cubic

xy 2 -4z 3 +g2x 2 y+g3x 3, and also the special form axz 2 -4by 3 of the cuspidal cubic. An investigation, by non-symbolic methods, is due to F.

2417Now geometry deals with points, lines, planes and cubic contents.

1772 - 9 m 2 (1 3 m 2)) 2 we have a cubic equation for determining m 2 as a function of the absolute invariant.

1513Its weight varies from 48 to about 55lb the cubic foot, but in very hard slowly-grown trunks sometimes approaches 60 lb.

1310In many experiments, however, different inductions and frequencies are employed, and the hysteresis-loss is often expressed as ergs per cubic centimetre per cycle and sometimes as horse-power per ton.

1110The unit to which they are ordinarily referred is I electrostatic unit of electricity per cubic metre of air.

1010For Tartaglia's discovery of the solution of cubic equations, and his contests with Antonio Marie Floridas, see Algebra (History).

1012We will write the cubic covariant (f, i) 2 =j, and then remark that the result, (f,j) 3 = o, can be readily established.

97A 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.

76The ternary cubic has been investigated by Cayley, Aronhold, Hermite, Brioschi and Gordan.

77Thar equal to 148930 foot pounds 4 2.37 cubic feet.

64Problems in artillery occupy two out of nine books; the sixth treats of fortification; the ninth gives several examples of the solution of cubic equations.

64For the quadratic it is the discriminant (ab) 2 and for ax2 the cubic the quadratic covariant (ab) 2 axbx.

65There are four invariants (i, i')2; (13, H)6; (f2, 151c.; (f t, 17)14 four linear forms (f, i 2) 4; (f, i 3) 5; (i 4, T) 8; (2 5, T)9 three quadratic forms i; (H, i 2)4; (H, 23)5 three cubic forms (f, i)2; (f, i 2) 3; (13, T)6 two quartic forms (H, i) 2; (H, 12)3.

54Working 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.

42In 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.

42For 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.

43Owing to these natural "locks," the Senegal never discharges less than 1700 or 1800 cubic ft.

31When 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.

31The 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.

32telluric acid forms cubic and monoclinic crystals from a hot nitric acid solution, and ammonium fluosilicate gives cubic and hexagonal forms from aqueous solutions between 6° and 13°.

32We 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.

32Hence, solving the cubic, R 2 j = (S -m i a) (S - m 2 a) (S - m3a) wherein m 1 m2, m 3 are invariants.

32The complete covariant and contravariant system includes no fewer than 34 forms; from its complexity it is desirable to consider the cubic in a simple canonical form; that chosen by Cayley was ax 3 +by 3 + cz 3 + 6dxyz (Amer.

32The discriminant, whose vanishing is the condition that f may possess two equal roots, has the expression j 2 - 6 i 3; it is nine times the discriminant of the cubic resolvent k 3 - 2 ik- 3j, and has also the expression 4(1, t') 6 .

312Again, for the cubic, we can find A3(z) - -a6z6 1 -az 3.1 -a 2 z 2.1 -a 3 z 3.1 -a4 where the ground forms are indicated by the denominator factors, viz.: these are the cubic itself of degree order I, 3; the Hessian of degree order 2, 2; the cubi-covariant G of degree order 3, 3, and the quartic invariant of degree order 4, o.

20The 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.

20Fleming, 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.

20Denoting by W the work in ergs done upon a cubic centimetre of the metal (=_fHdB or f HdI), he finds W =nips approximately, where n 47r is a number, called the hysteretic constant, depending upon the metal, and B is the maximum induction.

20But some phenomena are difficult to reconcile with pressed into less than one five-hundredth of a cubic foot, or, if allowed to expand, the air originally occupying the cubic foot can be made to fill, apparently uniformly, a space of a million cubic feet or more.

21West Virginia, estimates that in fairly good producing sand a cubic foot of rock contains from 6 to 12 pints of oil.

21The following are the " lowest level " discharges of the principal affluents of the Brahmaputra in Upper Assam, estimated in cubic feet per second: Lohit river, 9 m.

