Spherical sentence example

spherical
  • The problem then resolves itself in the solution of a spherical triangle.
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  • In such plants, the pollen grains are sometimes fihiform and not spherical in shape.
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  • In the case of more considerable distances, however, a globe of suitable size should be consulted, or - and this seems preferable - they should be calculated by the rules of spherical trigonometry.
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  • For safety during hibernation and moulting, book-scorpions spin a small spherical cocoon.
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  • His last publication, which appeared in 1878, was on spherical harmonics (Beitreige zur Theorie der Kugelf unctionen) .
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  • The earliest forms were "armillae" and spherical.
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  • Rayleigh points out that this clinging of the sound to the surface of a concave wall does not depend on the exactness of the spherical form.
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  • He used a spherical Helmholtz resonator resounding to the tone to be measured.
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  • Drop-shaped jars with spherical bases are typical, and scrabbled patterns of incised lines.
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  • In order to render an 'account of Tyndall's "residual blue" it is necessary to pursue the approximation further, taking for simplicity the case of spherical shape.
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  • Into each ovarian sac behind the transverse junction opens a slender tube, which is greatly coiled, and, in its turn, opens into a spherical "spermathecal sac."
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  • The embryo undergoes differentiation into an outer layer of cells that produce a chitinoid coat, a middle layer of cells, and a central spherical hexacanth body closely enveloped by the middle coat.
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  • They may be used either alone or in combination with spherical lenses.
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  • Let us then suppose a spherical shell 0 to be electrified.
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  • It may be regarded as an epicycloid in which the rolling and fixed circles are equal in diameter, as the inverse of a parabola for its focus, or as the caustic produced by the reflection at a spherical surface of rays emanating from a point on the circumference.
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  • Aristarchus is also said to have invented two sun-dials, one hemi spherical, the so-called scaphion, the other plane.
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  • There were two kinds, - spherical and planispheric.
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  • The solid enclosed by a small circle and the radii vectores from the centre of the sphere is a "spherical sector"; and the solid contained between two spherical sectors standing on copolar small circles is a "spherical cone."
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  • The fruit is a woody capsule of three cells, each containing one large nearly spherical seed, which consists mainly of two large hemispherical cotyledons.
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  • In "geodesy," and the cognate subject "figure of the earth," the matter of greatest moment with regard to the sphere is the determination of the area of triangles drawn on the surface of a sphere - the so-called "spherical triangles"; this is a branch of trigonometry, and is studied under the name of spherical trigonometry.
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  • But the nakshatras are twenty-eight, and are represented by as many " junction stars " (yogatara), carefully determined by their spherical co-ordinates.
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  • The motion of the well-known steady spherical vortex is an example of the latter case.
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  • Of the Ceylonese galls, " some are as symmetrical as a composite flower when in bud, others smooth and spherical like a berry; some protected by long spines, others clothed with yellow wool formed of long cellular hairs, others with regularly tufted hairs."
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  • Aleppo galls (gallae halepenses) are brittle, hard, spherical bodies, in.
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  • The best known of these, which is called Legendre's theorem, is usually given in treatises on spherical trigonometry; by means of it a small spherical triangle may be treated as a plane triangle, certain corrections being applied to the angles.
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  • For spherical shot is not constant, and a separate ballistic table must be constructed; but may be taken as 1.7 on the average.
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  • For the mathematical investigation see Spherical Harmonics and for tables see Table, Mathematical.
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  • The " new invention in Denmark " to which Anthony Wood refers as having given the hint to Napier was probably the method of calculation called prosthaphaeresis (often written in Greek letters irpooOa4aipeats), which had its origin in the solution of spherical triangles.
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  • Melicertaceae; females tubicolous, usually attached, or forming spherical floating social aggregates; males free swimming.
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  • Asplanchnaceae, plankton, dwellers in small pools, are, however, ovoid, and Trochosphaera is spherical and must owe its floating powers to the low density of the liquid in its enormously dilated bodycavity.
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  • With Vieta, by reason of the advance in arithmetic, the style of treatment becomes more strictly trigonometrical; indeed, the Universales Inspectiones, in which the calculation occurs, would now be called plane and spherical trigonometry, and the accompanying Canon mathematicus a table of sines, tangents and secants.'
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  • The yellow stamen-bearing flowers are in sessile, nearly spherical catkins; the fertile ones vary in colour, from red or purple to greenish-white, in different varieties; the erect cones, which remain long on the branches, are above an inch in length and oblong-ovate in shape, with reddish-brown scales somewhat waved on the edges, the lower bracts usually rather longer than the scales.
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  • A circlet of cilia forms when the embryo is still nearly spherical in an equatorial position.
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  • Thomson 6 places spherical bulbs inside thick spiral conductors through which the oscillating discharge of a powerful battery is led.
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  • The spherical granules (G) are probably gland-secretions; the dark bodies (Z) are probably xanthellae, i.e.
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  • A spherical angle is a particular dihedral angle; it is the angle between two intersecting arcs on a sphere, and is measured by the angle between the planes containing the arcs and the centre of the sphere.
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  • Suppose two small smooth spherical bodies which can be regarded as particles to be brought into collision, so that the velocity of each, relative to any base which is unaffected by the collision, is suddenly changed.
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  • Some years later he succeeded in showing that Kepler's elliptic orbit for planetary motion agreed with the assumed law of attraction; he also completed the co-ordination with terrestrial gravity by his investigation of the attractions of homogeneous spherical bodies.
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  • The almost spherical head is covered by a hood which can be retracted; it bears upon its side a number of sickle-shaped, chitinous hooks and one or more short rows of low 89 spines - both of these features are used in characterizing the various species.
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  • Experience shows that, although spherical pebbles are to be avoided, Portland cement adheres tightly to smooth flint surfaces, and that rough stones often give a less compact concrete than smooth ones on account of the difficulty of bedding them into the matrix when laying the concrete.
