers which eventually terminate in the deserts of Gobi and Takla-makan grow increasingly larger in magnitude from east to west.

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  • 3 The twin ranges of the Astin-tagh are fairly equivalent in point of magnitude and regularity; but while the Lower Range, on the north, sensibly decreases in altitude towards the east,the Upper Range, on the south, maintains its general altitude in a remarkable way, and is gapped by steep, wild, deeply incised transverse glens directed towards the north, and generally fenced in by dark precipitous walls of rock.

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  • For while the self-contained basins of Tibet generally possess a salt lake in the middle, into which brooks and streams of greater or less magnitude gather, often from very considerable distances, these self-contained basins of the Astintagh are very small in area, and it is extremely seldom that their central parts receive any water at all, only in fact after copious rain.

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  • A chart on an isographic projection, exhibiting all the stars contained in the Bonn Durchmusterung, was designed to show the laws according to which the stars down to the 9 - 10th magnitude are distributed over the northern heavens.

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  • But no formula has yet been invented, derived on theoretical principles from the physical data, which will assign by calculation a definite magnitude to 3.

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  • Ptolemy catalogued 8 stars, Tycho 7 and Hevelius Of these, the seven brightest (a of the 1st magnitude, 0, y, of the 2nd magnitude, and b of the 3rd magnitude) constitute one of the most characteristic figures in the northern sky; they have received various names - Septentriones, the wagon, plough, dipper and Charles's wain (a corruption of " churl's wain," or peasant's cart).

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  • The well-established doctrine that the House of Lords could not amend, though it might reject, a money-bill, coupled with the fact that it never had gone so far as to reject a budget, was relied on by the extremists as dictating the obvious party tactics; and before the year 1909 opened, the possibility of the Lords being driven to compel a dissolution by standing on their extreme rights as regards the financial provision for the year was already canvassed in political circles, though it was hardly credited that the government would precipitate a constitutional crisis of such magnitude.

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  • The term "weight" denotes a magnitude of the same nature as a force; the weight of a body is the product of the mass of the body by the acceleration of gravity; in particular, the normal weight of a body is the product of the mass of the body by the normal acceleration of gravity.

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  • It has no attributes of any kind; it is being without magnitude, without life, without thought; in strict propriety, indeed, we ought not to speak of it as existing; it is " above existence," " above goodness."

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  • With the first instrument of this kind, having objectives of 1 5 inch aperture, he measured the brightness of 4260 stars, including all stars down to the 6th magnitude between the North Pole and - 30° declination.

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  • The magnitudes of nearly 8000 southern stars were determined, including 1428 stars of the 6th magnitude and brighter.

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  • The instrument was then returned to Cambridge (U.S.A.), where the survey extended so as to include all stars of magnitude 7.5 down to - 40° declination, after which it was once more sent back to Arequipa.

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  • By beginning the table at 20,000 instead of at io,000 the differences are halved in magnitude, while the number of them in a page is quartered.

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  • In view of the magnitude of the undertaking it is on the contrary highly probable that other translators besides Wycliffe and Nicholas de Herford took part in the work, and that already existing versions, with changes when necessary, were incorporated or made use of by the translators.

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  • The first mill in Bradford was built in 1798; there were 20 mills in the town in 1820, 34 in 1833, and 70 in 1841; and at the present time there are over 300, of much greater magnitude than the earlier factories.

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  • The magnitude in 1905 of each of the leading items, and its increase since 1900, then appear as follows: number of factories, 216,262, increase 4.2%; capital invested, $12,686,265,673, increase 41.3% salaries, $574,761,231, increase 50.9%; total wages, $2,009,735,799, increase 29.9%; miscellaneous expenses, $1,455,019,473, increase 60-7%; cost of materials, $8,503,949,756, increase 29.3%; value of products, including custom work and repairing (in such factories), $14,802,147,087, being an increase of 29.7%.

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  • The remainder, or element of foreign exports, has been of similarly small relative magnitude since about 1880, but was of course much larger while the carrying trade was of importance.

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  • The magnitude of these items is so great as to defy exact determination; data for the formation of some idea of them can be found in the account of the mineral, forest and agricultural resources of the country.

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  • P. Austin, chief of the national bureau of statistics, using data of 1903, that the internal commerce of the United States exceeds in magnitude the total international commerce of the world., (F.

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  • St Laura is exceeded in magnitude by the convent of Vato pede, also on Mount Athos.

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  • The most famous of the lakes are those of the St Lawrence system, which form part of the southern boundary of Canada and are shared with the United States; but many others have the right to be called " Great Lakes " from their magnitude.

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  • He would even be drawn into this process by his writing materials, which were papyrus rolls of some magnitude; he would tend to write discourses on separate rolls, and then fasten them together in a bundle into a treatise.

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  • number in arithmetic, magnitude in geometry, stars in astronomy, a man's good in ethics; concentrates itself on the causes and appropriate principles of its subject, especially the definition of the subject and its species by their essences or formal causes; and after an inductive intelligence of those principles proceeds by a deductive demonstration from definitions to consequences: philosophy is simply a desire of this definite knowledge of causes and effects.

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  • " The other dimensions may be had from the drawing, which is one-sixth of the linear magnitude of the instrument itself.

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  • corum, a double star, of magnitudes 3 and 6; this star was named Cor Caroli, or The Heart of Charles II., by Edmund Halley, on the suggestion of Sir Charles Scarborough (1616-1694), the court physician; a cluster of stars of the firth magnitude and fainter, extremely rich in variables, of the goo stars examined no less than 132 being regularly variable.

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  • The diagonal AD of the parallelogram, of which AB and AC are adjacent sides, will represent, both in direction and magnitude, the motion of the rain as apparent to the observer.

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  • Hooke, in 1674, published his observations of y Draconis, a star of the second magnitude which passes practically overhead in the latitude of London, and whose observations are therefore singularly free from the complex corrections due to astronomical refraction, and concluded that this star was 23" more northerly in July than in October.

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  • (g) Increased pressure nearly always diminishes the frequency of vibration, but this effect is generally of a smaller order of magnitude than the widening which takes place in the other cases.

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  • These rays are apparently the trajectories of positively charged particles having masses of the order of magnitude of the gaseous molecules.

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  • Two events of the first magnitude make his reign one of the most memorable in the century.

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  • It has since been discovered, however, that the magnitude of the acceleration in question is not exactly the same at different places on the earth, the range of variation amounting to about 2%.

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  • Galileo proceeded to measure the motion of a body on a smooth, fixed, inclined plane, and found that the law of constant acceleration along the line of slope of the plane still held, the acceleration decreasing in magnitude as the angle of inclination was reduced; and he inferred that a body, moving on a smooth horizontal plane, would move with uniform velocity in a straight line if the resistance of the air, and friction due to contact with the plane, could be eliminated.

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  • A force is said to act upon each of two particles forming a pair, its magnitude being the product of mass and component acceleration of the particle on which it acts, and its direction that of this component acceleration.

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  • - Wherever there is a flower garden of considerable magnitude, and in a separate situation, it should be constructed on principles of its own.

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  • Deposits of such cupriferous pyrites are widely distributed and are often of great magnitude.

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  • But, though their publications count a large number of first editions, and some are works of considerable magnitude, they were not brought out with the scholarly perfection at which Aldo aimed.

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  • Polymerism required no particular explanation, since this was given by the difference in molecular magnitude.

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  • The following table shows the amount of exports and imports between Belgium and the more important foreign states: - In the relative magnitude of the annual value of its commerce, excluding that in transit, Belgium stands sixth among the nations of the world, following Great Britain, the United States, Germany, France and Holland.

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  • With the gradual disuse of the old barbarous punishments so universal in medieval times came also a reversal of opinion as to the magnitude of the crime involved in killing a child not yet born.

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  • But he and his followers appear to have greatly exaggerated both the magnitude and the urgency of the dangers to which they pointed.'

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  • The magnitude of the stress per unit area parallel to the direction of flow is evidently proportional to the velocity gradient, or the rate of change of velocity per cm.

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  • Thus, in the first decade of the 20th century a great advance had been made in the way in which the whole problem was being viewed in America, though the very immensity of the problem of bringing the Federal power to bear on operations on so vast a scale, involving the limitation of private land speculation in important areas, still presented political difficulties of considerable magnitude.

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  • The magnitude of the task he had accomplished is shown by the preceding pages, and it need only be added that the transformation effected in Egypt and the Sudan, during his twenty-fout years occupancy of the British Agency, was carried out in every department under his guidance and inspiration.