21d x the first evectant; and thence 4cxdi the second evectant; in fact the two evectants are to numerical factors pres, the cubic covariant Q, and the square of the original cubic.

21The transformation to the normal form, by the solution of a cubic and a quadratic, therefore, supplies a solution of the quartic. If (Xï¿½) is the modulus of the transformation by which a2 is reduced to 3 the normal form, i becomes (X /2) 4 i, and j, (Ap) 3 j; hence?

21Now, 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.

21from the invariant a2 -2a 1 a 3 -2aoa4 of the quartic the diminishing process yields ai-2a 0 a 21 the leading coefficient of the Hessian of the cubic, and the increasing process leads to a3 -2a 2 a 4 +2a i a 5 which only requires the additional term-2aoa 6 to become a seminvariant of the sextic. A more important advantage, springing from the new form of S2, arises from the fact that if x"-aix n- +a2x n-2.

21This method of solution fails when the discriminant R vanishes, for then the Hessian has equal roots, as also the cubic f.

23we find that Di must be equal to p x g x for then t x (p x) 3 +, u (g x) 3, Hence, if px, qx be the linear factors of the Hessian 64, the cubic can be put into the form A(p x) 3 +ï¿½(g x) 3 and immediately solved.

27For, since -2t 2 =0 3 -21f 2, 6,-3j(-f) 3, he compares the right-hand side with cubic resolvent k 3 -21X 2 k - j 2.

214Hexachlorethane is trimorphous, forming rhombic, triclinic and cubic crystals; the successive changes occur at about 44° and 71°, and are attended by a decrease in density.

10Ammonium 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.

10Hesse 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.

10By the x process of Aronhold we can form the invariant S for the cubic ay+XH:, and then the coefficient of X is the second invariant T.

10Classification of Cubic Curves.

10For more details about cubic zirconia and this leading company for cz jewelry, visit the official website www.ziamond.com or call 1-866-942-6663.

10The wood is variable in quality and, though hard in texture, is less durable than the best oak of British growth; the heart-wood is of a light reddish brown varying to an olive tint; a Canadian specimen weighs 524 lb the cubic foot.

11He assumes that in what is considered a good producing district the amount of petroleum which can be obtained from a cubic foot of rock would not be more than a gallon, and that the average thickness of the oil-bearing rock would not exceed 5 ft.

11The mere retention of the same crystal form by homologous substances is not a sufficient reason for denying a morphotropic effect to the substituent group; for, in the case of certain substances crystallizing in the cubic system, although the crystal form remains unaltered, yet the structures vary.

11Of these all except points are quantities: lines involve lengths, planes involve areas, and cubic contents involve volumes.

11The Flos of Leonardo turns on the second question set by John of Palermo, which required the solution of the cubic equation x 3 -{-2x'-}-lox = 20.

11It became clear that only very rough estimates of the numbers of planktonic organisms in a volume of sea-water as large as (say) 10 cubic metres could be made, but that these estimates could nevertheless be trusted to show very marked regional and seasonal differences.

11Let x be the number of molecules which dissociate per second when the number of undissociated molecules in unit volume is unity, then in a dilute solution where the molecules do not interfere with each other, xp is the number when the concentration is p. Recombination can only occur when two ions meet, and since the frequency with which this will happen is, in dilute solution, proportional to the square of the ionic concentration, we shall get for the number of molecules re-formed in one second ye where q is the number of dissociated molecules in one cubic centimetre.

11Many celebrity rings are available as inexpensive replicas, using cubic zirconia or other imitation stones set in cheaper metals.

11Choosing synthetic diamonds such as cubic zirconia or crystal, particularly for accent stones or smaller gems.

11Semi-precious gemstones with bright yellow colors include yellow sapphires, citrine, tourmaline, topaz, and cubic zirconia.

11Cubic zirconia rings for a more affordable alternative to authentic diamonds.