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  • When the free ends of the hyphae emerge again into the air they swell up into spherical bodies which may either fall off and behave as conidia, each putting out a germ-tube and infecting the host; or the germ-tube itself swells up into a zoosporangium which develops a number of zoospores.
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  • The seed is rather larger than a hazel nut, with a thicker and darker shell and per- Planting fectly spherical shape.
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  • Spherical hard stone hammers (6) were held in the hand for dressing down granite.
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  • Fischer has further established the fact that the peripheral mass, which is a hollow sphere in spherical cells, and either a hollow cylinder or barrel-shaped body in filamentous forms, must be regarded as the single chromatophore of the Cyanophyceous cell.
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  • Thus, although isogamy consists in typical cases of a union of naked motile gametes by a fusion which begins at the beaked ends, and results in the formation of an immotile spherical zygote surrounded by a cell-wall, in Leptosira it is noticeable that the fusion begins at the blunt end; in a species of Chlamydomonas the two gametes are each included in a cell-wall before fusion; and in many cases the zygote retains for some time its motility with the double number of cilia.
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  • The antheridia are spherical orange-coloured bodies of very complex structure.
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  • Then usually these layers successively give way, and the spherical naked oospheres float free in the water.
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  • The thallus is somewhat spherical and unicellular, exhibiting a distinction between anterior and posterior extremities, and dorsal and ventral surfaces.
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  • In Synura and Chromulina the cells form a spherical motile colony, recalling Volvocaceae.
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  • Until Newton's discovery of the different refrangibility of light of different colours, it was generally supposed that object-glasses of telescopes were subject to no other errors than those which arose from the spherical figure of their surfaces, and the efforts of opticians were chiefly directed to the construction of lenses of other forms of curvature.
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  • James Gregory, in his Optica Promota (1663), discusses the forms of images and objects produced by lenses and mirrors, and shows that when the surfaces of the lenses or mirrors are portions of spheres the images are curves concave towards the objective, but if the curves of the surfaces are conic sections the spherical aberration is corrected.
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  • When in 1666 he made his discovery of the different refrangibility of light of different colours, he soon perceived that the faults of the refracting telescope were due much more to this cause than to the spherical figure of the lenses.
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  • He did not attempt the formation of a parabolic figure on account of the probable mechanical difficulties, and he had besides satisfied himself that the chromatic and not the spherical aberration formed the chief faults of previous telescopes.
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  • The practical difficulty of constructing Gregorian telescopes of good defining quality is very considerable, because if spherical mirrors are employed their aberrations tend to increase each other, and it is extremely difficult to give a true elliptic figure to the necessarily deep concavity of the small speculum.
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  • The reflecting surface is first ground to a spherical form, the parabolic figure being given in the final process by regulating the size of the pitch squares and the stroke of the polishing machine.
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  • In such a system the tidal forces must be very great, and under their influence the stars will not be spherical, but will be elongated in the direction of the line joining their centres.
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  • What is spherical waxes.
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  • What waxes is spherical.
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  • The moon is spherical.
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  • Perhaps to the student there is no part of elementary mathematics so repulsive as is spherical trigonometry.
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  • But every quaternion formula is a proposition in spherical (sometimes degrading to plane) trigonometry, and has the full advantage of the symmetry of the method.
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  • The spherical A isosceles triangles AJB, BJC are con gruent, and we see that AB can be brought into the position BC by a rotation about the axis OJ through an FIG.
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  • If we construct a, the spherical triangles ABC,
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  • The above problem is identical with that of the oscillation of a particle in a smooth spherical bowl, in the neighborhood of the lowest point, If the bowl has any other shape, the axes Ox, Oy may, ..--7 be taken tangential to the lines tof curvature ~ / at the lowest point 0; the equations of small A motion then are dix xdiy (II) c where P1, P2, are the principal radii of curvature at 0.
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  • Take next the case of a sphere rolling on a fixed spherical surface.
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  • Let a be the radius of the rolling sphere, c that of the spherical surface which is the locus of its centre, and let x, y, I be the co-ordinates of this centre relative to axes through 0, the centre of the fixed sphere.
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  • The case of a sphere spinning about a vertical axis at, the lowest point of a spherical bowl is obtained by reversing the signs of a and c. It appears that this position is always stable.
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  • As a first application of Lagranges formula (II) we may form the equations of motion of a particle in spherical polar co-ordinates.
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  • In the case of the spherical pendulum we have r=l, e= mgi sin 0, s=o, if OZ be drawn vertically downwards, and therefore sin 0 cos Ol1 ~ sin 0, ~- (23)
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  • As regards the most general motion of a spherical pendulum, it is obvious that a particle moving under gravity on a smooth sphere cannot pass through the highest or lowest point unless it describes a vertical circle.
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  • An example is furnished by the spherical pendulum (~ 13).
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  • The path of a point P in or attached to the rolling cone is a spherical epitrochoid traced on the surface of a sphere of the radius OP. From P draw PQ perpendicular to the instantaneous axis.
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  • Perpendicular to 01 draw A1IA2, cutting the axe8 in Ai, A2 make the outer rims of the patterns and of the wheels portions of the cones A1B1I, A,B2I, of which the narrow zones occupied by the teeth will be sufficiently near to a spherical surface described about 0 for practical purposes.
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  • Between the concave spherical surfaces of those cups is placed a steel 0 ball, being either a complete sphere or a lens having convex surfaces of a somewhat less radius p i than the concave surfaces of the cups.
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  • The ventral side of the body in the atrial region is broad and convex, so that the body presents the appearance of a spherical triangle in transverse section, the apex being formed by the dorsal fin and the angles bordered by two hollow folds, the metapleural folds, each of which contains a continuous longitudinal lymph-space, the metapleural canal.
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  • A more recondite work is his Compendium of Spherical Astronomy (1906).
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  • On fracture these spherical growths are found to be radiated in structure.
