Cubic sentence example

cubic
  • Its weight varies from 48 to about 55lb the cubic foot, but in very hard slowly-grown trunks sometimes approaches 60 lb.

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  • Working with two different specimens, he found that the hysteresis loss in ergs per cubic centimetre (W) was fairly represented by o 00125B 1 6 and o o0101B 1 ' 6 respectively, the maximum induction ranging from about 300 to 3000.

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  • In one case the hysteresis loss per cubic centimetre per cycle was 16,100 ergs for B =1 5,900, and only 1200 ergs for B = 20,200, the highest induction obtained in the experiment; possibly it would have vanished before B had reached 21,000.2 These experiments prove that actual friction must be almost entirely absent, and, as Baily remarks, the agreement of the results with the previously suggested deduction affords a strong verification of Ewing's form of the molecular theory.

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  • The wood is very heavy and hard, weighing 70 lb the cubic foot; the colour is dark brown; it is used in Spain and Italy for furniture, and in the former country for firewood and charcoal.

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  • West Virginia, estimates that in fairly good producing sand a cubic foot of rock contains from 6 to 12 pints of oil.

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  • Problems in artillery occupy two out of nine books; the sixth treats of fortification; the ninth gives several examples of the solution of cubic equations.

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  • A standard sodium hydrate solution can be prepared by dissolving 42 grammes of sodium hydrate, making up to a litre, and diluting until one cubic centimetre is exactly equivalent to one cubic centimetre of the sulphuric acid.

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  • Ammonium iodide assumes cubic forms with perfect cubic cleavage; tetramethyl ammonium iodide is tetragonal with perfect cleavages parallel to {100} and {o01} - a difference due to the lengthening of the a axes; tetraethyl ammonium iodide also assumes tetragonal forms, but does not exhibit the cleavage of the tetramethyl compound; while tetrapropyl ammonium iodide crystallizes in rhombic form.

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  • We may therefore regard the nitrogen atoms as occupying the centres of a cubic space lattice composed of iodine atoms, between which the hydrogen atoms are distributed on the tetrahedron face normals.

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  • For the cubic (ab) 2 axbx is a covariant because each symbol a, b occurs three times; we can first of all find its real expression as a simultaneous covariant of two cubics, and then, by supposing the two cubics to merge into identity, find the expression of the quadratic covariant, of the single cubic, commonly known as the Hessian.

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  • For the quadratic it is the discriminant (ab) 2 and for ax2 the cubic the quadratic covariant (ab) 2 axbx.

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  • We will write the cubic covariant (f, i) 2 =j, and then remark that the result, (f,j) 3 = o, can be readily established.

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  • Hence, solving the cubic, R 2 j = (S -m i a) (S - m 2 a) (S - m3a) wherein m 1 m2, m 3 are invariants.

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  • Now, evidently, the third transvectant of f, expressed in this form, with the cubic pxgxrx is zero, and hence from a property of the covariant j we must have j = pxgxrx; showing that the linear forms involved are the linear factors of j.

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  • Hesse showed independently that the general ternary cubic can be reduced, by linear transformation, to the form x3+y3+z3+ 6mxyz, a form which involves 9 independent constants, as should be the case; it must, however, be remarked that the counting of constants is not a sure guide to the existence of a conjectured canonical form.

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  • The closed figure a c d e a is variously called a hysteresis curve or diagram or loop. The area f HdB enclosed by it represents the work done in carrying a cubic centimetre of the iron through the corresponding magnetic cycle; expressed in ergs this work is I HdB.

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  • Fleming, it 47r requires about 18 foot-pounds of work to make a complete mag netic cycle in a cubic foot of wrought iron, strongly magnetized first one way and then the other, the work so expended taking the form of heat in the mass.

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  • When the magnetizing current is twice reversed, so as to complete a cycle, the sum of the two deflections, multiplied by a factor depending upon the sectional area of the specimen and upon the constants of the apparatus, gives the hysteresis for a complete cycle in ergs per cubic centimetre.

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  • Cubic equations were solved geometrically by determining the intersections of conic sections.

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  • Archimedes' problem of dividing a sphere by a plane into two segments having a prescribed ratio,was first expressed as a cubic equation by Al Mahani, and the first solution was given by Abu Gafar al Hazin.

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  • Although the foundations of the geometrical resolution of cubic equations are to be ascribed to the Greeks (for Eutocius assigns to Menaechmus two methods of solving the equation x 3 = a and x 3 = 2a 3), yet the subsequent development by the Arabs must be regarded as one of their most important achievements.

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  • This contest over, Tartalea redoubled his attempts to generalize his methods, and by 1541 he possessed the means for solving any form of cubic equation.

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  • Cardan or Cardano, who was at that time writing his great work, the Ars Magna, could not restrain the temptation of crowning his treatise with such important discoveries, and in 1 545 he broke his oath and gave to the world Tartalea's rules for solving cubic equations.

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  • Cubic equations having been solved, biquadratics soon followed suit.

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  • The alluvial extracted, which in the Malay Peninsula and Archipelago carries from 5 to 60 lb of tinstone (or "black tin," as it is termed by Cornish miners) to the cubic yard of gravel, is washed in various simple sluicing appliances, by which the lighter clay, sand and stones are removed and tinstone is left behind comparatively pure, containing usually 65 to 75% of metallic tin (chemically pure tinstone contains 78.7%).

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  • Of the water received by Albert Nyanza annually (omitting the Victoria Nile from the calculation) between 50 and 60% is lost by evaporation, whilst 24,265,000,000 cubic metres are annually withdrawn by the Bahr-el-Jebel.

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  • Then 4, =o over the cylinder r = a, which may be considered a fixed post; and a stream line past it along which 4, = Uc, a constant, is the curve (r - ¢2) sin 0=c, (x2 + y2) (y - c) - a 2 y = o, (3) a cubic curve (C3).

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  • Chile saltpetre, cubic nitre or sodium nitrate, NaNO,, occurs under the same conditions as ordinary saltpetre in deposits covering immense areas in South America, which are known locally as caliche or terra salitrosa, and abound especially in the provinces of Tarapaca and Antofagasta in Chile.