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  • Finally, a barrow of great magnitude was heaped over the remains and the funeral feast was celebrated.

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  • In the great plains of North America the dead were buried in barrows of enormous magnitude, which occasionally present a remarkable similarity to the barrows of Great Britain.

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  • There are some repetitions and some inconsistencies, but not more than may fairly be allowed for in a compilation of such magnitude executed so rapidly.

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  • Prosecutions were few in number, which is surprising considering the length and magnitude of the war.

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  • Instead of a single relatively large The Chlorophyceae excel all other groups of algae in the magnitude and variety of form of the chlorophyll-bodies.

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  • His principal work was, however, a catalogue of 12,441 stars to the 7th magnitude between the South Pole and 25° S.

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  • At Oxford he extended the Cape observations of stars to the 7th magnitude from 25° S.

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  • The imports of ore in that year amounted to 1,862,444 tons of the value of £1,420,379 The oil shale industry is wholly modern and has attained to considerable magnitude since it was established (in 1851 and following years).

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  • Wallace, whilst insisting that the range of observed and measured variation was much larger in proportion to the size of the organisms or parts of organism affected than was generally believed, leaned to the Darwinian view in excluding from the normal factors in the origin of species variations of the extremer ranges of magnitude.

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  • de Vries, have urged that as species are discontinuous - that is to say, marked off by structural differences of considerable magnitude - it is more probable that they have arisen from similarly discontinuous variations.

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  • It is doubtful, however, if there is any philosophical basis for distinguishing between variations merely by their magnitude.

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  • Even amongst the extreme advocates of the theory of mutations, the importance of magnitude is being discounted by their suggestion that some of the minute variations which have hitherto been regarded by them as insignificant "fluctuating variations" may be significant mutations.

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  • This in effect is to say that not magnitude but something else has to be sought for if we are to pick out amongst observed variations those which may be the material for the differentiation of species.

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  • So far as magnitude is concerned, the attack on the Darwinian position has failed, and it is agreed that species may be discontinuous and none the less have been produced from minute variations.

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  • With our present knowledge it is impossible to discriminate between variation that may or that may not be the material for the differentiation of species by scrutinizing either magnitude or probable causation.

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  • This group is particularly rich in bright stars, and is full of nebulosity, but there are fewer faint stars than in equal areas of the surrounding sky; the central star is Alcyone (3rd magnitude); PleIone and Atlas are also of the 3rd magnitude.

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  • He goes on to show that eternal being must also be unlimited in magnitude, and, therefore, one and unchangeable.

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  • But this and the following years were signalized by a series of catastrophes of the first magnitude.

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  • The most interesting members are: a Coronae, a binary consisting of a yellow star of the 6th magnitude, and a bluish star of the 7th magnitude; R Coronae, an irregular variable star; and T Coronae or Nova Coronae, a temporary or new star, first observed in 1866.

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  • In addition to Arcturus, the brightest in the group, the most interesting stars of this constellation are: e Bootis, a beautiful double star composed of a yellow star of magnitude 3, and a blue star of magnitude 62; Bootis, a double star composed of a yellow star, magnitude 41, and a purple star, magnitude 61-; and W.

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  • In the former even the Pliocene beds are crumpled and folded, overfolded and overthrust in the most violent fashion; in the latter none but the oldest beds, certainly none so late as the Permian, have been crumpled or crushed - occasionally they are bent and frequently they are faulted, but the faults, though sometimes of considerable magnitude, are simple dislocations, unaccompanied by any serious disturbance of the strata.

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  • This period was marked by two wars of the first magnitude, the campaigns against the Gurkhas of Nepal, and the third and last Mahratta War.

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  • Man, said the Stoic, is a rational animal; and in virtue of that rationality he is neither less nor worse than the gods, for the magnitude of reason is estimated not by length nor by height but by its judgments.

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  • This method has been very generally recommended, but it is really bad, because, although it diminishes the absolute magnitude of the correction, it greatly increases the uncertainty of it and therefore the probable error of the result.

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  • At 30° He Considered That, Owing To The Increasing Magnitude And Uncertainty Of The Radiation Correction, There Fig.

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  • With the development of observational astronomy the sidereal universe was arbitrarily divided into areas characterized by special assemblages of stars; these assemblages were named asterisms by Ptolemy, who termed the brightest stars "of the fi rst magnitude," and the progressively fainter Stars.

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  • P g Y stars of progressively greater magnitude.

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  • In this system one star is defined to be unit magnitude higher than another if its light is less in the ratio I:2 512.

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  • The faintest stars visible to the naked eye on clear nights are of about the sixth magnitude; exceptionally keen, well-trained eyes and clear moonless nights are necessary for the perception of stars of the seventh magnitude.

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  • Heis the numbers and magnitudes of stars between the north pole and a circle 35° south of the equator are: - From the value of the light-ratio we can construct a table showing the number of stars of each magnitude which would together give as much light as a first magnitude star, viz.: - Comparing these figures with the numbers of stars of each magnitude we notice that the total light emitted by all the stars of a given magnitude is fairly constant.

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  • - Although the majority of the stars are unchanging in magnitude, there are many exceptions.

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  • Many of these stars seem to vary quite irregularly; the changes of magnitude do not recur in any orderly way.

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  • The varying brightness, ranging from the ninth to the second magnitude, was recognized in 1639 by John Phocylides Holwarda, and in 1667 Ismael Boulliau (1605-1694) established a periodicity of 333 days.

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  • The different maxima differ considerably in brightness; thus in 1906 (the brightest maximum since 1779) the second magnitude was reached, but in other years (as in 1868) it has failed to reach the fifth magnitude.

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  • The change of magnitude takes place gradually, but the rise to maximum brilliance is rather more rapid than the decline.

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  • X Cygni is another star of this class, remarkable for its range of magnitude.

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  • The recognition of stars is primarily dependent on their brightness or " magnitude "; and it is clear that stars admit of classification on this basis.

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  • Algol is ordinarily of magnitude 2.3, but once in a period of 2d.

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  • it suffers partial eclipse and fades to magnitude 3.5.

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  • from a maximum of magnitude 3.4 it falls to 3.9, rises again to 3.4, then falls to 4.5 and returns to magnitude 3.4.

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  • Supposing that the two stars are of unequal surface brilliancy, the magnitude at minimum will depend on which of the two stars is the nearer to us, accordingly there are two unequal minima in each revolution.

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  • In five days its light had reached the first magnitude, and a little later it even equalled Venus in brilliancy and was observed in full daylight.

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  • Anderson on the 21st-22nd of February, its magnitude at that time being 2.7.

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  • In the next two days it reached zero magnitude, thus becoming the brightest star in the northern heavens, but after that it rapidly decreased.

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  • On the 15th of March it was of the fourth magnitude; during the next three months it oscillated many times between magnitudes 4 and 6, and by the end of the year it had faded to the seventh magnitude.

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  • In July 1903 it was of the twelfth magnitude, and its light has remained constant since then.

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  • In the case of this star there is evidence that the outburst must have been extremely rapid, for the region where Nova Persei appeared had been photographed repeatedly at Harvard during February, and in particular no trace of the star was found on a plate taken on the 19th of February, which showed eleventh magnitude stars.

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  • It is now about magnitude 7.5.

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  • Of the first magnitude red stars Antares is the most deeply coloured, Betelgeux,.Aldebaran and Arcturus being successively less conspicuously red.

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  • stars are known, but none conspicuous; 19 Piscium, the brightest, is of magnitude 5.5.

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  • He chose for his purpose the binary star 61 Cygni, which was the star with the most rapid apparent motion then known and therefore likely to be fairly near us, although only of the sixth magnitude.

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  • These two stars must have an intrinsic brilliancy enormously greater than that of the sun, for if the sun were removed to such a distance (parallax o oi"), it would appear to be of about the tenth magnitude.

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  • These stars include most of the brighter ones visible in the latitude of Greenwich, ranging down to about the seventh magnitude.

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  • An early catalogue which includes large numbers of stars of magnitude as low as 8.5 is that of S.

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  • The stars composing this all have equal and parallel motions; about 40 stars brighter than the seventh magnitude are known to belong to it.

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  • They have been shown to prevail among fainter stars down to magnitude 9.5, by an examination of the Greenwich-Carri,Igton proper motions; these, however, only cover a region within 9° of the north pole.

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  • Of the behaviour of stars fainter than magnitude 9.5 there is at present no direct evidence.

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  • But notwithstanding the great variety of intrinsic brightness of the stars, the ratio of the number of stars of one magnitude to the number of the magnitude next lower (the " star-ratio ") is a guide to the uniformity of their distribution.