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  • Coulomb has made his name for ever famous by his invention and application of his torsion balance to the experimental verification of the fundamental law of electric attraction, in which, however, he was anticipated by Cavendish, namely, that the force of attraction between two small electrified spherical bodies varies as the product of their charges and inversely as the square of the distance of their centres.
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  • Let two spherical pith balls of radius r and weight W, covered with gold-leaf so as to be conducting, be suspended by parallel silk threads of length 1 so as just to touch each other.
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  • If there be refraction at a collective spherical surface, or through a thin positive lens, 0' 2 will lie in front of O' 1 so long as the angle u2 is greater than u 1 (" under correction "); and conversely with a dispersive surface or lenses (" over correction ").
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  • It requires the middle of the aperture stop to be reproduced in the centres of the entrance and exit pupils without spherical aberration.
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  • Of thin positive lenses with n= 1-5, four are necessary to correct spherical aberration of the third order.
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  • Spherical aberration and changes of the sine ratios are often represented graphically as functions of the aperture, in the same way as the deviations of two astigmatic image surfaces of the image plane of the axis point are represented as functions of the angles of the field of view.
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  • In a plane containing the image point of one colour, another colour produces a disk of confusion; this is similar to the confusion caused by two " zones " in spherical aberration.
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  • The Gaussian theory is only an approximation; monochromatic or spherical aberrations still occur, which will be different for different colours; and should they be compensated for one colour, the image of another colour would prove disturbing.
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  • Let us measure it in the case of the spherical soap-bubble by considering the stress exerted by one hemisphere of the bubble on the other, across the circumference of a great circle.
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  • To determine the relation between the surface-tension and the pressure which balances it when the form of the surface is not spherical, let us consider the following case: Let fig.
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  • They therefore shorten themselves, and after a series of oscillations in which they become alternately elongated and flattened, settle down into the form of spherical drops.
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  • This process, which we have followed as it takes place on an individual portion of the falling liquid, goes through its several phases at different distances from the orifice, so that if we examine different portions of the stream as it descends, we shall find next the orifice the unbroken column, then a series of contractions and enlargements, then elongated drops, then flattened drops, and so on till the drops become spherical.
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  • The detached masses into which a jet is resolved do not at once assume and retain a spherical form, but execute a series of vibrations, being alternately compressed and elongated in the direction of the axis of symmetry.
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  • A formula, similar to (5), may be given for the frequencies of vibration of a spherical mass of liquid under capillary force.
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  • If, as before, the frequency be p7211, and a the radius of the sphere, we have p 2 =n(n-1)(n+2)P a3, (6) n denoting the order of the spherical harmonic by which the deviation from a spherical figure is expressed.
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  • They consist of single cells, which may be spherical, oblong or cylindrical in shape, or of filamentous or Definition.
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  • He proceeded in the main on the assumption that the forms of bacteria as met with and described by him are practically constant, at any rate within limits which are not wide: observing that a minute spherical micrococcus or a rod-like bacillus regularly produced similar micrococci and bacilli respectively, he based his classification on what may be considered the constancy of forms which he called species and genera.
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  • Cocci: spherical or spheroidal cells, which, according to their relative (not very well defined) sizes are spoken of as Micrococci, Macrococci, and perhaps Monas forms.
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  • Characteristic forms may be assumed by the young zoogloea of different species, - spherical, ovoid, reticular, filamentous, fruiticose, lamellar, &c., - but these vary considerably as the mass increases or comes in contact with others.
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  • The poppy blossoms about the middle of February, and the petals when about to fall are collected for the purpose of making " leaves " for the spherical coverings of the balls of opium.
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  • He wrote upon nearly every subject of pure mathematics, and also upon theoretical dynamics and spherical and physical astronomy.
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  • Microspore spherical or oval, with or without a bladder-like extension of the exine, containing a prothallus of two or more cells, one of which produces two non-motile or motile male cells.
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  • It is easy to calculate that this would be produced by an annual fall of matter equal to one nineteen millionth of the sun's mass, which would make an envelope eight metres thick, at the sun's mean density; this would be collected during the year from a spherical space extending beyond the orbit of Jupiter.
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  • The conclusion is that the photosphere is very sharply defined and shows no definite departure from a truly spherical shape.
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  • He was an admirable lecturer and writer of popular books on his subject, as well as of more learned works such as his Treatise on Spherical Astronomy (1885) and Treatise on the Theory of Screws (1900); and he was a congenial figure in all circles.
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  • In Actinians the epithelio-muscular cells of the endoderm are crowded with yellow spherical bodies, which are unicellular plants or Algae, living symbiotically in the tissues of the zooid.
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  • In a small commonplace book, bearing on the seventh page the date of January 1663/1664, there are several articles on angular sections, and the squaring of curves and " crooked lines that may be squared," several calculations about musical notes, geometrical propositions from Francis Vieta and Frans van Schooten, annotations out of Wallis's Arithmetic of Infinities, together with observations on refraction, on the grinding of " spherical optic glasses," on the errors of lenses and the method of rectifying them, and on the extraction of all kinds of roots, particularly those " in affected powers."
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  • It is one; it is eternal; it is whole and continu- =ous, both in time and in space; it is immovable and immutable; it is limited, but limited only by itself; it is evenly extended in every direction, and therefore spherical.
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  • The male flowers are developed at the ends of short lateral branches, are rounded or oblong in form, and consist of several antheriferous scales in two or three rows, each scale bearing three or six almost spherical pollen-sacs on its under side.
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  • The author considers not only plane curves, but also cones, or, what is almost the same thing, the spherical curves which are their sections by a concentric sphere.
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  • It has a complicated structure in both genera; in Pilularia its shape is nearly spherical, while in Marsilia it is elongated and bean-shaped.