11All these are strikingly alike in appearance and general characters, differing essentially only in chemical composition, and it would seem better to reserve the name cerargyrite for the whole group, using the names chlorargyrite (AgC1), embolite (Ag(Cl, Bl)), bromargyrite (AgBr) and iodembolite (Ag(C1, Br, I)) for the different isomorphous members of the group. They are cubic in crystallization, with the cube and the octahedron as prominent forms, but crystals are small and usually indistinct; there is no cleavage.

00(a) What would be the dimensions of a cubical vessel which would exactly hold 125 litres; a litre being a cubic decimetre ?

00Cubic equations were solved geometrically by determining the intersections of conic sections.

00Archimedes' 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.

00Although 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.

00This contest over, Tartalea redoubled his attempts to generalize his methods, and by 1541 he possessed the means for solving any form of cubic equation.

00Cardan 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.

00Cubic equations having been solved, biquadratics soon followed suit.

00The 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%).

00or more per annum), the volume of water entering Albert Nyanza by the Semliki when in flood being not less than 700 cubic metres per second.

00Of 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.

00diameter, discharging hundreds of thousands of cubic feet of air per minute.

00Then 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).

00sal, salt, petra, a rock), the commercial name given to three naturally occurring nitrates, distinguished as (1) ordinary saltpetre, nitre, or potassium nitrate, (2) Chile saltpetre, cubic nitre, or sodium nitrate, (3) wall-saltpetre or calcium nitrate.

00Chile 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.

00It forms colourless, transparent rhombohedra, like those of Iceland spar; the angles are nearly equal to right angles, being 73° 30', so that the crystals look like cubes: hence the name of "cubic saltpetre."

00An irrigation canal, deriving water from the Sega, furnishes 112 cubic metres per second to the fields of the upper Veronese district.

00Massimo to the suburb of Tombetta, furnishes 26 cubic metres of water per second, and generates 4000 horse-power.

00The native metal crystallizes in the cubic system, the octahedron being the commonest form, but other and complex combinations have been observed.

00as grammes per cubic centimetre.

00In commerce, however, other expressions are met with, as, for example, "pounds per cubic foot" (used for woods, metals, &c.), "pounds per gallon," &c. The standard substances employed to determine relative densities are: water for liquids and solids, and hydrogen or atmospheric air for gases; oxygen (as 16) is sometimes used in this last case.

00system is the weight of a cubic centimetre of water at this temperature.

00The formulae show the number of cubic centimetres of gas absorbed by i litre of sea-water; t indicates the temperature in degrees centigrade and CI the salinity as shown by the amount of chlorine per mille: 02 = 10.291 - 0 .

00Seven-tenths of a cubic metre of animal bones were found: deer, bear, wolf, raccoon, opossum, beaver, buffalo, elk, turkey, woodchuck, tortoise and hog; all contemporary with man's occupancy.

00Pure 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.

00When 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.

00He also showed that the roots of a cubic equation can be derived by means of the infinitesimal calculus.

00MARCASITE, a mineral with the same chemical composition as pyrites, being iron disulphide FeS2, but crystallizing in the orthorhombic instead of in the cubic system.

00The orthorhombic form of the crystals, as distinct from the cubic form of pyrites, was recognized by Rome de 1'Isle in 1772, though later R.

00Hairy considered the crystals to be only distorted cubic forms.

00Calculations 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.

00For 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.

00The same formula will also hold (§ 52) for any cubic trapezette through the points.

00long in its course to the south-east coast, discharges a volume of water estimated at nearly i,ioo,000 cubic ft.

00Although 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.

00U cubic centimetres move in per second at B, and if the density is po the mass moving in through a square centimetre is po U.

00The 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.

00Hence the work done on the air is (P-+zw)v, and the work done per cubic centimetre is (P+Zw)v/V.

002 The energy in sunlight per cubic cm.

00Hydrated 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.

00Sodium combines directly with the halogens to form salts which are soluble in water and crystallize in the cubic system.

00Iooi), who obtained cubic crystals from a supersaturated solution of sodium and aluminium sulphates below 20°, higher temperatures giving monoclinic crystals.