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  • An irrigation canal, deriving water from the Sega, furnishes 112 cubic metres per second to the fields of the upper Veronese district.

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  • Massimo to the suburb of Tombetta, furnishes 26 cubic metres of water per second, and generates 4000 horse-power.

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  • The native metal crystallizes in the cubic system, the octahedron being the commonest form, but other and complex combinations have been observed.

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  • Pure crystalline calcium carbide yields 5.8 cubic feet of acetylene per pound at ordinary temperatures, but the carbide as sold commercially, being a mixture of the pure crystalline material with the crust which in the electric furnace surrounds the ingot, yields at the best 5 cubic feet of gas per pound under proper conditions of generation.

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  • When acetylene is burnt from a 000 union jet burner, at all ordinary pressures a smoky flame is obtained, but on the pressure being increased to 4 inches a magnificent flame results, free from smoke, and developing an illuminating value of 240 candles per 5 cubic feet of gas consumed.

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  • He also showed that the roots of a cubic equation can be derived by means of the infinitesimal calculus.

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  • Hairy considered the crystals to be only distorted cubic forms.

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  • Calculations involving feet and inches are sometimes performed by means of duodecimal arithmetic; i.e., in effect, the tables of square measure and of cubic measure are amplified by the insertion of intermediate units.

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  • For square measure 12 square inches = I superficial prime, 12 superficial primes = I square foot; while for cubic measure 12 cubic inches = I solid second, 12 solid seconds = I solid prime, 12 solid primes = I cubic foot.

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  • The same formula will also hold (§ 52) for any cubic trapezette through the points.

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  • Although Hippocrates could not determine the proportionals, his statement of the problem in this form was a great advance, for it was perceived that the problem of trisecting an angle was reducible to a similar form which, in the language of algebraic geometry, is to solve geometrically a cubic equation.

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  • The kinetic energy per cubic centimetre is 2 pu t, where is the density and u is the velocity of disturbance due to the passage of the wave.

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  • Hence the work done on the air is (P-+zw)v, and the work done per cubic centimetre is (P+Zw)v/V.

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  • Hydrated sulphates occur at several localities in the province of Madrid and in other provinces of Spain, and at Miihlingen in Aargau, and copious deposits of glauberite, the double sulphate of sodium and calcium, are met with in the salt-mines of Villarrubia in Spain, at Stassfurt, and in the province of Tarapaca, Chile, &c. A native nitrate of soda is obtained in great abundance in the district of Atacama and the province of Tarapaca, and is imported into Europe in enormous quantities as cubic nitre for the preparation of saltpetre.

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  • Sodium combines directly with the halogens to form salts which are soluble in water and crystallize in the cubic system.

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  • Now these integrations are quite intractable, even for a very simple mathematical assumption of the function f(v), say the quadratic or cubic law, f(v) = v 2 /k or v3/k.

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  • Chemically, it is thus indentical with the cubic mineral diamond, but between the two there are very wide differences in physical characters.

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  • The Habra barrage holds 38,000,000 cubic metres; that on the Sig 18,000,000.

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  • In such definition an attempt has been made to avoid former confusion of expression as to capacity, cubic measure, and volume; the litre being recognized as a measure of capacity holding a given weight of water.

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  • Hence a cubic foot of water would weigh 62.281 lb avoir., and not 62.321 lb as at present legally taken.

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  • The two standards, the cubic inch and the cubic decimetre, may not be strictly comparable owing to a difference in the normal temperature (Centigrade and Fahrenheit scales) of the two units of extension, the metre and the yard.

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  • The weight of a cubic decimetre of water reaches 1000 grammes under a pressure of four atmospheres; but in vacuo, at all temperatures, the weight of water is less than a kilogram.

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  • To illustrate how easy it is to go astray in this line, observe the continual reference in modern handbooks to the cubic foot as 1000 oz.

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  • Again, there are many theories of the equivalence of different cubic cubits of water with various multiples of talents (2, 3, 18, 24, 33); but connexion by lesser units would be far more probable, as the primary use of weights is not to weigh large cubical vessels of liquid, but rather small portions of precious metals.

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  • The Roman amphora being equal to the cubic foot, and containing 80 librae of water, is one of the strongest cases of such relations, being often mentioned by ancient writers.

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  • He shows that the length of the cubit arose through the weights; that is to say, the original cubit of Egypt was based on the cubic double -- cubit of water -- and from this the several nations branched off with their measures and weights.

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  • It is curious, however, to find that an ancient nation of the East, so wise in geometrical proportions, should have followed what by modern experience may be regarded as an inverse method, that of obtaining a unit of length by deducing it through weights and cubic measure, rather than by deriving cubic measure through the unit of length.

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  • All quantities stated in this article without distinguishing names are in British units of inch, cubic inch or grain.

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  • Beside the equivalence of the hon to 5 utens weight of water, the mathematical papyrus (35) gives 5 besha = (2/3)cubic cubit (Revillout's interpretation of this as 1 cubit cubed is impossible geometrically; see Rev. Eg., 1881, for data); this is very concordant, but it is very unlikely for 3 to be introduced in an Egyptian derivation, and probably therefore only a working equivalent.

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  • The Roman theory of the amphora being the cubic foot makes it 1569 cub.

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  • Another theory (3) derives the uten from 1/1000 of the cubic cubit of 24 digits, or better of 6/7 of 20.63; that, however, will only fit the very lowest variety of the uten, while there is no evidence of the existence of such a cubit.

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  • Though it has no exact relation to the congius or amphora, yet it is closely = 4977 grains, the 1/80th of the cubic foot of water.

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  • The galena group includes several other cubic minerals, such as argentite (q.v.).

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  • Mention may also be made here of clausthalite (lead selenide, PbSe) and altaite (lead telluride, PbTe), which, with their lead-grey colour and perfect cubic cleavage, closely resemble galena in appearance; these species are named after the localities at which they were originally found, namely, Klausthal in the Harz and the Altai mountains in Asiatic Russia.

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  • The compound FeS 2 is dimorphous, and the modern practice is to distinguish the cubic forms as pyrites and the orthorhombic as marcasite (q.v.).

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  • Sometimes, however, the term pyrites is loosely applied to both species, and the cubic pyrites is then differentiated by the name "pyrite" - a form which brings the last syllable into harmony with the spelling of the names of most minerals.