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  • Among these subjects were the transit of Mercury, the Aurora Borealis, the figure of the earth, the observation of the fixed stars, the inequalities in terrestrial gravitation, the application of mathematics to the theory of the telescope, the limits of certainty in astronomical observations, the solid of greatest attraction, the cycloid, the logistic curve, the theory of comets, the tides, the law of continuity, the double refraction micrometer, various problems of spherical trigonometry, &c. In 1742 he was consulted, with other men of science, by the pope, Benedict XIV., as to the best means of securing the stability of the dome of St Peter's, Rome, in which a crack had been discovered.
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  • The stars are supposed to be generally spherical, like the sun, in form, and to have fairly well-defined boundaries; while the nebulae are generally irregular in outline and have no well-defined limits.
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  • Considering as general or descriptive astronomy a description of the universe as we now understand it, the other branches of the subject generally recognized are as follows: Geometrical or Spherical Astronomy, by the principles of which the positions and the motions of the heavenly bodies are defined.
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  • Let us study the effect of this deviation from the spherical form upon the attraction exercised by a distant body.
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  • The Jesuits could not understand how spherical bodies like sun and moon could be mistaken for human beings.
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  • The Red Men accounted to the Jesuits for the spherical forms of sun and moon by saying that their appearance was caused by their bended bows.
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  • The spherical aberration of a diamond lens can be brought down to one-ninth of a glass lens of equal focus.
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  • With this mineral also spherical and chromatic aberration are a fraction of that of a glass lens, but double refraction, which involves a doubling of the image, is fatal to its use.
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  • This is a glass cylinder, the two ends of which are spherical surfaces.
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  • When well made such constructions are almost free from spherical aberration, and the chromatic errors are very small.
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  • By introducing a dispersive lens of flint the magnifying glass could be corrected for both chromatic and spherical aberrations.
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  • As shown in Lens and Aberration, for reproduction through a single lens with spherical surfaces, a combination of the rays is only possible for an extremely small angular aperture.
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  • The aberrations, both spherical and chromatic, increase very rapidly with the aperture.
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  • In other words, a sufficiently good and distinct image as the resolving power permits cannot be arrived at, until the elimination, or a sufficient diminution, of the spherical and chromatic aberrations has been brought about.
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  • The spherical aberrations, however, can be overcome, or at least so diminished that they are quite harmless, by forming appropriate combinations of lenses.
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  • Correction of the spherical aberration in strong systems with very large aperture can not be brought about by means of a single combination of two lenses, but several partial systems are necessary.
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  • If, by these methods, a point in the optic axis has been freed from aberration, it does not follow that a point situated only a very small distance from the optic axis can also be represented without spherical aberration.
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  • The removal of the spherical aberration and the sine-condition can be accomplished only for two conjugate points.
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  • A second method of correcting the spherical aberration depends FIG.
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  • By experiment Abbe proved that old, good microscope objectives, which by mere testing had become so corrected that they produced usable images, were not only free from spherical aberrations, but also fulfilled the sine-condition, and were therefore really aplanatic systems.
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  • - Showing a system with chromatic difference of spherical aberration.
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  • By using these glasses and employing minerals with special optical properties, it is possible to correct objectives so that three colours can be combined, leaving only a quite slight tertiary spectrum, and removing the spherical aberration for two colours.
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  • A second method for diminishing the spherical aberration was to alter the distances of the single systems, a method still used.
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  • This method makes it specially possible to overcome the chromatic and spherical aberrations of higher orders and to fulfil – the sine-condition, and the chief merit of this improvement belongs to Amici.
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  • In the apochromats the chromatic difference of the spherical aberrations is eliminated, for the spherical aberration is completely avoided for three colours.
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  • A diaphragm s is placed in the middle of the spherical surface, and this keeps back the central rays.
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  • The combination of rays is also sufficient in practice if the cardioid surface is replaced, by a spherical one.
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  • A supplementary spherical surface c is necessary for the completion of the condenser.
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  • The definition is better according as the chromatic and spherical aberrations are removed; there always remains in even the best constructions some slight aberration.
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  • Pollen-grains are also spherical; cylindrical and curved, as in Tradescantia virginica; C From Vines' Students' Text-Book of Botany, by permission of Swan Sonnenschein & Co.
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  • The ovary is usually of a more or less spherical or curved form, sometimes smooth and uniform on its surface, at other times hairy and grooved.
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  • The non-cellular order Siphoneae is fairly well represented in Palaeozoic strata, especially by calcareous verticillate forms referable to the family Dasycladeae; the separate tubular joints of the articulated thallus, bearing the prints of the whorled branches, are sometimes cylindrical (Arthroporella, Vermiporella, &c.), sometimes oval (Sycidium) or spherical (Cyclocrinus).
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  • Pachytheca, a spherical organism, usually about the size of a small pea, found in rocks of Silurian and Devonian age, has been much investigated and discussed, without any decisive light having been thrown on its nature.
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  • In one case the spherical thallus was found seated in a cup-like receptacle.
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  • Spherical sacs, bearing forked spines, described by Williamson under the name of Zygosporites, are frequent, usually in an isolated state.
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  • In the same volume are treatises on "Geometric Loci, or Spherical Tangencies," and on the "Rectification of Curves," besides a restoration of "Apollonius's Plane Loci," together with the author's correspondence addressed to Descartes, Pascal, Roberval, Huygens and others.
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  • Using perspective projection the spherical panorama would lose much of its phenomenal reality.
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  • The image, despite the spherical aberration, was by far superior to any existing microscope made by his contemporaries.
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  • All pivots will be by ball joints or spherical bearings.
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  • And don't forget a spherical ice cream bombe - a real center piece.
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  • The spherical aberration correction is in this region too.
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  • He rejected all the Greek philosophers, and in doing so also rejected a spherical earth.
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  • The extra hardness caused the droplets to form spherical globules.
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  • The former includes graphite as flakes and the latter includes graphite in spherical or nodular form.
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  • The current state of the art makes use of spherical harmonics.
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  • Flowers are borne in terminal or axillary panicles, clusters or cymes which are spherical, domed or flattened like a lacecap hydrangea.