00These values of p refer to a standard density of the air, of 534.22 grains per cubic foot, which is the density of dry air at sea-level in the latitude of Greenwich, at a temperature of 62° F.

00Now 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.

003 by the height AH, such that the rectangle Ahkb is equal to the area Apdb; and the M.E.P. multiplied by 41rd 2, the cross-section of the bore in square inches, gives in tons the mean effective thrust of the powder on the base of the shot; and multiplied again by 1, the length in inches of the travel AB of the shot up the bore, gives the work realized in inch-tons; which work is thus equal to the M.E.P. multiplied by 41+-d 2 l = B -C, the volume in cubic inches of the rifled part AB of the bore, the difference between B the total volume of the bore and C the volume of the powder-chamber.

00=0.504, the upper figure 55.01 denoting the specific volume of the charge measured in cubic inches per lb, filling the chamber in a state of gas, the product of the two numbers 55.01 and 0.504 being 2 7.73; and the chamber capacity C =1 3' 2 5 X 55.01 =730 cub.

00Chemically, it is thus indentical with the cubic mineral diamond, but between the two there are very wide differences in physical characters.

00The Habra barrage holds 38,000,000 cubic metres; that on the Sig 18,000,000.

00(b) In determinations of volume which do not admit of a high degree of accuracy the cubic decimetre can be taken as equivalent to the litre; and in these determinations expressions of volumes based on the cube of the unit of linear measure can be substituted for expressions based on the litre as defined above.

00In 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.

00In the measurement of the cubic inch it has been found that 2 the specific mass of the cubic inch of distilled water freed from air, and weighed in air against brass weights (= 8.13), at the temperature of 62° F., and under an atmospheric pressure equal to 30 in.

00Hence a cubic foot of water would weigh 62.281 lb avoir., and not 62.321 lb as at present legally taken.

00For the specific mass of the cubic decimetre of water at 4° C., under an atmospheric pressure equal to 760 mm., Guillaume and Chappuis of the Comite International des Poids et Mesures at Paris (C.I.P.M.) have obtained 0.9999707 kg., which has been accepted by the committee.

00The 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.

00For the weight of the cubic decimetre of water, as deduced from the experiments made in London in 1896 as to the weight of the cubic inch of water, D.

00The 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.

00To 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.

00of water; also the cubic inch is very nearly 250 grains, while the gallon has actually been fixed at 10 lb of water; the first two are certainly mere coincidences, as may very probably be the last also, and yet they offer quite as tempting a base for theorizing as any connexions in ancient metrology.

00Again, 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.

00The 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.

00He 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.

00It 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.

00All quantities stated in this article without distinguishing names are in British units of inch, cubic inch or grain.

00in., this would show a cubic of 25 in.

00Beside 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.

00in.; their log-measure, holding six hen's eggs, shows it to be over rather than under this amount; but their reckoning of bath = a half cubit cubed is but approximate; by 21.5 it is 1240, by 25.1 it is 1990 cubic in.

00The Roman theory of the amphora being the cubic foot makes it 1569 cub.

00(This result is from a larger number than other students have used, and study by diagrams.) The theory (3) of the derivation of the uten from 1/1500 cubic cubit of water would fix it at 1472, which is accordant; but there seems no authority either in volumes or weights for taking 1500 utens.

00Another 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.

00Though 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.

00Cubic Measures.

00-- 1000 (litre), 500, 200, 100, 50, 20, 10, 5, 2 cubic centimetres, 1 c.c. or 1000 cubic millimetres.

00The galena group includes several other cubic minerals, such as argentite (q.v.).

00Mention 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.

00of water per second, or 785,190,000,000 cubic yds.

00the number of oxygen molecules per cubic centimetre determines the width of the oxygen lines, though nitrogen molecules may be mixed with them without materially affecting the appearance.

00in diameter, found that the current given by it could only electrolyse acidulated water in 40 hours sufficient to liberate one cubic centimetre of mixed gases.