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  • Iron pyrites, or pyrite, belongs crystallographically to the parallelfaced hemihedral class of the cubic system.

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  • Pyrites presents a conchoidal fracture, and a very indistinct cubic cleavage.

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  • It crystallizes in the cubic system, usually in cubes, pentagonal dodecahedra or octahedra, often of great beauty and perfection.

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  • Crystals belonging to the cubic system should not be birefringent unless strained; diamond often displays double refraction particularly in the neighbourhood of inclusions, both liquid and solid; this is probably due to strain, and the spontaneous explosion of diamonds has often been observed.

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  • Carbonado or " black diamond," found in Bahia (also recently in Minas Geraes), is a black material with a minutely crystalline structure somewhat porous, opaque, resembling charcoal in appearance, devoid of cleavage, rather harder than diamond, but of less specific gravity; it sometimes displays a rude cubic crystalline form.

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  • The ground is transferred in trucks to the shaft where it is automatically tipped into skips holding 96 cubic ft.

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  • Graphitic carbon in cubic form (cliftonite) has also been found in certain meteoric " irons," for example in those from Magura in Szepes county, Hungary, and Youndegin near York in Western Australia.

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  • Crystals of blende belong to that subclass of the cubic system in which there are six planes of symmetry parallel to the faces of the rhombic dodecahedron and none parallel to the cubic faces; in other words, the crystals are cubic with inclined hemihedrism, and have no centre of symmetry.

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  • It becomes then the duty of the engineer in charge to use every effort to get its full value out of every cubic foot of water.

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  • This would increase the storage capacity 22 times, or to about 9,375,000 millions of cubic feet.

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  • The method of estimating the area of irregular fields and the cubic contents of granaries, &c., is very faulty.

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  • Halite or rock-salt crystallizes in the cubic system, usually in cubes, rarely in octahedra; the cubes being solid, unlike the skeleton-cubes obtained by rapid evaporation of brine.

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  • The mineral has perfect cubic cleavage.

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  • Cubic pseudomorphs representing rock-salt are sometimes seen in strata which have been deposited in shallow water, especially on the margin of a salt-lake.

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  • The salt has been dissolved out of its original matrix, and the cavity so formed has then been filled with fine clayey or other mineral matter, forming a cubic cast.

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  • In the geometry of plane curves, the term parabola is often used to denote the curves given by the general equation a' n x n = ym+n, thus ax= y 2 is the quadratic or Apollonian parabola; a 2 x = y 3 is the cubic parabola, a 3 x = y4 is the biquadratic parabola; semi parabolas have the general equation ax n-1 = yn, thus ax e = y 3 is the semicubical parabola and ax 3 = y 4 the semibiquadratic parabola.

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  • The cartesian parabola is a cubic curve which is also known as the trident of Newton on account of its three-pronged form.

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  • John Wallis utilized the intersections of this curve with a right line to solve cubic equations, and Edmund Halley solved sextic equations with the aid of a circle.

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  • Diverging parabolas are cubic curves given by the equation y 2 = 3 -f-bx 2 -cx+d.

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  • Newton discussed the five forms which arise from the relations of the roots of the cubic equation.

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  • The standard of measurement most in use is the St Petersburg standard, which contains 165 cubic ft.

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  • It weighs about 36 lb to the cubic foot.

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  • A cubic foot weighs about 35 to 40 lb.

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  • A cubic foot weighs about 45 lb.

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  • Spanish mahogany weighs about 56 lb to the cubic ft., and the Honduras variety about 36 lb.

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  • The average weight of a cubic foot is about 61 lb.

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  • The annual timber yield of the Indian forests is about fifty millions of cubic feet, excluding what is used for local purposes.

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  • This quantity is now, as the result of further experiments, added to the values of h, and also represented in the formula for the specific heat itself by the cubic term.

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  • Even then, however, the amount of operative heat is very small in comparison with that which passes through the steam-engine, per cubic foot swept through by the piston, for the change of state which water undergoes in its transformation into steam involves the taking in of much more heat than can be communicated to air in changing its temperature within such a range as is practicable.

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  • Chalcopyrite crystallizes in the tetragonal system with inclined hemihedrism, but the form is so nearly cubic that it was not recognized as tetragonal until accurate measurements were made in 1822.

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  • Then the variation of the cubic contents of the vessel in a unit of time by reason of the motion of one piston is Va.

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  • It is estimated, however, that the domestic use of wood (especially for fuel) represents nearly five times as many cubic feet as the wood used for export in different shapes.

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  • It crystallizes in the cubic system, but the crystals are often flattened, elongated, rounded or otherwise distorted.

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  • Immense quantities are still exported, especially from Canada, its smooth easily-worked grain rendering it a favourite wood for the housecarpenter and joiner; it weighs about 28 lb per cubic foot.

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  • More important, however, are the supplies to be derived from the control of flood water, millions of cubic feet of the best soil being annually washed into the sea.

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  • In the case of diphtheria the antitoxic power of the serum may reach Boo units per cubic centimetre, or even more.

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  • Fluor-spar, though cubic, sometimes exhibits weak double refraction, probably due to internal tension.

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  • The simple "syrup" of the British Pharmacopoeia is prepared by adding 1000 grams (or 5 lb) of refined sugar to 500 cubic centimetres (or two pints) of boiling distilled water, heating until it is dissolved and subsequently adding boiling distilled water until the weight of the whole is 1500 grams (or 71 lb).

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  • Silver sulphide, Ag 2 S, occurs naturally as the orthorhombic acanthite, and the cubic argentite; the telluride, Ag 2 Te, named hessite, assumes cubic forms; other tellurides containing silver are petzite, (Ag,Au) 2 Te, and sylvanite, AuAgTe 4.

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  • Among his most remarkable works may be mentioned his ten memoirs on quantics, commenced in 1854 and completed in 1878; his creation of the theory of matrices; his researches on the theory of groups; his memoir on abstract geometry, a subject which he created; his introduction into geometry of the "absolute"; his researches on the higher singularities of curves and surfaces; the classification of cubic curves; additions to the theories of rational transformation and correspondence; the theory of the twenty-seven lines that lie on a cubic surface; the theory of elliptic functions; the attraction of ellipsoids; the British Association Reports, 1857 and 1862, on recent progress in general and special theoretical dynamics, and on the secular acceleration of the moon's mean motion.