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  • There is here evidence that even among stars of the Durchmusterung (9.5 magnitude), a limit of the universe has been reached, at least in the direction normal to the plane of the Milky Way.

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  • The following table shows the density with which stars brighter than the ninth magnitude are distributed in each of nine zones into which Seeliger divided the heavens and more generally recognized that the stars are not unrelated; they are parts of a greater system, and we have to deal with, not merely the history of a number of independent units, but with a far vaster conception, the evolution and development of an ordered universe.

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  • The star-gauges of the Herschels exhibit a similar result; the Herschels counted the number of stars visible with their powerful telescopes in different regions of the sky, and thus formed comparative estimates of the density of the stars extending to a very high magnitude.

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  • Thus the figure represents a section the (ideally simplified) uni verse cut perpendicular to C P' D the planes AB and CD between which the stars are contained, 1 This number is the 3/2th power of the ratio of the brightness of stars differing by a unit magnitude.

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  • Dyson and Thackeray's tables show the same result for the Groombridge stars down to magnitude 6.5; but the fainter stars (with centennial proper motions greater than 5") show a marked tendency to draw towards the galactic circle.

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  • We infer that nearly all the stars down to magnitude 6.5, whose proper motions exceed 5", are at a distance from the sun less than SP, whilst of the fainter stars with equally great proper motions a large proportion are at a distance greater than SP. This result enables us to form some sort of idea of the distance SP.

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  • The result of course only applies to the brighter stars, for we have very little knowledge of the spectra 'of stars fainter than about magnitude 7.5.

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  • McClean, of the stars brighter than magnitude 3.5, only the helium and not the hydrogen stars of Type I.

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  • Thus we see that the effect of limiting the magnitude to 3.5 is that the hydrogen stars are now practically all within the sphere SP, and it is only the helium stars, whose absolute luminosity is still greater, that are more widely distributed.

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  • Taking a sphere whose radius is 560 light years (a distance about equal to that of the average ninth magnitude star), it will contain: I star giving fromloo,000 to io,000 times the light of the sun 26 stars „ 1,000 „ „ 1,000 „ 100 „ 22,000 „ „ 100 „ 10 „ „ „ 140,000 „ „ IO „ I „ 430,000, ,„ I, , 0.I, , n 650,000 „ „ 0 I „ 0.01 „ .„ Whether there is an increasing number of still less luminous stars is a disputed question.

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  • Kapteyn finds that magnitude for magnitude, the absolute brightness of the solar stars is only one-fifth of that of the Sirian stars, so that in the mean they must be at less than half the distance.

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  • It is a fact of first-rate magnitude that in the 15th century customary relations on one hand, the power of government on the other, ripened, as it were, to that extent that the judges of the king began to take cognizance of the relations of the peasants to their lords.

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  • arithmetic of number, geometry of magnitude, astronomy of stars, politics of government, ethics of goods.

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  • Thus, applied to a potential, it gives the direction and magnitude of the force; to a distribution of temperature in a conducting solid, it gives (when multiplied by the conductivity) the flux of heat, &c.

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  • The plane is of vector magnitude ZVq, its equation is ZSpq=Sr, and its expression is the bi-quaternion nVq+wSr; the point is of scalar magnitude 4Sq, and its position vector is [3, where 1Vf3q=Vr (or what is the same, fi = [Vr+q.

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  • By evening the magnitude of the initial enemy success was clear, though it was not yet clear to what extent the whole Italian left wing was crumbling.

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  • Western Europe was taken out of the imperial mould and broken up. This is a revolution of sufficient magnitude to be regarded as politically the opening of a new era.

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  • A force is conceived as an effort having a certain direction and a certain magnitude.

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  • It is therefore adequately represented, for mathematical purposes, by a straight line AB drawn in the direction in question, of length proportional (on any convenient scale) to the magnitude of the force.

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  • If three forces acting on a particle are represented as to magnitude and direction by the sides of a triangle taken in order, they are in equilibrium.

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  • it acts in a definite line and has a definite magnitude and sense.

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  • In all cases the magnitude and direction, and joining the vertices of the polygon thus formed to an arbitrary pole 0.

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  • Now x, x have a resultant through H, represented in magnitude and direction by 00, whilst y,y have a resultant through K represented in magnitude and direction by OO.

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  • The translation parallel to this axis is lox + mly + nhz (Xf + uv + vi) Ic. (8) The linear magnitude which measures the ratio of translation to rotation in a screw is called the pitch.

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  • Its type, as distinguished from its absolute magnitude, may be specified by a screw whose axis is the line of action of R, and whose pitch is the ratio G/R.

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  • since, in this proof the magnitude of P is arbitrary, it follows incidentally that couples of the same moment in parallel planes, 1.g.

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  • If we imagine the bar in question t be removed, equilibrium will still persist if we introduce two equal and opposite forces S, of suitable magnitude, at the joints which it connected.

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  • If we construct the quadric Axi+By2+Czi 2Fyz2Gzx 2HXy = M~4, (3c~) where e is an arbitrary linear magnitude, the intercept r which it makes on a radius drawn in the direction X, u, v is found by putting x, y, z=Ar, ur, Pr.

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  • the relative velocity of the two bodies is reversed in direction, but unaltered in magnitude.

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  • Thus the unit of velocity is that of a point describing the unit of length in the unit of time; it may be denoted by LTi, this symbol indicating that the magnitude of the unit in question varies directly as the unit of length and inversely as the unit of time.

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  • Ihe number which expresses a physical quantity of any particular kind will of course vary inversely as the magnitude of the corresponding unit.

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  • a point moving with a constant velocity having the magnitude and direction.

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  • Obviously OV is parallel to the tangent to the path atP, and its magnitude is ds/dt, where s is the arc. If we project OV on the co-ordinate axes (rectangular or oblique) in the usual manner, the projections u, v, w are called the component velocities parallel to the axes.

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  • Newtons Second Law asserts that change of momentum is equal to the impulse; this is a statement as to equality of vectors and so implies identity of direction as well as of magnitude.

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  • The locus of the point V is called the hodograp/z (q.v.); and it appears that the velocity of the point V along the hodograph represents in magnitude and in directon tbt acceleration in the original orbit.

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  • For the velocity of a particle m at P may be replaced by two components one of which (ii) is identical in magnitude and direction with the velocity of G, whilst the other (v) is the velocity relative to G.

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  • If OK be the vector representing the former component at time t, the vector which represents it at time 1+&t will be OK, equal to oi~ in magnitude and making with it an angle o~.

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  • Further, at any one of the centres of load let PL represent the magnitude and direction of the gross load, and Pa, Pb the two resistances by which the piece to which that load is applied is supported; then wifl those three lines be respectively the diagonal and sides of a parallelogram; or, what is the same thing, they will be equal to the three sides of a triangleS and they must be in the same plane, although the sides of the polygon of resistances may be in different planes.

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  • direction and magnitude.

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  • For the condition of equilibrium of forces not parallel is that they shall be represented in direction and magnitude by the sides and diagonals of certain parallelograms, and of parallel forces that they shall divide certain straight lines in certain ratios; and the parallel projection of a parallelogram is a parallelogram, and that of a straight line divided in a given ratio is a straight line divided in the same ratio.

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  • Conditions of Stiffness and Strength.After the arrangement of the pieces of a structure and the size and figure of their joints or surfaces of contact have been determined so as to fulfil the conditions of stabilityconditions which depend mainly on the position and direction of the resultant or total load on each piece, and the relative magnitude of the loads on the different piecesthe dimensions of each piece singly have to be adjusted so as to fulfil the conditions of stiffness and strengthconditions which depend not only on the absolute magnitude of the load on each piece, and of the resistances by which it is balanced, but also on the mode of distribution of the load over the piece, and of the resistances over the joints.

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  • Method 1.By reference to 30 it will be seen that the motion of a cylinder rolling on a fixed cylinder is one of rotation about an instantaneous axis T, and that the velocity both as regards direction and magnitude is the same as if the rolling piece B were for the instant turning about a fixed axis coincident with the instantaneous axis.

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  • Then Ob is the velocity of the point b in magnitude and direction, and cb is the tangential velocity of B relatively to C. Moreover, whatever be the actual magnitudes of the velocities, the instantaneous velocity ratio of the points C and B is given by the ratio Oc/Ob.

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  • 123 and 124) is the following: If points X and x are taken dividing the link BC and the tangential velocity cb, sothat cx: xb=CX:XB, then Ox represents the velocity of the point X in magnitude and direction.