00PYRITES, a term applied to iron disulphide when crystallized in the cubic system, but used also in a general sense to designate a group of metallic sulphides of which this mineral is the most characteristic example.

00The compound FeS 2 is dimorphous, and the modern practice is to distinguish the cubic forms as pyrites and the orthorhombic as marcasite (q.v.).

00Sometimes, 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.

00Iron pyrites, or pyrite, belongs crystallographically to the parallelfaced hemihedral class of the cubic system.

00Pyrites presents a conchoidal fracture, and a very indistinct cubic cleavage.

00It crystallizes in the cubic system, usually in cubes, pentagonal dodecahedra or octahedra, often of great beauty and perfection.

00Now taking the isomers H 3 C CC1 3 (M„ = 108) and C1H 2 C CHC1 2 (M„ = we see the negative chlorine atoms heaped up in the left hand formula, but distributed in the second; the former therefore may be presumed to occupy a larger space, the molecular volume, that is, the volume in cubic centimetres occupied by the molecular weight in grams, actually being 108 in the former, and 103 in the latter case (compare Chemistry: Physical).

00Unlike other cubic crystals, diamond experiences a diminution of refractive index with increase of temperature.

00Crystals 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.

00Carbonado 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.

00The ground is transferred in trucks to the shaft where it is automatically tipped into skips holding 96 cubic ft.

00Graphitic 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.

00Crystals 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.

00It 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.

00This would increase the storage capacity 22 times, or to about 9,375,000 millions of cubic feet.

00The method of estimating the area of irregular fields and the cubic contents of granaries, &c., is very faulty.

00In most cases several ingredients are prescribed together: when the amounts are indicated it is by measure not by weight, and evidently no very potent drugs were employed, for the smallest measure specified is equal to about half of a cubic inch.

00- Assuming that each gallon of sea water contains 0.2547 lb of salt, and allowing an average density 2.24 for rocksalt, it has been computed that the entire ocean if dried up would yield no less than four and a half million cubic miles of rock-salt, or about fourteen and a half times the bulk of the entire continent of Europe above high-water mark.

00Halite 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.

00The mineral has perfect cubic cleavage.

00Cubic pseudomorphs representing rock-salt are sometimes seen in strata which have been deposited in shallow water, especially on the margin of a salt-lake.

00The 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.

00In 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.

00The cartesian parabola is a cubic curve which is also known as the trident of Newton on account of its three-pronged form.

004) is a cubic curve having the equation y= 3 +- 2 -+cx-+d.

00John 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.

00Diverging parabolas are cubic curves given by the equation y 2 = 3 -f-bx 2 -cx+d.

00Newton discussed the five forms which arise from the relations of the roots of the cubic equation.

00The standard of measurement most in use is the St Petersburg standard, which contains 165 cubic ft.

00ft., and a load of unhewn timber 40 cubic ft.

00Its weight per cubic foot averages about 33 lb.

00It weighs about 36 lb to the cubic foot.

00A cubic foot weighs about 35 to 40 lb.

00A cubic foot weighs about 45 lb.

00Spanish mahogany weighs about 56 lb to the cubic ft., and the Honduras variety about 36 lb.

00The average weight of a cubic foot is about 61 lb.

00per cubic foot, and dry S7 lb 3 oz.

00The annual timber yield of the Indian forests is about fifty millions of cubic feet, excluding what is used for local purposes.

00S = 0.9944 00O 04T 0.000,0009 T 2 (Regnault Above 60° To 200° Corrd.) S =1.000 0.000,22 (T 60), (Bosscha Corrd.) The Addition Of The Cubic Term Below 20° Is Intended To Represent The Somewhat More Rapid Change Near The Freezing Point.

00This 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.

00Even 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.

00Chalcopyrite 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.

00Then the variation of the cubic contents of the vessel in a unit of time by reason of the motion of one piston is Va.

00It 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.

00It crystallizes in the cubic system, but the crystals are often flattened, elongated, rounded or otherwise distorted.

00lightness and elasticity it is well adapted for the construction of yachts and other small fast-sailing craft, and is said to be the best of all wood for masts and large spars; its weight varies from 30 to 40 lb the cubic foot.