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  • This average has decreased with some regularity from a maximum of 5.75 in 1821, but there is no certain evidence on which to affirm or deny that the average cubic capacity of dwelling-houses has been maintained.

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  • He was professor of mathematics in the university of Deseret and wrote several books on this subject, these including Cubic and Biquadratic Equations (1866).

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  • It has been calculated that the average daily discharge of the Muir in summer is 30,000,000 cubic ft.

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  • Ladoga discharges its surplus water by means of the Neva, which flows from its south-western corner into the Gulf of Finland, rolling down its broad channel 104,000 cubic ft.

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  • In the first volume Of the Entwickelungen he applied the method of abridged notation to the straight line, circle and conic sections, and he subsequently used it with great effect in many of his researches, notably in his theory of cubic curves.

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  • The capacity of the cranium is estimated in cubic measure by filling it with sand, &c., with the general result that the civilized white man is found to have a larger brain than the barbarian or savage.

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  • Some of the valleys are of considerable width; in other cases the opposite walls of the gorges are but two or three hundred yards apart, and fall almost vertically thousands of feet, representing an erosion of hard rock of many millions of cubic feet.

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  • The discharge of the lake is computed to be 75,200 cubic ft.

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  • The cost of buildings of the same class and finish is in direct proportion to their cubic contents, and each cubic foot constructed is commercially unprofitable which does not do its part in paying interest on the capital invested.

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  • Although, like the other streams which cross the Karroo, the river is sometimes dry in its upper course, it has an estimated annual discharge of 51,724,000,000 cubic ft.

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  • Mountain areas of io,000 acres and upwards, largely covered with moorland, upon nearly imper meable rocks with few water-bearing fissures, yield in temperate climates, towards the end of the driest seasons, and therefore solely from underground, between a fifth and .a quarter of a cubic foot per second per 1000 acres.

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  • Thus, for example, on woo acres or less, it commonly falls to onetenth of a cubic foot, and upon an upland Silurian area of 940 acres, giving no visible sign of any peculiarity, the discharge fell, on the 21st of September 1893, to one-thirty-fifth of a cubic foot per second per woo acres.

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  • The Thames at Teddington, fed largely from cretaceous areas, fell during ten days in September 1898 (the artificial abstractions for the supply of London being added) to about one-sixth of a cubic foot, and since 1880 the discharge has occasionally fallen, in each of six other cases, to about one-fifth of a cubic foot per second per woo acres.

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  • We have seen that the average flow from mountain areas in Great Britain towards the end of a dry season does not exceed one-fifth of a cubic foot per second per 1000 acres.

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  • In Wales it is usually about one-fourth, and elsewhere still less; but in any case it amounts to many times the above unit of one-fifth of a cubic foot per second per 1000 acres.

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  • The diagram applies to ordinary areas suitable for reservoir construction and in which the minimum flow of the stream reaches about one-fifth of a cubic foot per second per moo acres.

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  • The average volume in dry weather, of such flow, generally reduced to terms of the fraction of a cubic foot per second, per thousand acres of the contributing area, is commonly known in water engineering as the " dry weather flow " and its volume at the end of the dry season as the " extreme dry weather flow."

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  • In nearly all cases several of these chambers are connected so as to form a set of a cubic capacity of from 100,000 to 200,000 cub.

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  • Murray estimates the total land area draining to the Indian Ocean at 5,050,000 geographical square miles, almost the same as that draining to the Pacific. The annual rainfall draining from this area is estimated at 4380 cubic miles.

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  • The litre is equal to a cubic decimetre.

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  • The gramme was intended to be equal to the weight of a cubic centimetre of pure water at a certain temperature, but the equality is only approximate.

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  • Below the mouth of the Tambopata, the flow is estimated at 191,250 cubic metres per minute.

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  • A curve of the third order is called a cubic; one of the fourth order a quartic; and so on.

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  • Various properties of curves in general, and of cubic curves, are established in Colin Maclaurin's memoir, "De linearum geometricarum proprietatibus generalibus Tractatus " (posthumous, say 1746, published in the 6th edition of his Algebra).

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  • We have in it a particular kind of correspondence of two points on a cubic curve, viz.

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  • By means of Pliicker's equations we may form a table - The table is arranged according to the value of in; and we have m=o, n= r, the point; m =1, n =o, the line; m=2, n=2, the conic; of m = 3, the cubic, there are three cases, the class being 6, 4 or 3, according as the curve is without singularities, or as it has 1 node or r cusp; and so of m =4, the quartic, there are ten cases, where observe that in two of them the class is = 6, - the reduction of class arising from two cusps or else from three nodes.

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  • We may further consider the inflections and double tangents, as well in general as in regard to cubic and quartic curves.

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  • The whole theory of the inflections of a cubic curve is discussed in a very interesting manner by means of the canonical form of the equation x +y +z +6lxyz= o; and in particular a proof is given of Plucker's theorem that the nine points of inflection of a cubic curve lie by threes in twelve lines.

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  • It may be noticed that the nine inflections of a cubic curve represented by an equation with real coefficients are three real, six imaginary; the three real inflections lie in a line, as was known to Newton and Maclaurin.

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  • For an acnodal cubic the six imaginery inflections disappear, and there remain three real inflections lying in a line.

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  • For a crunodal cubic the six inflections which disappear are two of them real, the other four imaginary, and there remain two imaginary inflections and one real inflection.

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  • For a cuspidal cubic the six imaginary inflections and two of the real inflections disappear, and there remains one real inflection.

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  • The theory of the invariants and covariants of a ternary cubic function u has been studied in detail, and brought into connexion with the cubic curve u = o; but the theory of the invariants and covariants for the next succeeding case, the ternary quartic function, is still very incomplete.

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  • Again, when there is in question only one pair of points or lines, these, if coincident, must be real; thus, b line meets a cubic curve in three points, one of them real, and other two real or imaginary; but if two of the intersections coincide they must be real, and we have a line cutting a cubic in one real point and touching it in another real point.