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  • 124), then a vector drawn from 0 to any point on the new drawing of the rod will represent the velocity of that point of the actual rod in magnitude and direction.

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  • 125) have plane motion and the acceleration of any point C be given in magnitude and direction, the acceleration of any c other point B is the vector sum of X

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  • The magnitude of the radial acceleration is given by the expression vi/BC, v being the velocity of the point B about the point C. This velocity can always be found from the velocity diagram of the chain of which the link forms a part.

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  • If dw/dt is the angular acceleration of the link, dw/dt X CB is the tangential acceleration of the point B about the point C. Generally this tangential acceleration is unknown in magnitude, and it becomes part of the problem to find it.

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  • An important property of the diagram is that if points X and x are taken dividing the link CB and the whole acceleration of B about C, namely, cb in the same ratio, then Ax represents the acceleration of the point X in magnitude and direction; cb is called the acceleration image of the rod.

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  • Variable Effort and Resistance.Jf an effort has different magnitudes during different portions of the motion of its point of application through a given distance, let each different magnitude of the effort P be multiplied by the length Lts of the corresponding portion of the path of the point of application; the sum ~.

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  • Its magnitude is the product of the normal pressure or force which presses the rubbing surfaces together in~ a direction perpendicular to themselves into a specific constant already mentioned in 14, as the coefficient of friction, which depends on the nature and condition of the surfaces of the unguent, if any, with which they are covered.

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  • The magnitude of the useful resistance.

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  • The magnitude of that reaction.

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  • The magnitude of the effort.

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  • p Thus is determined the direction of the reaction of the bearing; and the magnitude FIG.

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  • Centrifugal Force of a Rotating BodyThe centrifugal force exerted by a rotating body on its axis of rotation is the same in magnitude as if the mass of the body were concentrated at its centre of gravity, and acts in a plane passing through the axis of rotation and the centre of gravity of the body.

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  • In drawing these polygons the magnitude of the vector of the type Wr is the product Wr, and the direction of the vector is from the shaft outwards towards the weight W, parallel to the radius r.

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  • The magnitude of the vector is the product War.

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  • Hence by drawing a couple polygor for the given weights the vector which is required to close the polygor is at once found and from it the magnitude and position of the balanci weight which must be added to the system to balance the couplo follow at once.

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  • * To find the force competent to produce the instantaneous acceleration of any link of a meclianism.In many practical problems it is necessary to know the magnitude and position of the forces acting to produce the accelerations of the several links of a mechanism.

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  • Hence the magnitude F and the position of F relatively to the centre of gravity of the link, necessary to give rise to the couple M, are known, and this force is therefore the resultant force required.

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  • Consequently, he fails to understand the essential magnitude of the task, or to appreciate the vital vigour of the forces contending in Europe for mastery.

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  • Society at large was hardly aware that an intellectual force of stupendous magnitude and incalculable explosive power had been created by the new learning.

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  • The annual collection of 460 talents (I 10,400) shows sufficiently the magnitude of the league.

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  • To national debts there has been added a great mass of municipal and local indebtedness, which seems likely to equal, or even exceed in magnitude the liabilities of the central governments.

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  • Unfortunately, prudential motives hindered the publication of the whole evidence; the people, consequently, were still ignorant of the magnitude of the crime, and, till recently, biographers of Bacon have been in a like ignorance.

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  • " The knowledge whereof the world is now possessed, especially that of nature, extendeth not to magnitude and certainty of works."

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  • Thus Sweden emerged from the war not only a military power of the first magnitude, but also one of the largest states of as Europe, possessing about twice as much territory as modern Sweden.

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  • The relative magnitude and value of these mineral products may be seen in the following abstract from the official returns of 1903: - Government.

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  • the relative position and magnitude of the images, are not special properties of optical systems, but necessary consequences of the supposition (in Abbe) of the reproduction of all points of a space in image points (Maxwell assumes a less general hypothesis), and are independent of the manner in which the reproduction is effected.

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  • With a considerable aperture, the neighbouring point N will be reproduced, but attended by aberrations comparable in magnitude to ON.

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  • If, in the first place, monochromatic aberrations be neglected - in other words, the Gaussian theory be accepted - then every reproduction is determined by the positions of the focal planes, and the magnitude of the focal lengths, or if the focal lengths, as ordinarily happens, be equal, by three constants of reproduction.

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  • For example, it is possible, with one thick lens in air, to achromatize the position of a focal plane of the magnitude of the focal length.

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  • (1766); " An Inquiry into the Probable Parallax and Magnitude of the Fixed Stars," ibid.

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  • (1767), " On the Means of Discovering the Distance, Magnitude, &c., of the Fixed Stars," ibid.

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  • The so-called rebellions which followed were many, but not of any magnitude.

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  • Brongniart, no doubt, was overwhelmed with the continually increasing magnitude of the task that he had undertaken.

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  • The shoulders and fore-limbs are feebly developed, and the hind-limbs of disproportionate strength and magnitude, which give the animals a peculiarly awkward appearance when moving about on all-fours, as they occasionally do when feeding.

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  • There are some fine stalactites near this pit, and others in the Fairy Grotto and in Pensico Avenue; but, considering the magnitude of Mammoth Cave, its poverty of stalactitic ornamentation is remarkable.

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  • From the absence of any well-marked unconformity it is evident that in the northern part of the Himalayan belt, at least in the Spiti area, there can have been no post-Archaean folding of any magnitude until after the deposition of the Nummulitic beds, and that the folding was completed before the later Tertiaries of Hundes were laid down.

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  • It is but lately, however, that any adequate conception of the magnitude and majesty of the most stupendous of the mountain groups which mass themselves about the upper tributaries and reaches of the Indus has been presented to us in the works of Sir F.

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  • Some idea of the magnitude of Himalayan mountain construction - a magnitude which the eye totally fails to appreciate - may, however, be gathered from the following table of comparison of the absolute height of some peaks above sea-level with the actual amount of their slopes exposed to view: - Relative Extent of Snow Slopes Visible.

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  • Instead of calculating the direction and magnitude of the resultant force on each particle arising from the action of neighbouring particles, he formed a single expression which is the aggregate of all the potentials arising from the mutual action between pairs of particles.

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  • Since e is a line of insensible magnitude compared with the dimensions of the mass of liquid and the principal radii of curvature of its surface, the volume of the shell whose surface is S and thickness will be and that of the interior space will be V - SE.

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  • When a drop of one liquid, B, is placed on the surface of another, A, the phenomena which take place depend on the relative magnitude of the three surface-tensions corresponding to the surface between A and air, between B and air, and between A and B.

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    0
  • The densities a 1, 'a' 2, Q3 being in descending order of magnitude, we may write T 31 = (01 - 02+a, - o"3)'T0 =T 12+ T 23 + 2 (e 1 - (72) (02-0.3)Tc; so that T31 necessarily exceeds the sum of the other two interfacial tensions.

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  • The second minus the first, or the increase in the sum of tensions, is thus 2 (U n - o' n+l) (o n+ 1 - Q n +2) Hence, if an+1 be intermediate in magnitude between a,, and a71+2, the sum of tensions is increased by the abolition of the stratum; but, if a-n+1 be not intermediate, the sum is decreased.

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  • We see, then, that the removal of a stratum from between neighbours where it is out of order and its introduction between neighbours where it will be in order is doubly favourable to the reduction of the sum of tensions; and since by a succession of such steps we may arrive at the order of magnitude throughout, we conclude that this is the disposition of minimum tensions and energy.

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  • The Magnitude Of A Drop Delivered From A Tube, Even When The Formation Up To The Phase Of Instability Is Infinitely Slow, Cannot Be Calculated A Priori.

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    0
  • But a disturbance of less favourable wave-length may gain the preponderance in case its magnitude be sufficient to produce disintegration in a less Lime than that required by the other disturbances present.

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  • principally the result of chlorophyll action on the carbon dioxide of the atmosphere decomposed by energy derived from the sun; and although we know little as yet concerning the magnitude of other processes of carbon-assimilation - e.g.

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  • Being is the Full i pes, plenum); not-Being is the Void (nEvov, vacuum), the infinite space in which moved the infinite number of atoms into which the single:Being of the Eleatics was broken up. These atoms are eternal and invisible; absolutely small, so small that their size cannot be diminished (hence the name IITOµos, "indivisible"); absolutely full and incompressible, they are without pores and entirely fill the space they occupy; homogeneous, differing only in figure (as A from N), arrangement (as AN from NA), position (as N is Z on its side), magnitude (and consequently in weight, although some authorities dispute this).