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  • First a spherical boss without lettering; secondly a ring with embossed lettering, the text of which is shown in the table.
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  • This includes probe linearity to pulse modulated and amplitude modulated signals, spherical isotropy, and spatial resolution.
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  • To address problems that arise in the resultant optimization we introduce a technique called spherical normalization that preconditions the Hessian matrix.
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  • Silica - gentle spherical microspheres to stimulate oxygenation and exfoliation before breaking down and disappearing.
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  • Atoms are found to be spherical but they are not miniscule billiard balls.
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  • All living organisms consist of cells; spherical aggregates of biological molecules surrounded by a thin membrane.
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  • They are borne in terminal or axillary panicles, clusters, corymbs or cymes, which are often spherical or domed.
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  • For those users with Apple's Quicktime plugin, fully immersive 360° spherical panoramas of each location are also available.
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  • If gravity and surface tension did not predominate, the water drops on the surface would still be spherical as well.
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  • They have profuse, fragrant, bright golden yellow, spherical, fluffy flowerheads, 5mm (0.25in) across.
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  • But could the net provide the ideal receptacle for Gadda, this most spherical of writers?
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  • The lamp tray carries a large pre-focus lampholder with a 6-in. diam. spherical anodised aluminum reflector.
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  • The spathe wraps around itself to form a space that encloses a spherical head of flowers, called a spadix (figure 2 ).
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  • An inflation force is used at each vertex to inflate the overall model, while surface tension attempts to keep the mesh spherical.
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  • Again, the planet does not appear perfectly spherical.
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  • One way for a three-dimensional object to decrease its surface area and to increase its volume is to become more spherical.
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  • Under the microscope, an anther can be seen to have many spherical to ellipsoidal pollen grains on its surface.
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  • Note also that wormholes should look spherical, not like tunnels!
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  • The eye is a roughly spherical organ built a bit like a football.
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  • The body is approximately spherical up to 30 m m in diameter.
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  • Gravity attracts matter together into spherical stars, like the Sun, and nearly spherical planets like our Earth.
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  • The almost spherical shape is due to the surface tension of the model.
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  • These are followed by edible, usually spherical, fruits.
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  • I realize that this extends the tube length and will cause some spherical aberration.
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  • It incorporates aspherical lens elements in the front, as well as rear lens groups, to correct spherical aberration.
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  • Its design employs three (3) aspherical lens elements to minimize spherical aberration, astigmatism and sagittal comma flare.
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  • Abu'l-Wafa and Abu Nasr Mansur both applied spherical geometry to astronomy and also used formulas involving sin and tan.
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  • This group studies the convection regime within the Earths Mantle in three dimensional spherical geometry at approaching Earth-like vigor.
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  • This quite perfect spherical structure is an equilibrium organ called a statolith, frequently encountered in marine creatures.
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  • Restrictions: The main restriction is related to the assumed spherical symmetry.
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  • The main highlights of the year include: First experimental campaign of our new spherical tokamak, MAST, which has been highly successful.
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  • The liquid wall can conceivably be applied to future magnetic fusion reactors, whether a spherical torus, a tokamak, or another design.
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  • There are many formulae relating the sides and angles of a spherical triangle.
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  • These texts were the precursors of spherical trigonometry, which became vital to astronomy.
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  • The tubular based flowers are bell, star or cup shaped which are borne in spherical umbels 1 - 10cm across.
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  • Very many species produce similar spherical BS of about 0.5 micron in diameter with characteristic latticework surface, looking like giant clathrin-coated transport vesicles.
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  • 2 For the corrections applicable to measures of position-angle in different hour angles, on account of errors of the equatorial instrument and of refraction, see Chauvenet's Practical and Spherical Astronomy, ii.
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  • The spherical particles are the second matter of Descartes, and their tendency to propel one another from the centre in straight lines towards the circumference of each vortex is what gives rise to the phenomenon of light radiating from the central star.
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  • Besides the logarithms and the calculating rods or bones, Napier's name is attached to certain rules and formulae in spherical trigonometry.
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  • When the blastula is spherical and not set free, the germ-layer formation is always multipolar, either by immigration or by delamination, i.e.
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  • The chloroplast consists of two parts, a colorless ground substance, and a green coloring matter, which is contained either in the form of fibrils, or in more or less regular spherical masses, in the colorless ground-mass.
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  • These were: (I) that the earth must be spherical, because of the tendency of matter to fall together towards a common centre; (2) that only a sphere could always throw a circular shadow on the moon during an eclipse; and (3) that the shifting of the horizon and the appearance of new constellations, or the disappearance of familiar stars, as one travelled from north to south, could only be explained on the hypothesis that the earth was a sphere.
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  • Love has shown that the great features of the relief of the lithosphere may be expressed by spherical harmonics of the first, second and third degrees, and their formation related to gravitational action in a sphere of unequal density.'
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  • Turning, therefore, to a globe, Asia, viewed as a whole, will be seen to have the form of a great isosceles spherical triangle, having its north-eastern apex at East Cape (Vostochnyi), in Bering Strait; its two equal sides, in length about a quadrant of the sphere, or 6500 m., extending on the west to the southern point of Arabia, and on the east to the extremity of the Malay peninsula; and the base between these points occupying about 60° of a great circle, or 4 500 m., and being deeply indented by the Arabian Sea and the Bay of Bengal on either side of the Indian peninsula.
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  • He examined the yeasts under the microscope, and at once saw that the globules from the sound beer were nearly spherical, whilst those from the sour beer were elongated; and this led him to a discovery, the consequences of which have revolutionized chemical as well as biological science, inasmuch as it was the beginning of that wonderful series of experimental researches in which he proved conclusively that the notion of spontaneous generation is a chimera.
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  • But the difficulties interposed by spherical and chromatic aberration had arrested progress in that direction until, in 1655, Huygens, working with his brother Constantijn, hit upon a new method of grinding and polishing lenses.