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  • And it then appears that there are two kinds of non-singular cubic cones, viz, the simplex, consisting of a single sheet, and the complex, consisting of a single sheet and a twin-pair sheet; and we thence obtain (as for cubic curves) the crunodal, the acnodal and the cuspidal kinds of cubic cones.

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  • And we then say that a curve consists of one or more circuits; thus the right line, or curve of the first order, consists of one circuit; a curve of the second order consists of one circuit; a cubic curve consists of one circuit or else of two circuits.

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  • A non-singular cubic is simplex, consisting of one odd circuit, or it is complex, consisting of one odd circuit and one even circuit.

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  • It at once appears from inspection of the figure of a non-singular cubic curve, which is the odd and which the even circuit.

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  • The circular cubic and the bicircular quartic, together with the Cartesian (being in one point of view a particular case thereof), are interesting curves which have been much studied, generally, and in reference to their focal properties.

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  • There are in some cases points termed centres, or singular or multiple foci (the nomenclature is unsettled), which are the intersections of improper tangents from the two circular points respectively; thus, in the circular cubic, the tangents to the curve at the two circular points respectively (or two imaginary asymptotes of the curve) meet in a centre.

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  • It is a form of the theorem for the case D = r, that the coordinates x, y, z of a point of the bicursal curve, or in particular the co-ordinates of a point of the cubic, can be expressed as proportional to rational and integral functions of the elliptic functions snu, cnu, dnu; in fact, taking the radical to be r -0 2 .r - k 2 0 2, and writing 8 =snu, the radical becomes = cnu, dnu; and we have expressions of the form in question.

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  • Thus, considering the several cases of a cubic 1.

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  • It is a leading point in the theory that a curve in space cannot in general be represented by means of two equations U= o, V = o; the two equations represent surfaces, intersecting in a curve; but there are curves which are not the complete intersection of any two surfaces; thus we have the cubic in space, or skew cubic, which is the residual intersection of two quadric surfaces which have a line in common; the equations U= o, V= o of the two quadric surfaces represent the cubic curve, not by itself, but together with the line.

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  • The latter has an average calorific power of 1732 calories per cubic metre, or 161 B.T.U.

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  • Further, certain cubic crystals, such as sodium chlorate and bromate, and also some liquids and even vapours, rotate the plane of polarization of the light that traverses them, whatever may be the direction of the stream.

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  • The polarizability in cubic angstroms of a molecule in any particular orientation can then easily be calculated.

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  • About 60 million cubic meters of dome and crater wall traveled to the south as a debris avalanche and pyroclastic density currents.

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  • It is extremely lightweight but is the third hardest material known to science, next to diamond and cubic boron nitride.

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  • One pound of liquid butane produces 6.4 cubic feet of gas.

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  • The density, about 0.2 grams per cubic centimeter, means it is a gas giant like Jupiter.

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  • A very interesting example is Fe in the face centered cubic (fcc) phase.

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  • The program should return the type of local structure (face centered cubic, etc.) for each atom of the system.

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  • Which saw cubic rising he adds big safe cars which was a. Buy it the dollar you mail.

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  • The measuring volume of the F25 is one cubic decimeter; measuring uncertainty 250 nm at a scale resolution of 7.5 nm.

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  • A mini excavator working in the jacking shield, just ahead of the first pipe, removed 290 cubic meters of spoil.

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  • One gallon of aviation gasoline that has completely evaporated will form about 30 cubic feet of vapor at sea level.

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  • The town is supplied with gas by the local gasworks, at 4/7 per 1,000 cubic feet.

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  • A cubic fourfold is called special if it contains a surface which is not homologous to a multiple of a plane section.

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  • Less radical plans turned out to be an increase in capacity to 74 cubic inches in the IoE form of the Js.

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  • The cylinders on the back are charged with 10 cubic feet of oxygen at a pressure of 18.000 lbs per square inch.

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  • In a formal garden you can also grow ivy into a cubic shape.

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  • To produce 1 kilogram of cereals takes from 0.4 to 3 cubic meters of water.

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  • In the 1939 eruption, lava of about 0.1 cubic kilometer flowed out.

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  • For the simple cubic lattice, all values of n will give Bragg peaks.

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  • There are several varieties in which the cubic non linearity is common to each.

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  • Samphire Hoe is a new piece of England created from 4.9 million cubic meters of chalk marl dug to create the Channel Tunnel.

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  • Cubic Transportation Systems, with WMATA, designed the two-year-old SmarTrip system, the nation's first mass transit Smart Card fare collection program.

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  • Millions of cubic meters of illegal wood were seized.

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  • If ozone concentrations exceed 180 micrograms per cubic meter, they must inform the public and provide health advice.

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  • Normal CD4 counts in adults range from around 500 to 1,500 cells per cubic millimeter of blood.

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  • The structure is a cubic close packing of equal spheres.

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  • In the dense center of the cluster, the star density can increase from 100 to 1000 per cubic parsec.

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  • This occurs as cubic crystals of what is often referred to as Fool's Gold.

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  • Finite generalized tetrahedron groups with a cubic relator 2003/21 Vincent Schmitt.

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  • The fields are estimated to contain recoverable reserves of 350 to 400 billion cubic feet.

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  • The Cubic smooth option fits a smooth cubic spline to the data.

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  • Still longer needs the cubic spline, yet, for a really smoothed out shape, this is the only way to go.

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  • The latest operation brings the total of oil removed from the wreck to over 670 cubic meters.

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  • The primary structure is a glulam frame consisting of over 1,000 cubic meters of renewable European whitewood formed into paired columns and beams.

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  • Ironically, the Kenyon Cutting, east of the Newton Viaduct, yielded 750,000 cubic yards of material.

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  • Two solid looking silver vertical bridges rise on either side of the cubic zirconia, framing the pink stones.

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  • Victoria came on the phone and said they wanted cubic zirconium on the detailing, and a large Union Jack somewhere too.

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  • This is one of the Platonic solids, and is treated in the article Polyhedron, as is also the derived Archimedean solid named the "truncated tetrahedron"; in addition, the regular tetrahedron has important crystallographic relations, being the hemihedral form of the regular octahedron and consequently a form of the cubic system.