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  • The United States contended that it must be a diligence commensurate with the emergency or with the magnitude of the results of negligence.

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  • Sagittae is a short period variable, period 8.38 days, range in magnitude 5.6 to 6.4.

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  • In Exhibition Park there is held annually an industrial and agricultural exhibition that has grown to great magnitude.

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  • Dom Bouquet's Historiens de la Gaule et de la France - the national repertory for French historians - is but one of a dozen tasks of similar magnitude.

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  • The most brilliant stars are a Andromedae or "Andromeda's head," and f3 Andromedae in the girdle (Arabic mirach or mizar), both of the second magnitude; y Andromedae in the foot (alamak or alhames), of the third magnitude.

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  • The glaciers too decrease in the same proportion both in magnitude and in extent.

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  • During the years 1821-1833, he observed all stars to the ninth magnitude in zones extending from-15° to +45° dec., and thus raised the number of those accurately determined to about 50,000.

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  • the " determinants " or ideas; secondly, mat hematical numbers, the abstractions of mathematics; and thirdly sensible numbers, numbers embodied in things - Speusippus rejected the ideal numbers, and consequently the ideas; (3) Speusippus traced number, magnitude and soul each to a distinct principle of its own.

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  • The planet showed a stellar disk varying in magnitude from 9 to 12.

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  • On some plates the stars were allowed to trail and the planet was followed, in others the reverse procedure was taken; in either case the planet's position is measured by referring it to " comparison stars " of approximately its own magnitude situated within 25' to 30' of the centre of the plate, while these stars are themselves fixed by measurement from brighter " reference stars," the positions of which are found by meridian observations if absolute places are desired.

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  • If we regard the sun as one of the stars, the first four questions we should seek to answer are its distance from its neighbours, proper motion, magnitude and spectral type.

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  • A star is said to rise one unit in magnitude when the logarithm of its brightness diminishes by 0.4.

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  • Taking as a star of magnitude I a Tauri or a Aquilae, where would the sun stand in this scale ?

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  • Several estimates have been made which agree well together; whether direct use is made of known parallaxes, or comparison is made with binaries of well-determined orbits of the same spectral type as the sun, in which therefore it may be assumed there is the same relation between mass and brilliancy (Gore), the result is found that the sun's magnitude is - 26.5, or the sun is Io n times as brilliant as a first magnitude star; it would follow that the sun viewed from a Centauri would appear as of magnitude 0.7, and from a star of average distance which has a parallax certainly less than o 1 ", it would be at least fainter than the fifth magnitude, or, say, upon the border-line for naked-eye visibility.

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  • The action of Sir Benjamin D'Urban was not approved by the home government, and on the instruction of Lord Glenelg, secretary for the colonies, who declared that " the great evil of the Cape Colony consists in its magnitude," the colonial boundary was moved back to the Great Fish river, and eventually (in 1837) Sir Benjamin was dismissed from office.

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  • The late Sir Benjamin Baker, F.R.S., suggested that the stresses might be measured by experiments with elastic models, and among others, experiments were carried out by Messrs Wilson and Gore a with indiarubber models of plane sections of dams (including the foundations) who applied forces to represent the gravity and water pressures in such a manner that the virtual density of the rubber was increased many times without interfering with the proper ratio between gravity and water pressure, and by this means the strains produced were of sufficient magnitude to be easily measured.

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  • It is important to notice that the maximum value of the tension at the toe lies in a direction approximately at 45° to the vertical, but at points lower down in the foundation this tension, while less in magnitude, becomes much more horizontal.

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  • Similar experiments upon models with rounded toes but otherwise of the same form showed a considerable reduction in the magnitude of the tensile stresses.

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  • Arrow heads at the ends of an axis of an ellipse indicate tension as distinct from compression, and the semi-axes in magnitude and direction represent the principal stresses.

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  • To Chevalier Hiilsemann, then representing Austria at Washington, who had demanded from the United States the disavowal of the acts of its agents, the complete surrender of Koszta, and " satisfaction proportionate to the magnitude of the outrage," Marcy wrote on the 26th of September 1853, that Koszta " when seized and imprisoned was invested with the nationality of the United States " and had a right to the protection of the United States government, and added: " Whenever by the law of nations an individual becomes clothed with our national state paper, and the principles it enunciates have been approved by leading authorities on international law.

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  • The magnitude of the unbalanced force, for a mass of w pounds at a radius of r feet and a velocity of v feet per second, is expressed by wv 2 /gr lb; and, since the force varies as the square of the velocity, it is necessary carefully to balance a pulley running at a high speed to prevent injurious vibrations.

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  • amounts proportional to the magnitude of each, and in addition to cause a loss M due to the weights of the parts themselves.

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  • - The work of Gratian, though prepared and made possible by those of his predecessors, greatly surpasses them in The scientific value and in magnitude.

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  • He therefore was led to inquire whether, if the earth's attraction extended to the moon, the force at that distance would be of the exact magnitude necessary to retain the moon in its orbit.

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  • This estimate of the earth's magnitude, giving 69.1 m.

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  • 3.5 (v.) Relative Magnitude

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  • The diversity of scales appears to be due mainly to four causes: (i) the tendency to group into scores (§ 20); (ii) the tendency to subdivide into twelve; (iii) the tendency to subdivide into two or four, with repetitions, making subdivision into sixteen or sixty-four; and (iv) the independent adoption of different units for measuring the same kind of magnitude.

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  • Representation of Geometrical Magnitude by Number.

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  • This is the most general expression of the relative magnitude of two quantities; i.e.

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  • This is the usual method; but the relative accuracy of two numbers expressed to the same number of significant figures depends to a certain extent on the magnitude of the first figure.

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  • If an unknown stranger or person without property caught red-handed in the commission of a crime refused to submit to arrest, it was lawful to maim or slay him according to the magnitude of the attempted crime.

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  • Hence according to the magnitude of each coil the total resistance may be made anything from I to 9, 10 to 90, or 100 to goo ohms, &c. Three or four of the " dials " thus composed are arranged side by side, the brass blocks being mounted on a slab of ebonite and the coils contained in the box underneath, and they are so joined up that the central block of one dial is connected to the outside block of the next marked O.

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  • The supremacy of the House of Commons would have been an evil of no common magnitude, if it had made government Beginning impossible.

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  • It is distinguished by a simple yet thoroughly philosophical treatment of the ideas of number and magnitude, as well as by the introduction of new abbreviated processes of computation, to which De Morgan always attributed much practical importance.

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  • For the purpose of getting rid of the water, and obviating the flooding of such deep workings, it has been found necessary to construct drainage works of some magnitude.

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  • Since the middle of the 18th century there have been five floods of extraordinary magnitude, - namely, in 1748, 1786, 1805, 1820 and 1845.

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  • Meanwhile, consciously and unconsciously, as is the way with men of genius, his mind was working upon problems of government, the magnitude, the relations and the natural developments of which he was more sensible of than any known politician of his time.

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  • The transportation of the wheat from the fields of the northwest to the seaport is a business of tremendous magnitude.

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  • dimensio, a measuring), in geometry, a magnitude measured in a specified direction, i.e.

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  • The magnitude of the foreign interests invested in Shanghai may be gathered from the following rough summary: Assessed value of land in settlements registered as foreign-owned £5,500,000; docks, wharves and other industrial public companies - market value of stock.

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  • The question of the possible number and magnitude of such bodies is therefore one that does not admit of accurate investigation.

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  • To the statistician of the stars, catalogues of spectra, magnitude, position and proper motions are of the same importance that census tables are to the student of humanity.

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  • The measurement of the speed with which the individual stars are moving towards or from our system is a work of such magnitude that what has yet been done is scarcely more than a beginning.

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  • This point in our middle latitudes is between the zenith and the north horizon, near a certain star of the second magnitude familiarly known as the Pole Star.

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  • Eighteen observatories scattered north and south of the equator divided the sky among them; and the outcome of their combined operations aimed at the production of a catalogue of at least 2,000,000 strictly determined stars, together with a colossal map in 22,000 sheets, showing stars to the fourteenth magnitude, in numbers difficult to estimate.

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  • Kempf with a polarizing photometer; but by far the most comprehensive work of the kind is the Harvard Photometric Durchmusterung (1901-1903), embracing all stars to 7.5 magnitude, and extended to the southern pole by measurements executed at Arequipa.

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  • C. Kapteyn and Simon Newcomb, to estimate, through the analysis of their proper motions, the " mean parallax " of stars assorted by magnitude.

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  • This inequality, which reaches the magnitude of nearly I°, is known as the variation.