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  • The expressions designated by Dr Whewell, Laplace's coefficients (see Spherical Harmonics) were definitely introduced in the memoir of 1785 on attractions above referred to.
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  • It is known (see Spherical Harmonics) that The maxima of C occur when d Ji(z) _Ji'(z) J1(z) =o; z) z z2 or by (17 when J2(z) =0.
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  • Another obvious inference from the necessary imperfection of optical images is the uselessness of attempting anything like an absolute destruction of spherical aberration.
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  • The gatherer dips the butt of the pipe into the molten " metal " and withdraws upon it a small ball of viscous glass, which he allows to cool in the air while constantly rotating it so as to keep the mass as nearly spherical in shape as he can.
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  • One view, the monozoic, regards the whole development as a prolonged metamorphosis; another, the polyzoic view, considers that not only is the Cestode a colony, the proglottides being produced asexually, but that the scolex which buds off these individuals is itself a bud produced by the spherical embryo or onchosphere.
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  • If, however, the unit point charge were defined to be that which produces a unit of electric flux through a circumscribing spherical surface or the electric force at distance r defined to be 1/47rr2, many theorems would be enunciated in simpler forms.
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  • It is at least a plausible conjecture, until the contrary is proved, that the atoms of all elements are spherical.'
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  • A "spherical sector" and "spherical cone" may be also regarded as the solids of revolution of a circular sector about one of its bounding radii, and about any other line through the vertex respectively.
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  • In astronomy, we are principally concerned with the orientation of points on a sphere - the so-called celestial sphere - with regard to certain planes and points within the sphere; this subject is treated in the article Astronomy (Spherical).
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  • But on the celestial sphere the great circles of these two planes are coincident, so that this distinction is not necessary (see Astronomy: Spherical).
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  • He made experiments, simultaneously with Wallis and Wren, on the collision of hard spherical bodies, and his statement of the results (1669) included a clear enunciation of the conservation of linear momentum, as demonstrated for these cases of collision, and apparently correct in certain other cases, mass being estimated by weight.
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  • This form has two distinct advantages: (I) if spherical mirrors are employed their aberrations have a tendency to correct each other; grain' (2) the instrument is shorter than the Gregorian, caeteris paribus, by twice the focal length of the small mirror.
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  • The vernal equinox is the initial point from which the right ascensions and the longitudes of the heavenly bodies are measured (see Astronomy: Spherical).
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  • A system fulfilling this condition and free from spherical aberration is called " aplanatic " (Greek a-, privative, irXavrl, a wandering).
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  • 8, c) (better perhaps termed a conjunctiva), below which the spherical lens projects into the optic vesicle, imbedded in the vitreous humour (v.b) which fills it; the retina (r) consists of visual cells with long cones (fig.
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  • Poinsot gave the formula E 2k = eV + F, in which k is the number of times the projections of the faces from the centre on to the surface of the circumscribing sphere make up the spherical surface, the area of a stellated face being reckoned once, and e is the ratio " angles at a vertex /21r" as projected on the sphere, E, V, F being the same as before.
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  • As regards the course - of the streams on refraction into the crystal, it is found that it is determined by the Huygenian law (see Refraction, § Double); as, however, the two streams in the direction of the axis have different speeds, the spherical and the spheroidal sheets of the wavesurface do not touch as in the case of inactive uniaxal crystals.
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  • These are: (I) chromatic aberration, (2) spherical aberration and (3) astigmatism (see Aberration).
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  • According to Huygens's principle (see Diffraction) each aether particle, set vibrating by an incident wave, can itself act as a new centre of excitement, emitting a spherical wave; and similarly each particle on this wave itself produces wave systems. All systems which are emitted from a single source can by a suitable optical device be directed that they simultaneously influence one and the same aether particle.
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  • Hence the importance of observing the length of the tube in strong systems. If the sine-condition is not fulfilled but the spherical aberrations in the axis have been removed, then the image shown in fig.
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  • If however the object-point does not lie in the medium with the index n, but before it, and the medium is, for example, like a front lens, still limited by a plane surface, just in front of which is the object-point, then in traversing the plane surface spherical aberrations of the under-corrected type again arise, and must be removed.
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  • This method makes it specially possible to overcome the chromatic and spherical aberrations of higher orders and to fulfil - the sine-condition, and the chief merit of this improvement belongs to Amici.
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  • As both eyepieces are used with very small apertures (about f : 20) no attempt has been made to overcome the spherical aberrations, which are usually very slight; neither, as a rule, are the eyepieces chromatically corrected, care has only to be taken by a suitable choice of the distance of one lens from the other, that the coloured images derived from a colourless object should have the same apparent size.
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  • The spathe wraps around itself to form a space that encloses a spherical head of flowers, called a spadix (figure 2).
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  • Very low aspect ratio tokamaks are often called spherical tokamaks.
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  • Be able to demonstrate the physical significance of closed shells by using plots of the spherical harmonics.
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  • Note also that wormholes should look spherical, not like tunnels !
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  • He declared that the Earth, which possessed a divine essence or ' world soul ', was perfectly spherical in shape.
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  • They were spherical with a diameter of 28 to 30 nm.
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  • This applies both to high speed low noise and to low speed tapered roller and spherical roller bearings subject to shock or vibration loads.
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  • It further noted Culham 's world leadership in developing the spherical tokamak concept.
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  • This contained work on planar and spherical trigonometry originally done much earlier in about 1464.
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  • Unlike composting bins, that have a twenty-five or fifty gallon capacities, these spherical composters have an amazing seventy-one gallon capacity.
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  • Today they're double-ended, spherical or shaped into a tiny nib.
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  • A black liquid eyeliner can be applied on the top of the eyelid in a cat eye style to help lift the hooded lid while adding curve to the spherical shape.
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  • Spherical wand: This wand may resemble a mini medieval torture device, but the round shape actually helps coax short lashes up and out, from corner to corner, which creates a wide eyed, lengthened look.
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  • Givenchy Phenomen'Eyes was the first mascara on the market with the spherical brush.