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  • From this we deduce for the charge p per cubic centimetre (I/41r)Xio-5 (volt/cm 2), or 2.7 X 101 electrostatic units.

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  • The heart-wood is dark in colour, takes a fine polish, and from the prominence of the medullary rays is valuable to the furniture maker; it weighs from 40 to 50 lb the cubic foot.

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  • The wood is very white, and, from its soft and even grain, is employed by turners and toy-makers, while, being tough and little liable to split, it is also serviceable for the construction of packing cases, the lining of carts and waggons, and many similar purposes; when thoroughly seasoned it makes good flooring planks, but shrinks much in drying, weighing about 58 lb per cubic foot when green, but only 331 lb when dry.

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  • The hypsographical map facilitates likewise the determination of the mean height of a country, and this height, combined with the area, the determination of volume, or cubic contents, is a simple matter.2 Relief Maps are intended to present a representation of the ground which shall be absolutely true to nature.

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  • The first difficulty to be overcome was the algebraical solution of cubic equations, the " irreducible case" (see Equation).

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  • One cubic centimetre of soil taken within a foot or so from the surface contains from II to 2 millions of bacteria of many different kinds, as well as large numbers of fungi.

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  • Thus, if a railway contractor has to make a tunnel through a hill of gravel., and if one cubic yard of the gravel is so like another cubic yard that for the purposes of the contract they may be taken as equivalent, then, in estimating the work required to remove the gravel from the tunnel, he may, without fear of error, make his calculations as if the gravel were a continuous substance.

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  • A "cubic equation" is one in which the highest power of the unknown is the cube (see Equation); similarly, a "cubic curve" has an equation containing no term of a power higher than the third, the powers of a compound term being added together.

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  • The theoretical assumptions of Newton and Euler (hypotheses magis mathematicae quam naturales) of a resistance varying as some simple power of the velocity, for instance, as the square or cube of the velocity (the quadratic or cubic law), lead to results of great analytical complexity, and are useful only for provisional extrapolation at high or low velocity, pending further experiment.

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  • It crystallizes in the cubic system, and well-developed crystals are of common occurrence; the usual form is the cube or the cubo-octahedron (fig.).

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  • The remedy is to spray with kerosene emulsion or whale-oil soap; or if on cucumbers or tomatoes, it is best to fumigate with hydrocyanic acid gas, using one ounce of potassium cyanide to each woo cubic ft.

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  • The divergent parabolas are of five species which respectively belong to and determine the five kinds of cubic curves; Newton gives (in two short paragraphs without any development) the remarkable theorem that the five divergent parabolas by their shadows generate and exhibit all the cubic curves.

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  • In 1875 the London Argand, giving a duty of 3.2 candles illuminating power per cubic foot of ordinary 16 candle gas, was looked upon as the most perfect burner of the day, and little hope was entertained that any burner capable of universal adoption would surpass it in its power of developing light from the combustion of coal gas; but the close of the century found the incandescent mantle and the atmospheric burner yielding six times the light that was given by the Argand for the consumption of an equal volume of gas, and to-day, by supplying gas at an increased pressure, a light of ten times the power may be obtained.

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  • The final book presents the solution of cubic and quartic equations.

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  • This is the case for all objects that involve the solution of a cubic or quartic polynomial.

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  • This occurs as cubic crystals of what is often referred to as Fool 's Gold.

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  • The smaller reverberant room has a volume of 112 cubic meters and the outer walls are 215mm Accrington brick.

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  • The second stage smoothes these oscillations by performing a least squares cubic spline fit to the data.

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  • The program uses a fast 2D cubic spline method to create data to give the appearance of a smoothed set of results.

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  • It can spot a fragment only a tenth of a cubic millimeter in size.

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  • Including manual indexing of a cubic cell, labeling HKLs and showing peak splitting when going from cubic to tetragonal cells.

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  • The cations are arranged into a face centered cubic structure with the anions occupying the tetrahedral sites.

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  • He also considered the equation associated with the problem of trisecting an angle, namely a cubic equation.

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  • There are no high active or medium active liquors in store and only 1.5 cubic meters of unconditioned intermediate level waste.

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  • Part of the appeal of cubic zirconia jewelry is its remarkable ability to look exactly like real diamond jewelry.

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  • Average range covered is about 250 to 350 cubic feet.

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  • For most individuals, the density of the foam should be at least 4 pounds, which means that a cubic foot (a 12 x 12 x 12 square) of foam will weigh four pounds.

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  • For example, paper recycling saves over three cubic yards of landfill space for every ton of paper made from recycled materials.

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  • Glaciers, which weigh approximately one ton per cubic meter, place pressure on the Earth's surface.

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  • Cape Wind, the nation's first approved offshore wind farm, estimates that its wind turbines will produce the equivalent of 570,000 tons of coal, or 113 million gallons of oil, or 10 billion cubic feet of natural gas.

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  • Cubic zirconias may not be allowed for your engagement ring, but for bridal jewelry it may just do the trick.

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  • In keeping with the geometric patterns and shapes, cubic or square shapes were used in shower curtains.

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  • Fill power is the number of cubic inches per single ounce of down.

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  • For instance, the highest and rarest quality of down has approximately 750 cubic inches per ounce.

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  • The average fill power is around 500 to 550 cubic inches per ounce.

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  • When you input these numbers into a mulch calculator, the numerical answer is the number of cubic feet of mulch you will need to cover the area at the depth indicated.

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  • The following online calculators make it simple to sit at the computer and get the number of cubic feet of mulch you need.

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  • This one not only gives you the number of cubic feet that you'll need, it also tells you how many bags of mulch to buy.

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  • You now have the number of cubic feet of mulch you need.

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  • Divide 40 by 12 = 3.3 cubic feet of mulch needed.

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  • That box contains approximately 2.5 cubic yards of mulch, or about equal to 6 cubic yards of traditional wood mulch.

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  • Pine needle mulch comes in round or square bales, sized from 3 to 6 cubic feet.

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  • Many necklaces are items of fine jewelry, using superior metals and precious stones or diamonds, and others utilize more affordable materials such as cubic zirconia.