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  • It was found on comparing the results of Hansen and Delaunay that there are some outstanding discrepancies which are of sufficient magnitude to demand the attention of those interested in the mathematical theory of the subject.

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  • They consist throughout of rocks and hills, separated from each other by narrow valleys or ravines; but, though the hills rise abruptly, there are often on their summits, or at different stages of their ascent, plains of considerable magnitude.

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  • A large proportion of the public officials and judiciary were also disaffected; their removal from their posts was a matter of elementary prudence for a Government engaged in a war of such magnitude.

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  • Since the Spanish conquest their huacas have been opened and rifled, and many of the larger masses of ruins have been extensively mined in search of treasure, but enough still remains to impress upon the observer the magnitude of the city and the genius of the people who built it.

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  • Along the other principal rivers there are also plains of more or less magnitude, some of them possessing tracts of very fertile soil.

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  • (I) If the Existent is Many, it must be at once infinitely small and infinitely great - infinitely small, because the parts of which it consists must be indivisible and therefore without magnitude; infinitely great,, because, that any part having magnitude may be separate from any other part, the intervention of a third part having magnitude is necessary, and that this third part may be separate from the other two the intervention of other parts having magnitude is necessary, and so on ad infinitum.

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  • Sixty miles lower down is the mouth of the (left hand) tributary the Kaduna, a river of some magnitude which gives access to Zungeru, the headquarters of the British administration in Northern Nigeria.

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  • - Alessandro Volta (1801) showed that although a separation of the two electricities was produced by the contact of two different metals (Volta Effect), which could be detected by a sensitive electrometer, a continuous current of corresponding magnitude could not be produced in a purely metallic circuit without the interposition of a liquid, because the electromotive force at one junction was exactly balanced by an equal and opposite force at the other.

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  • These measurements, though subject to some uncertainty on account of the great experimental difficulties, are a very valuable confirmation of the accuracy of Thomson's theory, because they show that the magnitude of the effect is of the required order, but they cannot be said to be strongly in support of Tait's hypothesis.

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  • of that magnitude situated at the junction which causes positive electricity to flow from the lead to the iron.

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  • It happens that the absolute magnitude of p" cannot be experimentally determined, but this is immaterial, as we are only concerned with differences.

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  • It is very probable that the absolute values of p in different metals are of the same sign and of the same order of magnitude, being large compared with the differences observed.

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  • At first the output was insignificant, but gradually the magnitude of the operations was enlarged until the competition became effective, and steel traders generally became aware that the firm of Henry Bessemer & Co.

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  • The magnitude of the bee industry in the United States may be judged from the fact of a single bee-farmer located in California having harvested from 150,000 lb of honey in one year from 2000 stocks of bees, and, as an instance of the enormous weight of honey obtainable from good hives in that favoured region, the same farmer secured 60,000 lb of comb-honey in one season from his best 300 colonies.

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  • The Oregon and California migration was of large magnitude by 1846.

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  • In Newton's method, two angles of constant magnitude are caused to revolve about their vertices which are fixed in position, in such a manner that the intersection of two limbs moves along a fixed straight line; then the two remaining limbs envelop a conic. Maclaurin's method, published in his Geometria organica (1719), is based on the proposition that the locus of the vertex of a triangle, the sides of which pass through three fixed points, and the base angles move along two fixed lines, is a conic section.

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  • It would have been thought impossible then that private individuals could have found the funds or maintained the magnitude of such enterprises.

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  • When there is no other means of entering into commercial relations with remote and savage races save by enterprise of such magnitude that private individuals could not incur the risk involved, then a company may be well entrusted with special privileges for the purpose, as an inventor is accorded a certain protection by law by means of a patent which enables him to bring out his invention at a profit if there is anything in it.

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  • The tables on the following pages contain chiefly the most important oils and fats together with their sources, yields and principal uses, arranged according to the above classification, and according to the magnitude of the iodine value.

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  • The magnitude of that what-if scenario was downright scary.

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  • After she managed to calm herself she added, If Quinn didn't realize the magnitude of what we've done and can do, I think he'd buy Howie a ticket out of here.

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  • While I felt a secret of that magnitude couldn't remain so in an intimate relationship, I equally dreaded immersing myself so deeply into Howie's life.

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  • Whenever I considered such a course of action even hinting about what we're doing, I tended to temporarily forget the magnitude of Howie's gift.

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  • She listened, unable to fathom the magnitude of chaos he spoke of.

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  • However, the magnitude of the Arab boycott of US products is minimized by economists.

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  • Remember the more luminous star has an absolute magnitude that is less than a fainter star's absolute magnitude!

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  • absolute magnitudeis given, then the value has been computed from the absolute visual magnitude already given in the catalog.

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  • Normally, the largest aftershock is about one magnitude unit smaller than the main shock.

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  • A 5.6 magnitude aftershock woke me up " --An American schoolteacher in Taiwan describes life after an earthquake.

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  • Star A has an apparent magnitude = 5.4 and star B has an apparent magnitude = 2.4.

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  • For instance, when they insisted that the visual apparent magnitude of IUMA was lower than its absolute magnitude.

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  • Sort by Sort output list by distance from search center (in arcminutes ), increasing right ascension or declination, or stellar magnitude.

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  • caldera of an exceedingly ancient volcano of extraordinary magnitude.

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  • Imag The DENIS I-band total magnitude calibrated by comparison with the I-band measurements of Mathewson at al.

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  • A kilo of pure cocaine has a street value an order of magnitude higher than a kilo of muesli.

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  • Nevertheless, it is still assumed to occur, and its purely conjectural magnitude determines what we call the ' velocity of light ' .

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  • despise driving on hot, blue-sky days, because the sheer level of wank on the roads increases by orders of magnitude.

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  • Evaluation of the magnitude of such losses is important for determining thermal noise levels in bonded suspensions for gravitational wave detectors.

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  • First of all, the greater the magnitude a star has the dimmer it appears in the sky!

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  • Magnitude, on the other hand, was usually described as being continuous, or being divisible into parts that are infinitely divisible into parts that are infinitely divisible.

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  • earthquakes of magnitude 7 or 7.5 in the past.

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  • The magnitude of the numerical uncertainity of the results is controlled through the input parameter epsilon.

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  • equal in magnitude to the inverse of d 010.

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  • estimations of magnitude.

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  • A definition of the loudness of tones can be constructed from the results of experiments such as loudness ' magnitude estimation ' .

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  • gramicidin channel, is the same magnitude.

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  • Quantum creation scenarios produce gravitational waves of a calculable form and magnitude.

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  • undocumented immigrants analyzing the census small magnitude and but it's a. Increase by one-half under current lawsseveral.

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  • The magnitude of threat to red squirrels is the threat from gray squirrel incursion.

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  • But how can one convey the magnitude of this reconceptualization to 20th-century students so fully indoctrinated into thinking (knowing?

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  • Above all, this was probably the author's intention: to renovate the classical tragedy preserving intact its magnitude.

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  • ADSL modems can therefore tolerate impulses of arbitrary magnitude whose effect on the data stream lasts no longer than 500 ms.

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  • To be sure, the magnitude of the earth's magnetism has been dropping for a long time.

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  • magnitude of earthquakes, many centered in the localities of the wars and fighting.

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  • magnitude of the reflection coefficient is the same everywhere along the line.

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  • magnitude of the vector is proportional to the strength of the rotation.

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  • magnitude of the local velocity.

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  • magnitude of the optical counterpart as measured from the Palomar or UK Schmidt Surveys.

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  • Perhaps this way we can grasp the magnitude of ' cultural deprivation ' .

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  • The apparent magnitude is a measure of the star's flux received by us.

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  • The distance modulus = the apparent magnitude - absolute magnitude.

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  • You cannot visit the Eden Project without being amazed at the sheer magnitude of it all.

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  • This is one of those stories about a crime of a lesser magnitude than many of those that Harry has investigated before.

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  • magnitude quakes.

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  • magnitude modulation.

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  • magnitude estimation data are offline data that only represent a rough approximation of processing difficulty.

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  • vmag The V magnitude in the AB system measured in a 3 arcsecond diameter aperture.

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  • Care should also be taken with the quantification of tsunami magnitude in whatever catalog or theoretical model is used as a basis for analysis.

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  • Why do we need more than one earthquake magnitude scale?

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  • This difference in extrudate swell magnitude was also observed in results obtained using the laser scanning micrometer.

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  • ADSL modems can therefore tolerate impulses of arbitrary magnitude whose effect on the data stream lasts no longer than 500 ms.

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  • Two main problems are addressed: Combined component design of magnitude modulation.