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  • To do this, use a pre-molded cake pan, such as Wilton's Stand-Up Cuddly Bear Pan or a spherical pan that will bake two halves of a round cake.
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  • Fruits are spherical, purple black berries arranged in a large cluster.
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  • Shape: Although pearls come in a range of shapes, round or spherical pearls are usually preferred for studs.
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  • Since perfectly round pearls are very rare, many earrings utilize a near-round or spherical shape instead that might be flattened on one side.
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  • This frame has interchangeable lenses and is dual spherical.
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  • Two different lens types are available: spherical and cylindrical.
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  • The spherical lenses use ARC technology, while the cylindrical lenses are thermoformed, making them less expensive but also quite clear.
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  • Any of several species of spherical bacteria that form pairs or chains.
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  • Staphylococcus-Any of several species of spherical bacteria that occur in groups of four or in irregular clusters.
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  • The Scentbug's spherical casing has dozens of pores on each side, allowing the fragrance to be evenly distributed by the small internal fan.
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  • The gem should be spherical and symmetrical, though slightly elongated pearls can often be set into rings to disguise the malformation.
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  • The recent development of the "Revolution" spherical design has been estimated to reduce concussions by 31 percent, a welcome improvement to a dangerous game.
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  • As the small filings produced by friction seek to pass through the interstices between the rapidly revolving spherical particles in the vortex, they are detained and become twisted and channelled in their passage, and when they reach the edge of the inner ocean of solar dust they settle upon it as the froth and foam produced by the agitation of water gathers upon its surface.
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  • In Hydra viridis the polyp is of a green colour and produces a spherical egg with a smooth shell which is dropped into the mud.
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  • On their material side they are not absolutely unextended, but spherical.
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  • It may be in the form of an albumen crystal sometimes associated with a more or less spherical bodygloboid-composed of a combination of an organic substance with a double phosphate of magnesium and calcium.
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  • The Structure of the Nucleus.In the living condition the resting nucleus appears to consist of a homogeneous ground substance containing a large number of small chromatin granules and one or more large spherical granulesnucleolithe whole being surrounded by a limiting membrane which separates it from the cytoplasm.
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  • The Pythagorean school of philosophers adopted the theory of a spherical earth, but from metaphysical rather than scientific reasons; their convincing argument was that a sphere being the most perfect solid figure was the only one worthy to circumscribe the dwellingplace of man.
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  • He divides geography into The Spherical Part, or that for the study of which mathematics alone is required, and The Topical Part, or the description of the physical relations of parts of the earth's surface, preferring this division to that favoured by the ancient geographers - into general and special.
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  • Ptolemy Euergetes (247-222 B.C.) rendered the greatest service to geography by the protection and encouragement of Eratosthenes, whose labours gave the first ap proximate knowledge of the true size of the spherical The .
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  • Amongst the earliest mechanical contrivances of Fraunhofer was a machine for polishing mathematically uniform spherical surfaces.
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  • 3,641,000 2,873,000 large spherical areas on a flat surface being necessarily continent.
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  • They are essentially spherical, pear-shaped or oval sacs opening on to the exterior but closed at the coelomic end.
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  • In the former, the duct, leading from the ovarian sac, and swelling along its course into the spherical sac, the "spermatheca," is highly suggestive of the oviduct and receptaculum of the Eudrilidae.
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  • It has simply been traced as far as the formation of a diblastula which acquires a ciliated band, and becomes a nearly spherical trochosphere.
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  • The more highly organized species have often very numerous eyes (Amphiporus, Drepanophorus), which are provided with a spherical refracting anterior portion, with a cellular " vitreous body," with a layer of delicate radially arranged rods, with an outer sheath of dark pigment, and with a separate nerve-twig each, springing from a common or double pair of branches which leave the brain as n.
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  • The latter enlarges into a spherical stomach into which open the broad ducts of the so-called liver.
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  • The greatest of Gilbert's discoveries was that the globe of the earth was magnetic and a magnet; the evidence by which he supported this view was derived chiefly from ingenious experiments made with a spherical lodestone or lerrella, as he termed it, and from his original observation that an iron bar could be magnetized by the earth's force.
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  • Some importance attaches to the form of the pollen grains; the two principal forms are ellipsoidal with longitudinal bands forming the Convolvulus-type, and a spherical form with a spiny surface known as the Ipomaea-type.
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  • If, however, the primary wave be spherical, and of radius a at the wave-front of resolution, then we kno* that at a distance r further on the amplitude of the primary wave will be diminished in the ratio a:(r+a).
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  • - A very general problem in diffraction is the investigation of the distribution of light over a screen upon which impinge divergent or convergent spherical waves after passage through various diffracting apertures.
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  • When parallel rays fall directly upon a spherical mirror the longitudinal aberration is only about one-eighth as great as for the most favourably shaped single lens of equal focal length and aperture.
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  • In these instruments the lines are ruled upon a spherical surface of speculum metal, and mark the intersections of the surface by a system of parallel and equidistant planes, o; of which the middle member passes through the centre of the sphere.
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  • The same method of representation is applicable to spherical waves, issuing from a point, if the radius of curvature be large; for, although there is variation of phase along the length of the infinitesimal strip, the whole effect depends practically upon that of the central parts where the phase is sensibly constant.'
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  • It consisted of a spherical glass vessel opening below by means of a stop-cock and narrow nozzle into the cylinder of an "exhausting syringe," which inclined upwards from the extremity of the nozzle.
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  • Every natural development of the spherical form can be obtained by blowing and fashioning by hand.
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  • Although spherical forms can be obtained without the use of moulds, moulds are now largely used for even the simplest kinds of tableware in order to economize time and skilled labour.
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  • Irrotational Motion in General.-Liquid originally at rest in a singly-connected space cannot be set in motion by a field of force due to a single-valued potential function; any motion set up in the liquid must be due to a movement of the boundary, and the motion will be irrotational; for any small spherical element of the liquid may be considered a smooth solid sphere for a moment, and the normal pressure of the surrounding liquid cannot impart to it any rotation.