00Immense 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.

00More 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.

00In the case of diphtheria the antitoxic power of the serum may reach Boo units per cubic centimetre, or even more.

00name Flussspat or Fluss.) Fluor-spar crystallizes in the cubic system, commonly in cubes, either alone or combined with the octahedron, rhombic dodecahedron, four-faced cube, &c. The four-faced cube has been called the fluoroid.

00Fluor-spar, though cubic, sometimes exhibits weak double refraction, probably due to internal tension.

00A cubic inch of water weighs 252.458 grains.

00The 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).

00It crystallizes in the cubic system, but the crystals are usually distorted and indistinctly developed: twisted wire-like forms are much more common.

00Silver 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.

00Other pairs of isomorphous argentiferous minerals are: the cubic polybasite, 9Ag2S Sb2S3, and pearceite, 9Ag2S As2S3; and the germanium minerals argyrodite, 4Ag 2 S GeS2, and canfieldite, 4Ag 2 S (Sn, Ge) S2.

00Silver iodide is dimorphous; at ordinary temperatures the stable form is hexagonal; on heating to about 138° the colour changes from deep yellow to yellowish-white with the formation of cubic crystals.

00Among 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.

00This 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.

00He was professor of mathematics in the university of Deseret and wrote several books on this subject, these including Cubic and Biquadratic Equations (1866).

00It has been calculated that the average daily discharge of the Muir in summer is 30,000,000 cubic ft.

00Ladoga 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.

00In 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.

00The 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.

00Some 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.

00The discharge of the lake is computed to be 75,200 cubic ft.

00The 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.

00Although, 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.

00Mountain 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.

00Thus, 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.

00The 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.

00We 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.

00In 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.

00The 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.

00The 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."

00thick of a monolithic dam, subject to the pressure of water against its vertical side to the full depth ab= d in feet, the horizontal _ eL 2 pressure of water against the section of the dam, inI creasing uniformly with the depth, is properly represented by the isosceles right-angled triangle abe, in which be is the maximum water-pressure due to the Cent full depth d, while the area 2 abe = d is t h e total hor12 d3 6 If x be the width of the base, and p the density of the masonry, the weight of the masonry in terms of a cubic foot of water will be acting at its centre of gravity g, situated at 3x from the outer toe, and the moment of resistance to overturning on the outer toe, p x 2 d (2) In countries where good clay or retentive earth cannot be obtained, numerous alternative expedients have been adopted with more or less success.

00- Diagram of Right-Angled cubic feet of water, acting g at one-third its depth above Triangle Dam.

00per second per woo acres, or 1500 times the minimum dry weather flow, taken as one-fifth of a cubic foot; and if we provide against such an occasional discharge, with a possible maximum of 400 cub.

00In 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.

00Murray 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.

00WITCH OF AGNESI, in geometry, a cubic curve invented by Maria Gaetana Agnesi.

00The litre is equal to a cubic decimetre.

00The 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.

00as far as the Pilcopata river, where under:the name of Madre de Dios it continues with a flow of 22,000 cubic metres per minute.

00Below the mouth of the Tambopata, the flow is estimated at 191,250 cubic metres per minute.

00a curve is of the first order, second order, third order, &c., according as it is represented by an equation of the first order, ax+by+c = o, or say (1 x, y, 1) = o; or by an equation of the second order, ax 2 +2hxy+by e +2fy+2gx+c=o, say (*I x, y, 1) 2 =o; or by an equation of the third order, &c.; or what is the same thing, according as the equation is linear, quadric, cubic, &c.

00A curve of the third order is called a cubic; one of the fourth order a quartic; and so on.

001774) and Gabriel Cramer; the work also contains the remarkable theorem (to be again referred to), that there are five kinds of cubic curves giving by their projections every cubic curve whatever.

00Various 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).

00We have in it a particular kind of correspondence of two points on a cubic curve, viz.

00two points correspond to each other when the tangents at the two points again meet the cubic in the same point.