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  • The distance modulus = the apparent magnitude - absolute magnitude.

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  • orders of magnitude.

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  • ossifyexercise can be extremely good for your bones, IF the exercise puts strains of fairly high magnitude on your ossified parts.

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  • The photometry in Pix_M9 is simple ' relative photometry ' and will not automatically give you the magnitude of a star.

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  • precipitate withdrawal would be a disaster of immense magnitude.

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  • preserveall, this was probably the author's intention: to renovate the classical tragedy preserving intact its magnitude.

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  • Contrast that to less technologically complex parts of Turkey, Iran, China, or Central or South America hit by similar magnitude quakes.

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  • quake of the same magnitude.

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  • quantify the probability and magnitude of future rapid climate change.

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  • Our methodology offers not only refined dating techniques for these major Geological events, but also measures the minimum magnitude of these human disasters.

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  • Our experiments have measured the magnitude of the direction repulsion under various conditions.

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  • Sort by Sort output list by distance from search center (in arcminutes ), increasing right ascension or declination, or stellar magnitude.

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  • I from country health status to the magnitude of low-income parents seniors.

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  • For undamped sinusoids, the signal space can be inferred from the complex roots found with a magnitude very close to 1.0.

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  • An earthquake of magnitude 2.8 occurred on September 7, 1999 about 1.5 km southwest of the previous mining induced events.

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  • Vector quantities, for which both magnitude and direction are required, such as temperature gradient, are first rank tensors.

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  • 3-D digital comb filters are at least an order of magnitude more complex than the previous generation of comb filters.

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  • With a diesel particulate trap, particle mass and accumulation mode particles were reduced by several orders of magnitude.

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  • undamped sinusoids, the signal space can be inferred from the complex roots found with a magnitude very close to 1.0.

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  • unparalleled magnitude in history.

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  • To us defeat in a maritime war would mean a disaster of almost unparalleled magnitude in history.

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  • weepwept uncontrollably at the magnitude of what I had done, I had killed a living creature for my pleasure.

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  • But among archaeologists the word is usually restricted in its technical modern application to a sepulchral mound of greater or less magnitude.

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  • During rainfall, or near clouds or dust layers, the magnitude of this current might well be enormously increased; its direction would naturally vary with climatic conditions.

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  • 6, because it is evident that if the two components of the double star are not exactly equal in magnitude, there will be great tendency to systematic error if the web FIG.

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  • Especially important has been the problem of measuring the " catalogue plates " ofthe international Carte du ciel - a work that implies the determination of the positions of some millions of stars - that is to say, of all stars to the i ith or 12th magnitude.

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  • If it blows horizontally over the open end of a vertical tube it causes a decrease of pressure, but this fact is not of any practical use in anemometry, because the magnitude of the decrease depends on the wind striking the tube exactly at right angles to its axis, the most trifling departure from the true direction causing great variations in the magnitude.

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  • Now, whatever be the direction in which a body is moving, a frictionless constraint, like a string attached to the body, can cause its velocity to be changed into the vertical direction without any change taking place in the magnitude of the velocity.

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  • As the earth is used for completing the electric circuit, the signals received on such sensitive instruments as these are liable to be disturbed by the return currents of other systems in their immediate neighbourhood, which also use the earth as return, when such are of the magnitude generated by the working of electric tramways FIG.

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  • The reply of the Colonial Office contained the following statements of general policy: - " With the progressive development of society the tendency is to enlarge the functions and widen the sphere of action of the central government as well as of the local authorities, and to claim for them a more or less exclusive use of powers, and the performance of services where the desired result is difficult to attain through private enterprise, or where the result of entrusting such powers or services to private enterprise would be detrimental to the public interest, through their being in that event necessarily conducted primarily for the benefit of the undertakers rather than of the public. This tendency is specially manifested in cases where from the magnitude or other conditions of the enterprise the public is deprived of the important safeguard of unrestricted competition..

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  • The electromotive force of the coil is, however, great enough to create in these air gaps displacement currents which are of magnitude sufficient to be equivalent to the conduction current required to actuate a telephone.

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  • During his absence were manifested the beginnings of the troubles in the order that were to attain to such magnitude after his death.

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  • Vierteljahrsschrift (1902, 1903) Goetz has shown that Sabatier's presentation of St Francis's relations with the ecclesiastical authority in general, and with Cardinal Hugolino (Gregory IX.) in particular, is largely based on misconception; that the development of the order was not forced on Francis against his will; and that the differences in the order did not during Francis's lifetime attain to such a magnitude as to cause him during his last years the suffering depicted by Sabatier.

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  • Here the endless harmonious diversity of our cosmos, as well as of other worlds supposed to coexist with our own, is said to arise through the various combination of indivisible material elements differing in figure and magnitude only.

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  • The real world thus arising consists only of diverse combinations of atoms, having the properties of magnitude, figure, weight and hardness, all other qualities being relative only to the sentient organism.

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  • its figure, place, magnitude and motion, with the celestial appearances, &c. By some it is taken in too limited a sense, for a bare description of the several countries; and by others too extensively, who along with such a description would have their political constitution."

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  • In exceptional cases obstructions which it would be impossible or too costly to turn are overcome by a bridge or tunnel, the magnitude of such works increasing with the growth of engineering skill and financial enterprise.

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  • Thus one reform led to another; but Peter was not dismayed by the magnitude of the task, and worked vigorously in all departments with a sublime disregard for the clamour of reactionary opponents and for the feelings and prejudices of his subjects in general.

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  • To say that all traffic must bear its share of these interest and maintenance charges is to impose upon the railways a rate which would cut off much of the longdistance traffic, and much of the traffic in cheap articles, which is of great value to the public, and which, from its very magnitude, is a thing that railways could not afford to lose.

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  • But from § I, T=2DF; therefore F = pd 2 lE/D (25) F in this expression is twice the average magnitude of the equal and opposite forces constituting the couple for one driving-wheel illustrated in fig.

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  • The magnitude of F when p and e are put each equal to unity, is usually called the tractive force of the locomotive per pound of mean effective pressure in the cylinders.

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

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  • The component of a balance weight which is necessary to balance the reciprocating masses introduces a vertical unbalanced force which appears as a variation of pressure between the wheel and the rail, technically called the hammer-blow, the magnitude of which increases as the square of the speed of the train.

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  • The principles by means of which the magnitude and position of balance weights are worked out are given in the article Mechanics (Applied Mechanics), and the whole subject of locomotive balancing is exhaustively treated with numerous numerical examples in The Balancing of Engines by W.

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  • The Board may reject the order if it thinks the scheme to be of such magnitude or importance that it ought to come under the direct consideration of parliament, or it may modify it in certain respects, or it may remit it to the commissioners for further inquiry.

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  • He had been for many years collecting materials for a history of Philip II., but he hesitated for some time to attempt a work of such magnitude, occupying himself in the meantime with the slighter labours of a memoir of John Pickering for the Massachusetts Historical Society and the revision of Ticknor's History of Spanish Literature.

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  • Hess employed this principle to determine indirectly the heat of formation of compounds from their elements, when this magnitude, as is generally the case, was inaccessible to direct measurement.

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  • (i) Generally speaking, there is a considerable thermal effect when a substance is dissolved in water, and this effect varies in magnitude according to the amount of water employed.

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  • The thermochemical magnitude which is universally determined for organic compounds is the heat of combustion, usually by means of the calorimetric bomb.

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  • It is probably impossible to recover the whole truth either as to Crichton's death or as to the extent of his attainments, which were so quickly elevated into legendary magnitude.

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  • The changes of temperature and climate caused by difference of elevation are quite comparable in their magnitude and effect on all organized creatures with those due to differences of latitude; and the relative position of the high and low lands on the earth's surface, by modifying the direction of the winds, the fall of rain, and other atmospheric phenomena, produce effects in no sense less important than those due to the relative distribution of the land and sea.

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  • An interesting member of this constellation is a-Capricorni, a pair of stars of 3rd and 4th magnitudes, each of which has a companion of the 9th magnitude.

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  • On the average rather more than half the total of cattle is made up of store animals for fattening or breeding purposes, the fattening of Irish stores being a business of considerable magnitude in Norfolk and other counties.

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  • This elastic application renders it impossible in the following sketch of the history of ornithology to draw any sharp distinction between works that are emphatically ornithological and_those to which that title can only be attached by courtesy; for, since birds have always attracted far greater attention than any other group of animals with which in number or in importance they can be compared, there has grown up concerning them a literature of corresponding magnitude and of the widest range, extending from the recondite and laborious investigations of the morphologist and anatomist to the casual observations of the sportsman or the schoolboy.