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  • Hill's spherical vortex, advancing through the surrounding liquid with uniform velocity.
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  • He also showed that the total gravitation of the earth, assumed as spherical, on external bodies, would be the same as if the earth's mass were concentrated in the centre.
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  • Until recently these spherical lenses were numbered in terms of their focal length, the inch being used as the unit.
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  • The thurible, the proper ecclesiastical term for the vessel in the Western Church, is usually spherical in form, though often square or polygonal, containing a small receptacle for the charcoal and covered by a perforated lid; it is carried and swung by three chains, a fourth being attached to the lid, thus allowing it to be raised at intervals for the volume of smoke to be increased.
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  • The animal body, if it be composed of many cells, follows a different architectural plan; the compact nature of its food, and the yielding nature of its cell-walls, result in a form of structure consisting essentially of tubular or spherical masses of cells arranged concentrically round the food-cavity.
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  • The thinnest possible spherical shell of metal, such as a sphere of insulator coated with gold-leaf, behaves as a conductor for static charge just as if it were a sphere of solid metal.
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  • It is a fundamental theorem in attractions that a thin spherical shell of matter which attracts according to the potential law of the inverse square acts on all external points as of a if it were concentrated at its centre.
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  • Let R 1 be the radius of the inner sphere, R2 the inside radius of the outer sphere, and R2 the outside radius of the outer spherical shell.
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  • The reader is also referred to an article by Lord Kelvin (Reprint of Papers on Electrostatics and Magnetism, p. 178), entitled " Determination of the Distribution of Electricity on a Circular Segment of a Plane, or Spherical Conducting Surface under any given Influence," where another equivalent expression is given for the capacity of an ellipsoid.
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  • Then this produces a charge - Q on the inside of the enclosing spherical shell, and a concentric charge +Q on the outside of the shell.
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  • The same reasoning can be applied to determine the electrical image of a point-charge of positive electricity in a spherical surface, and therefore the distribution of induced electricity over a metal sphere connected to earth produced by a point-charge near it.
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  • If then we put a negative point-charge -qr/d at B, it follows that the spherical surface will be a zero potential surface, for q rq 1 (24).
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  • Hence this charge is the electrical image of the charge +q at A in the spherical surface.
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  • The molecules of gases for which n = o must accordingly be spherical in shape and in internal structure, or at least must behave at collisions as though they were spherical, for they would otherwise be set into rotation by the forces experienced at collisions.
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  • In the light of these results it is of extreme significance that the four gases for which n = o are all believed to be monatomic: the molecules of these gases consist of single atoms. Moreover, these four are the only monatomic gases for which the value of y is known, so that the only atoms of which the shape can be determined are found to be spherical.
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  • Now this is exactly the shape which we should expect to find in molecules composed of two spherical atoms distorting one another by their mutual forces, and all gases for which n=2 are diatomic.
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  • The spherical blanks soon gave place to lenticular-shaped ones.
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  • They have characteristic conidiophores bearing numerous conidia, and also cleistothecia which are spherical in form and yellowish in colour.
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  • They are sometimes spherical (" shot bort ").
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  • This investigator just missed a great discovery, for he did not consider the spherical forms to be living organisms but compared them with starch granules.
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  • The result of cleavage in all cases is a typical blastula, which when set free becomes oval and develops a flagellum to each cell, but when not set free, it remains spherical in form and has no flagella.
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  • They are spherical, oval, fusiform, or rod-like, and are always found in the cytoplasm, never in the cell-sap. They appear to be permanent organs of the cell, and are transmitted from one cell to another by division.
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  • At the an ~ ~ tenor end are attached - two cilia or flagella In, , C the Vascular Cryptogams -- ~ the structure is much the;il ~.: -; same, but a more or less ~ ~ ~ spherical mass of cyto 4 i~- - ~ plasm remains attached .8 ~ :~ to the posterior spirals, -.
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  • For the subjects of this heading see the articles DIFFERENTIAL EQUATIONS; FOURIER'S SERIES; CONTINUED FRACTIONS; FUNCTION; FUNCTION OF REAL VARIABLES; FUNCTION COMPLEX; GROUPS, THEORY OF; INFINITESIMAL CALCULUS; MAXIMA AND MINIMA; SERIES; SPHERICAL HARMONICS; TRIGONOMETRY; VARIATIONS, CALCULUS OF.
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  • - Section through a portion of the lateral eye of Limulus, showing three ommatidia - A, B and C. hyp, The epidermic cell-layer (so-called hypodermis), the cells of which increase in volume below each lens, 1, and become nerve-end cells or retinula-cells, rt; in A, the letters rh point to a rhabdomere secreted by the cell rt; c, the peculiar central spherical cell; n, nerve fibres; mes, mesoblastic skeletal tissue; ch, chitinous cuticle.
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  • Turning, therefore, to a globe, Asia, viewed as a whole, will be seen to have the form of a great isosceles spherical triangle, having its north-eastern apex at East Cape (Vostochnyi), in Bering Strait; its two equal sides, in length about a quadrant of the sphere, or 6500 m., extending on the west to the southern point of Arabia, and on the east to the extremity of the Malay peninsula; and the base between these points occupying about 60° of a great circle, or 4 500 m., and being deeply indented by the Arabian Sea and the Bay of Bengal on either side of the Indian peninsula.
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  • The kettle is spherical, and is suspended over a fire-place by a broad rim resting on a wall; it is usually of cast iron.
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  • A magnetizable substance was supposed to consist of an indefinite number of spherical particles, each containing equivalent quantities of the two fluids, which could move freely within a particle, but could never pass from one particle to another.
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  • Ball, Spherical Astronomy, p. 303.
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  • If the latitudes differ, we have to solve an oblique-angled spherical triangle, of which two sides and the included angle are given.
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