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  • If you can't afford the pricier versions of the pink gemstones, there are many alternatives from cubic zirconia to less pricey topaz rings.

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  • Some styles include a choice of diamond or cubic zirconia.

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  • Tanzanite cubic zirconica has recently become available and can be found at a variety of gemstone suppliers.

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  • Gemstone stimulants such as cubic zirconia are a good alternative.

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  • Many of these are Chanel knockoffs, such as the star shaped earrings studded with cubic zirconia gems.

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  • Overstock Jeweler offers a variety of designer inspired jewelry items, including cubic zirconia pieces that have classy look like that of Chanel.

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  • Smaller families often use some of the spaces on the pendant for the mother's birthstone, for a pearl, diamond, or cubic zirconia.

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  • Rock crystal or even man made stones such as cubic zirconia make perfect alternatives.

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  • In some cases, they include pave cubic zirconias for a bit of extra life.

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  • It's a 38 centimeter chain with the typical Chanel logo at the end, studded in pave cubic zirconias.

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  • Show your love by giving that someone special a cubic zirconia journey circle pendant.

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  • There are even versions featuring cubic zirconia accents.

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  • Almost Diamonds.com has a variety of journey pendants accented with cubic zirconia.

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  • New Outlet.com has several journey pendants accented with cubic zirconia.

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  • Macy's has a wide selection of cubic zirconia jewelry.

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  • They feature pendants such as the CRISLU Cubic Zirconia Circle Pendant and the Sterling Silver Cubic Zirconia Pendant.

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  • Pearl and cubic zirconia sterling silver stud earrings can be the perfect complement to any outfit.

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  • A popular combination seen in stud earrings is pearls and cubic zirconia.

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  • Cubic zirconia adds all the sparkle of a diamond without the high price tag.

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  • They feature a 10 mm faux white pearl and three cubic zirconia accents set in rhodium plated sterling silver.

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  • Often sold out, the Black Tahitian Pearl and Cubic Zirconia Earrings are set in sterling silver and feature a faux black Tahitian pearl and accents of cubic zirconia.

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  • Kohl's has the Silvertone Simulated Pearl with Cubic Zirconia Stud Earrings.

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  • Each earring has a 12 mm faux white pearl surrounded by a wreath of cubic zirconias.

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  • Depending on what you plan to carry, you should look for a pack with a capacity ranging from 4000 to 5000 cubic inches.

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  • The LX - This camper measures 113" by 38" and has 26 cubic feet of storage space.

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  • Its storage space is reduced to 16 cubic feet.

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  • It holds up to 20 cubic feet of camping essentials and has an optional luggage rack.

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  • It provides six cubic feet of storage room.

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  • Sharp's mini has a half-pint of capacity, and the most recent variations of the new classic are only about fourteen cubic inches.

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  • Small and compact ovens typically can hold 0.5 to 0.8 cubic feet.

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  • Regular sized microwaves can hold 1.0 to 2.0 cubic feet of food.

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  • Larger models, including convection-oven microwave combinations, have a capacity of 2.2 cubic feet or greater.

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  • Sharp offers inexpensive and compact models that have a capacity of 0.8 cubic feet and wattage rating of 800, costing less than $100.

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  • Their higher end models include a capacity of 2.0 cubic feet and cost upwards of $800.

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  • Kenmore microwaves can hold 1.5 to 2.0 cubic feet and cost $200 to $800.

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  • The oven has a .7 cubic foot capacity and can accommodate up to six slices of bread.

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  • Upright freezers classified as small models typically range from just over one cubic foot to just over eight cubic feet.

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  • Sub-Zero BI-36R has a 23.3 cubic foot interior complete with glass shelves, door shelves and various components designed to keep your food organized and within reach.

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  • This stainless steel model has a 2.2 cubic foot interior and a sturdy 16-inch turntable to easily hold two-quart casserole dishes and large dinner plates.

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  • This 1.2 cubic foot oven also uses inverter technology and includes a handy cooking sensor.

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  • It has a 1.6 cubic foot interior as well as a 13.6 inch turntable and cooking sensor.

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  • The oven has a spacious 1.8 cubic foot interior, electronic touch keypad and a 14-inch turntable.

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  • This unit has 1800 watts of cooking power and a sizeable four-fifths of a cubic foot interior.

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  • It's one of the largest countertop models available, with a full 1.1 cubic foot interior.

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  • If you are looking for a traditionally beautiful ring, but cannot afford a diamond, consider a cubic zirconia engagement ring.

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  • In reality, however, cubic zirconia is a beautiful synthetic gemstone with many desirable properties suitable for the finest adornments, including high quality engagement rings.

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  • Cubic zirconia (often abbreviated CZ) is a lab-created crystalline cubic form of zirconium oxide stabilized with small quantities of other minerals, typically yttrium or calcium.

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  • While cubic zirconia can occur naturally, it is very rare because it requires temperatures in excess of 5,000 degrees Fahrenheit in order to form substantial crystals.

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  • Cubic zirconia is a popular synthetic diamond because if used properly, it cannot be distinguished from a real diamond by the naked eye.

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  • Thus, a cubic zirconia engagement ring is often mistaken for a true diamond.

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  • There are several ways to distinguish cubic zirconia from natural diamonds.

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  • Cubic zirconia also has different heat conductivity, and when measured, will have a red indicator instead of the green that diamonds produce.

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  • When shopping for a cubic zirconia engagement ring, be as discriminating as you would if shopping for the most flawless diamond on earth.

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  • Cubic zirconia is naturally less expensive than diamonds or other gemstones because of its massive abundance.

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  • Colored cubic zirconia stones are rarer in jewelry, however, and are subsequently more expensive.

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  • Many couples choose combination rings that use a natural gemstone for the center stone but the accent stones are cubic zirconia or other synthetic diamonds.

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  • Cubic zirconia stones are more brittle and softer than diamonds and should be stored individually to prevent scratches, nicks, or damage caused by rubbing against other jewelry.

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  • A beautiful and affordable gemstone, cubic zirconia is a splendid choice for an engagement ring.

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  • Because of the cost factor, many couples choose moissanite or cubic zirconia as more affordable gem options.

