Magnitudes sentence example

magnitudes
  • The magnitudes, on the other hand, which we meet with in geometry, are essentially continuous.
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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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  • These show the magnitudes of the layers of different salinity and temperature beneath the surface, and when a number of sections are compared the differences from season to season and from year to year can be seen.
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  • One of the fragments may again be broken, and again two bipolar magnets will be produced; and the operation may be repeated, at least in imagination, till we arrive at molecular magnitudes and can go no farther.
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  • While mensuration is concerned with the representation of geometrical magnitudes by numbers, graphics is concerned with the representation of numerical quantities by geometrical figures, and particularly by lengths.
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  • Although this transition from the discontinuous to continuous is not truly scientific, yet it materially augmented the development of algebra, and Hankel affirms that if we define algebra as the application of arithmetical operations to both rational and irrational numbers or magnitudes, then the Brahmans are the real inventors of algebra.
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  • To get an idea of the magnitudes of the quantities involved, let us take the case of an aperture of 1 in., about that of the pupil of the eye.
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  • His only extant work is a short treatise (with a commentary by Pappus) On the Magnitudes and Distances of the Sun and Moon.
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  • This use of formulae for dealing with numbers, which express magnitudes in terms of units, constitutes the broad difference between mensuration and ordinary geometry, which knows nothing of units.
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  • As a result of the importance both of the formulae obtained by elementary methods and of those which have involved the previous use of analysis, there is a tendency to dissociate the former, like the latter, from the methods by which they have been obtained, and to regard mensuration as consisting of those mathematical formulae which are concerned with the measurement of geometrical magnitudes (including lengths), or, in a slightly wider sense, as being the art of applying these formulae to specific cases.
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  • These last two steps may introduce magnitudes which have to be subtracted, and which therefore have to be treated as negative quantities in the arithmetical.
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  • Let E and F be two magnitudes so related that whenever F has any value (within certain limits) E has a definite corresponding value.
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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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  • The volume of a frustum of a cone, for instance, can be expressed in terms of certain magnitudes by a certain formula; but not only will there be some error in the measurement of these magnitudes, but there is not any material figure which is an exact cone.
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  • In the case of a trapezette, for instance, the data are the magnitudes of certain ordinates; the problem of interpolation is to determine the values of intermediate ordinates, while that of mensuration is to determine the area of the figure of which these are the ordinates.
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  • The first important work undertaken with it was a revision of the magnitudes given in the Bonn Durchmusterung.
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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 Galileo-Newton theory of motion is that, relative to a suitably chosen base, and with suitable assignments of mass, all accelerations of particles are made up of mutual (so-called) actions between pairs of particles, whereby the two particles forming a pair have accelerations in opposite directions in the line joining them, of magnitudes inversely proportional to their masses.
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  • This ratio is adopted so that a difference of five magnitudes may correspond to a light-ratio of i: loo.
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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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  • In its period of 406 days it fluctuates between the thirteenth and the fourth magnitudes; thus at maximum it emits 4000 times as much light as at minimum.
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  • The range of variation is much smaller, the difference between maximum and minimum rarely exceeding two magnitudes.
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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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  • Thus a rise of at least eight magnitudes in two days must have occurred.
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  • From 1750 until about 1832 it seems to have varied irregularly between the second and the fourth magnitudes.
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  • These clusters present many unsolved problems. Thus Perrine, from an examination of ten globular clusters (including Messier 13 and Centauri), has found in each case that the stars can be separated into two classes of magnitudes.
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  • About one-third of the stars are between magnitudes 11 and 13, and the remaining two-thirds are between magnitudes 15.5 and 16.5.
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  • Stars of magnitudes intermediate between these two groups are almost entirely absent.
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  • The magnitudes of the stars are distributed in the same way in each drift.
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  • If the uniform distribution extends indefinitely, or as far as the telescope can penetrate, the star-ratio should have the theoretical value 3.98, 1 any decrease in density or limit to the distribution of the stars will be indicated by a continual falling off in the star-ratio for the higher magnitudes.
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  • For the higher magnitudes C. Kapteyn has.
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  • If the stars were all of the same intrinsic brightness it is evident that the comparison of the number of stars of successive magnitudes would show directly where the decreased density of distribution began.
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  • The two diagrams being supposed constructed, it is seen that each of the given systems of forces can be replaced by two components acting in the sides of the funicular which meet at the corresponding vertex, and that the magnitudes of these components will be given by the corresponding triangle of forces in the force-diagram; thus the force 1 in the figure is equivalent to two forces represented by 01 and 12.