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  • Interesting objects in this constellation are: a Geminorum or Castor, a very fine double star of magnitudes 2.0 and 2.8, the fainter component is a spectroscopic binary; i Geminorum, a long period (231 days) variable, the extreme range in magnitude being 3.2 to 4; Geminorum, a short period variable, 10.15 days, the extreme range in magnitude being 3.7 to 4.5; Nova Geminorum, a "new" star discovered in 1903 by H.

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  • With rare combination of facilities and advantages, made available with remarkable skill and enterprise, the production of cotton in America seems likely for a long series of years to continue to increase in magnitude and importance.

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  • It is plausible, then, to suppose that the dealing syndicate primarily, and the speculations of the public secondarily (secondarily, because in all likelihood the effect of its operation would be much less in magnitude), may account for the change.

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  • A closer examination will reveal further that the magnitude of these gaps varies a great deal; and Attempts to explain them were made in an article in the Economic Journal in December 1904, and in the paper already referred to read to the Royal Statistical Society.

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  • According to the modern theory of auxochromic action, the introduction of a group into the molecule is accompanied by some strain, and the alteration in colour produced is connected with the magnitude of the strain.

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  • The magnitude of this separation would obviously depend on the magnitude of the substituent group, which may be so large (in this case propyl is sufficient) as to cause unequal horizontal deformation and at the same time a change in the vertical direction.

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  • But the king of Prussia's taunt is deprived of its sting by the almost incredible candour of her own words to Kaunitz, that if she was to lose her reputation before God and man for respecting the rights of others it must not be for a small advantage - if, in fact, Austria was to share in the plunder of Poland, she was to be consoled for the distress caused to her feelings by the magnitude of her share of the booty.

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  • It has been usual to define mathematics as "the science of discrete and continuous magnitude."

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  • All these topics require thorough discussion before we can rest content with the definition of mathematics as the general science of magnitude; and by the time they are discussed the definition has evaporated.

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  • A set of cardinal numbers have an order of magnitude, often called the order of the set because of its insistent obviousness to us; but, if they are the numbers drawn in a lottery, their time-order of occurrence in that drawing also ranges them in an order of some importance.

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  • Consider the serial arrangement of the rationals in their order of magnitude.

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  • It is sufficient to observe here that they are concerned with special types of classes of classes and of classes of relations, and that the connexion of geometry with number and magnitude is in no way an essential part of the foundation of the science.

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  • Furthermore, the sort of continuity of the series (in order of magnitude) of rational numbers is known to be different from that of the series of real numbers.

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  • Most philosophers refer in their works to mathematics more or less cursorily, either in the treatment of the ideas of number and magnitude, or in their consideration of the alleged a priori and necessary truths.

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  • even below the level of his old opponents; and that this was not the consequence of temporary depression naturally resulting from the accumulated load of his misfortunes, is sufficiently shown by the downright puerility of the arguments by which he seeks to justify his own successes in the St Helena memoirs, which one may search in vain for any indication that Napoleon was himself aware of the magnitude of his own discovery.

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  • No diplomatic questions of the first magnitude arose during his service as secretary of state, but the settlement of long-standing claims against France was prepared for, and trade with the British West India colonies was opened.

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  • If we multiply the elements of the second row by an arbitrary magnitude X, and add to the corresponding elements of the first row, A becomes Zai,A18+XEa28A13 = Lia13A18 =A, showing that the value of the determinant is unchanged.

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  • - The value of a determinant is unchanged if we add to the elements of any row or column the corresponding elements of the other rows or other columns respectively each multiplied by an arbitrary magnitude, such magnitude remaining constant in respect of the elements in a particular row or a particular column.

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  • The order of the numbers in the bracket (p l p 2 ...p n) is immaterial; we may therefore always place them, as is most convenient, in descending order of magnitude; the numbers then constitute an ordered partition of the weight w, and the leading number denotes the degree.

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  • The general term in a solution involves the product ao°ai 1 a2 2 ...an" wherein Tr =0, Zs7r s =w; the number of such products that may appear depends upon the number of partitions of w into B or fewer parts limited not to exceed n in magnitude.

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  • There Is A Still More General Form Of Seminvariant; We May Have Instead Of 0, 0 Any Collections Of Nonunitary Integers Not Exceeding 0, 0 In Magnitude Respectively, (2 A2 3 A3 ...0 Ae)A(L S 2 G2 3 G3 ...0' Ge') B (12 A2 3 A3 ..0 Ab)A(1 S I 2 G2 3 G3 ...B Ge) B (1 22A23A3 ...0 Ae) A(1822 G2 3 G3 ...0' Ge ') B () 8 (1 8 2 A2 3 A3 ...19'°) A(2 G2 3 G3 ...0' ' ') B, Is A Seminvariant; And Since These Forms Are Clearly Enumerated By 1 Z.

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  • Faraday's lines not only show the direction of the magnetic force, but also serve to indicate its magnitude or strength in different parts of the field.

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  • Physical quantities such as magnetic force, magnetic induction and magnetization, which have direction as well as magnitude, are termed vectors; they are compounded and resolved in the same manner as mechanical force, which is itself a vector.

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  • The direction of F is given by the following construction: Trisect OP at C, so that OC =OP/3; draw CD at right angles to OP, to cut the axis produced in D; then DP will be the direction of the force at P. For a point in the axis OX, 0 =0; therefore cos 0 = 1, and the point D coincides with C; the magnitude of the force is, from (14), Fx=2M / r3, (15) its direction being along the axis OX.

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  • The magnitude of the force is in this case F5 = M/r 3, (16) and its direction is parallel to the axis of the magnet.

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  • The magnitude of the flux produced by a given magnetic force differs in different media.

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  • Finally, experiments were made to ascertain the effect of ' The loads were successively applied in decreasing order of magnitude.

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  • The experimental results agreed in sign though not in magnitude with those calculated from the changes produced by simple longitudinal magnetization, discrepancies being partly accounted for by the fact that the metals employed were not actually isotropic. Heusler's alloy has been tested for change of length by L.

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  • When such precautions are adopted it is found that the " electromotive force of magnetization " is, for a given specimen, perfectly definite both in direction and in magnitude; it is independent of the nature of the corrosive solution, and is a function of the field-strength alone, the curves showing the relation of electromotive force 'to field-intensity bearing a rough resemblance to the familiar I-H curves.

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  • It consists of three stars of the 1st magnitude, four of the 2nd, and many of inferior magnitude.

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  • a Orionis, or Betelgeuse, is a bright, yellowish-red star of varying magnitude (0.5 to 1.4, generally 0.9).

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  • [3 Orionis or Regel is a 1st magnitude star.

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  • y Orionis or Bellatrix, and x Orionis are stars of the 2nd magnitude.

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  • Three collinear stars ?', c and 3 Orionis constitute the "belt of Orion"; of these E, the central star, is of the ist magnitude, 3 of the 2nd, while Orionis is a fine double star, its components having magnitudes 2 and 6; there is also a faint companion of magnitude io.

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  • The chief characteristic of the Amazonian forest, aside from its magnitude, is the great diversity of genera and species.

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  • are by reason of their magnitude and peculiar character the most important in South America, though the per capita aggregate is less than that of Argentina.

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  • The magnitude of Richelieu's achievement grows when one considers his relations with the king.

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  • If, therefore, we take r i /(i+x) as equal to I -xdx2-...+ (-) r x r, there is an error whose numerical magnitude is I xr+1/ (I +x) I; and, if I x

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  • The development is based on the necessity of being able to represent geometrical magnitude by arithmetical magnitude; and it may be regarded as consisting of three stages.

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  • Hermann Hankel has pointed out the readiness with which the Hindus passed from number to magnitude and vice versa.

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  • 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.

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  • Further, it is evident that account must be taken of the variation of phase in estimating the magnitude of the effect at P of the first zone.

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  • If, on the other hand, the point be well immersed in the geometrical shadow, the earlier zones are altogether missing, and, instead of a series of terms beginning with finite numerical magnitude and gradually diminishing to zero, we have now to deal with one of which the terms diminish to zero at both ends.

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  • (It is easy to see that the radius of the bright spot is of the same order of magnitude.) The experiment succeeds in a dark room of the length above mentioned, with a threepenny bit (supported by three threads) as obstacle, the origin of light being a small needle hole in a plate of tin, through which the sun's rays shine horizontally after reflection from an external mirror.

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  • " Thus the magnitude of the central spot is diminished, and the brightness of the rings increased, by covering the central parts of the object-glass."

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