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  • Synthetic stones are common for necklaces, especially those that use multiple gems, and cubic zirconia is a frequent substitute, especially if the diamonds are accents to another stone or a larger design.

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  • Non-engagement rings are often made with high-quality synthetic stones such as moissanite or cubic zirconia without any negative connotations.

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  • For decades, cubic zirconia has endured a reputation as a low quality, low value imitation diamond, but Ziamond, a world leader in exquisitely pure cubic zirconia, is changing that misconception.

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  • As a company, Ziamond endorses the right of high quality cubic zirconia to be considered a gemstone rather than a diamond knock-off.

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  • Bare mountings to embrace the couple's chosen center stone, which may be a cubic zirconia or a natural diamond.

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  • With such a wide range of cubic zirconia rings available, every couple is sure to be able to find one that suits their personalities and symbolizes their commitment to one another.

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  • In addition to colorless cubic zirconia, Ziamond also reproduces artificial colored gems, including yellow diamonds, sapphires, rubies, and emeralds.

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  • Cubic zirconia is durable and virtually indistinguishable from diamond, but it is not indestructible.

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  • Cubic zirconia is so attractive and practical as an exquisite alternative to diamonds that even many celebrities opt for artificial pieces.

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  • In addition to celebrities sporting cubic zirconia pieces, the company also offer replicas of celebrity engagement rings for enthusiastic fans.

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  • Unlike imitation diamonds such as cubic zirconia or cleverly cut quartz, artificial diamonds are real diamonds, they just form through a more controlled, supervised process.

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  • Couples can help control the costs, however, by choosing gemstones instead of diamonds as accents, or opting for cubic zirconia or diamond chips as less expensive alternatives.

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  • Couples on a budget, however, can lower the cost of a micro pave style by opting for cubic zirconia or other artificial accents instead of real diamonds in the pave.

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  • Stephen Lux, President and CEO of Gemesis, a company that produces quality, lab-created diamonds explains, "Diamond-like materials such as cubic zirconium, moissanite and diamond-coated materials are not diamond.

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  • If you are looking for something a little different from your engagement ring, but without breaking the bank, why not consider a sterling silver cubic zirconia engagement ring.

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  • The combination of cubic zirconia (CZ) and silver can make an interesting option for an engagement ring and can be found in exciting and unusual designs as well as being low cost.

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  • Cubic zirconia is a manmade stone and popular diamond alternative.

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  • Cubic zirconia has many of the features of a natural diamond, including sparkle and clarity, but without the cost.

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  • Some people would even say that a good quality cubic zirconia has more fire and sparkle than a low grade diamond that may be cloudy and dull.

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  • Sterling silver is less costly than gold or platinum therefore a cubic zirconia set in silver can be very competitively priced.

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  • People may therefore worry about wearing these rings every day and seek a low cost alternative, perhaps made from silver and cubic zirconia, for every day wear and save their special engagement ring for occasional wear.

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  • A good alternative is to buy a high fashion engagement ring created from silver and cubic zirconia knowing that the ring can be changed frequently without breaking the bank.

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  • Buying a cubic zirconia ring is a great way to bring some bling to your engagement ring.

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  • While your local jewelry store probably only has diamonds and occasionally other gemstones up for grabs when it comes to wedding jewelry, cubic zirconia wedding bands are easy enough to find online.

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  • Almost Diamonds has an amazing selection of cubic zirconia wedding rings as well as wedding sets.

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  • You can keep the cubic zirconia ring put aside until you go somewhere that makes you uneasy about wearing the real thing.

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  • For example, if you're going on vacation, lock your "real" engagement ring away for safekeeping and wear the less expensive cubic zirconia engagement ring.

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  • Overstock Jeweler has a wide variety of cubic zirconia band styles to choose from.

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  • This exquisite cubic zirconia piece will look stunning next to an engagement ring or alone.

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  • It seems to swirl upward on the finger a bit, with cubic zirconias that graduate in size along a sterling silver band.

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  • Inspired by Tiffany 14K Gold Vermeil Channel Set Diamond CZ Bridal Wedding Band Ring-Most cubic zirconia wedding pieces feature a white metal, such as silver.

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  • There's no reason to shy away from cubic zirconia wedding jewelry anymore.

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  • While cubic zirconia is an option for those who still want the look of a diamond without paying the high prices, some would prefer to forego the diamond look altogether if they aren't actually purchasing a genuine diamond.

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  • Earrings set in sterling silver are also less expensive, or the couple could substitute cubic zirconia or treated diamonds instead of natural diamonds.

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  • Consider choosing a cubic zirconia ring instead of a diamond, particularly if the design is a semi mount engagement ring that is lacking the center stone.

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  • Similarly, diamond chips are more affordable than full stones, or the ring could use cubic zirconia rather than diamonds.

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  • Often made with cubic zirconia and inexpensive metals, these fashionable pieces of jewelry are outstanding promise rings that offer Hollywood bling at a price anyone can afford.

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  • For couples who are watching their budget, Diamonique engagement rings are a great option and an interesting alternative to cubic zirconia engagement rings.

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  • Some stones such as cubic zirconia, quartz, and moissanite can be faceted into lovely jewels, but they are not diamonds.

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  • Plain metal rings are available without diamond accents, or couples could opt for more elaborate designs that use cubic zirconia instead of real diamonds.

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  • Many high-end cubic zirconias are hard to distinguish from a real diamond to an untrained eye.

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  • They do not last as long as cubic zirconia or simulated diamonds.

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  • Women's rings with center stones come with cubic zirconia but customers can arrange to replace the cubic zirconia with a diamond.

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  • For example, if the jeweler tells you an estate ring is a diamond set in gold but it looks like a cubic zirconia set in plated metal, don't purchase it.

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  • An emerald or a ruby ring, for example, is by far preferable to buying a cubic zirconia ring simply because it looks like a diamond.

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  • However, inexpensive cubic zirconia versions are ideal for stacking.

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  • Bella's Twilight engagement ring made from cubic zirconia, sterling silver and marcasite is a popular item for engagement and promise rings among Twilight fans.

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  • The cubic zirconia, sterling silver and marcasite version of Bella's engagement ring is a beautiful but affordable reproduction of the Twilight engagement ring.

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