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  • The directions and magnitudes of the reactions at A and C are then easily ascertained.
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  • When parallel forces of given magnitudes act at given points, the resultant acts through a definite point, or centre of parallel forces, which is independent of the special direction of the forces.
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  • If we imagine a rigid body to be acted on at given points by forces of given magnitudes in directions (not all parallel) which are fixed in space, then as the body is turned about the resultant wrench will assume different configurations in the body, and will in certain positions reduce to a single force.
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  • The theory of dimensions often enables us to forecast, to some extent, the manner in which the magnitudes involved in any particular problem will enter into the result.
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  • The lines representing the forces in the second figure show theii relative directions and magnitudes.
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  • To find their absolute directioru and magnitudes, a vertical line is to be drawn in the first figure, o:
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  • It consists of two elements, the velocity ratio, which is the ratio of any two magnitudes bearing to each other the proportions of the respective velocities of the two points at a given instant, and the directional relation, which is the relation borne to each other by the respective directions of the motions of the two points at the same given instant.
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  • The relation between the advance and the rotation, which compose the motion of a screw working in contact with a fixed screw or helical guide, has already been demonstrated in 32; and the same relation exists between the magnitudes of the rotation of a screw about a fixed axis and the advance of a shifting nut in which it rotates.
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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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  • The relative importance of two harmonic disturbances depends upon their initial magnitudes, and upon the rate at which they grow.
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  • The magnitudes of the maximum shearing stresses are indicated by the algebraic differences of the thicknesses of the lines of principal stress.
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  • But no art of discovery, such as Bacon anticipated, follows, for "invention, sagacity, genius" are needed at each step. He analyses induction into three steps: - (I) the selection of the (fundamental) idea, such as space, number, cause or likeness; (2) the formation of the conception, or more special modification of those ideas, as a circle, a uniform force, &c.; and (3) the determination of magnitudes.
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  • He attempted no detailed discussion of planetary theory; but his catalogue of 1 080 stars, divided into six classes of brightness, or " magnitudes," is one of the finest monuments of antique astronomy.
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  • In the statics two magnitudes have to be determined: (I) the amount of the suppression or inhibition (Hemmungssumme), and (2) the ratio in which this is shared among the opposing presentations.
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  • With magnitudes 3.1 and 5.1 they are regarded as the most beautiful double star that can be seen in the sky.
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  • In the newly released Bulletin data, the ISC has computed 3567 surface wave magnitudes.
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  • Hence, ' things by removal ' may be one way of explaining perceptible magnitudes qua lengths.
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  • When the Normalize option is checked, the spectral magnitudes are adjusted so that power is conserved.
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  • Our services include: Measurement of hand arm vibration magnitudes.
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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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  • 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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  • Writing A ' = ' - 'o and 077' =7 1' - 770, then g' and 077' are the aberrations belonging to, and x, y, and are functions of these magnitudes which, when expanded in series, contain only odd powers, for the same reasons as given above.
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  • Aristarchus of Samos observed at Alexandria 280-264 B.C. His treatise on the magnitudes and distances of the sun and moon, edited by John Wallis in 1688, describes a theoretically valid method for determining the relative distances of the sun and moon by measuring the angle between their centres when half the lunar disk is illuminated; but the time of dichotomy being widely indeterminate, no useful result was thus obtainable.
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  • If the structure was refined anisotropically, the orientations and the magnitudes of vibrational ellipsoids should be displayed.
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  • The measure of the loss of symmetry associated with the introduction of alkyl groups depends upon the relative magnitudes of the substituent group and the rest of the molecule; and the larger the molecule, the less would be the morphotropic effect of any particular substituent.
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  • The additions of velocity which the two bodies receive respectively, relative to such a base, are in opposite directions, and if the bodies are alike their magnitudes are equal.
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  • If the bodies though of the same substance are of different sizes, the magnitudes of the additions of velocity are found to be inversely proportional to the volumes of the bodies.
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  • But if the bodies are of different substances, say one of iron and the other of gold, the ratio of these magnitudes is found to depend upon something else besides bulk.
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  • When, as in the case of contact, a mutual relation is perceived between the motions of two particles, the changes of velocity are in opposite directions, and the ratio of their magnitudes determines the ratio of the masses of the particles; the motion being reckoned relative to any base which is unaffected by the change.
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