00By 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.

00We may further consider the inflections and double tangents, as well in general as in regard to cubic and quartic curves.

00The 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.

00It 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.

00For an acnodal cubic the six imaginery inflections disappear, and there remain three real inflections lying in a line.

00For 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.

00For a cuspidal cubic the six imaginary inflections and two of the real inflections disappear, and there remains one real inflection.

00The 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.

00Again, 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.

00- We may now consider the various forms of cubic curves as appearing by Newton's Enumeratio, and by the figures belonging thereto.

00The genera may be arranged as follows: 1,2,3,4 redundant hyperbolas 5,6 defective hyperbolas 7,8 parabolic hyperbolas 9 hyperbolisms of hyperbola To „ II „ „ parabola 12 trident curve 13 divergent parabolas 14 cubic parabola; and thus arranged they correspond to the different relations of the line infinity to the curve.

00We have herein a better principle of classification; considering cubic curves, in the first instance, according to singularities, the curves are non-singular, nodal (viz.

00And 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.

00And 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.

00We may now state in a more convenient form the fundamental distinction of the kinds of cubic curve.

00A non-singular cubic is simplex, consisting of one odd circuit, or it is complex, consisting of one odd circuit and one even circuit.

00It at once appears from inspection of the figure of a non-singular cubic curve, which is the odd and which the even circuit.

00Similarly a cubic through the two circular points is termed a circular cubic; a quartic through the two points is termed a circular quartic, and if it passes twice through each of them, that is, has each of them for a node, it is termed a bicircular quartic. Such a quartic is of course binodal (m = 4, 6= 2, K = o); it has not in general, but it may have, a third node or a cusp. Or again, we may have a quartic curve having a cusp at each of the circular points: such a curve is a " Cartesian," it being a complete definition of the Cartesian to say that it is a bicuspidal quartic curve (m= 4, 6 = o, K= 2), having a cusp at each of the circular points.

00The 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.

00There will be from each circular point X tangents (X, a number depending on the class of the curve and its relation to the line infinity and the circular points, 2 for the general conic, 1 for the parabola, 2 for a circular cubic, or bicircular quartic, &c.); the X tangents from the one circular point and those from the other circular point intersect in X real foci (viz.

00There 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.

00If D =t, then the transformed curve is a cubic; it can be shown that in a cubic, the axes of co-ordinates being properly chosen, 4) can be expressed as the square root of a quartic function of 0; and the theorem is that the co-ordinates x, y, z of a point of the bicursal curve can be expressed as proportional to rational and integral functions of 0, and of the square root of a quartic function of 0.

00It 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.

00Similarly as regards cubics, or curves of any other order: a cubic depends on 9 constants, and the elementary problems are to find the number of the cubics (9 p), (8p, 1l), &c., which pass through 9 points, pass through 8 points and touch 1 line, &c.; but it is in the investigation convenient to seek for the characteristics of the systems of cubics (8p), &c., which satisfy 8 instead of 9 conditions.

00Thus, considering the several cases of a cubic 1.

00(1873), considers the problem in reference to curves of any order, and applies his results to cubic and quartic curves.

00It 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.

00The latter has an average calorific power of 1732 calories per cubic metre, or 161 B.T.U.

00p°r cubic foot, at o° and 760 mm.

00by the action of the aluminium-mercury couple and water), but better, according to C. Goldschmidt (Ber., 1896, 29, p. 2307) by dissolving nitrobenzene in ten times its weight of ether containing a few cubic centimetres of water, and heating with excess of zinc dust and anhydrous calcium chloride for three hours on a water bath.

00The cistern of Arcadius, to the rear of the mosque of Sultan Selim (having, it has been estimated, a capacity of 6,571,720 cubic ft.

00This concept is extended to algebra: since a line, surface and solid are represented by linear, quadratic and cubic equations, and are of one, two and three dimensions; a biquadratic equation has its highest terms of four dimensions, and, in general, an equation in any number of variables which has the greatest sum of the indices of any term equal to n is said to have n dimensions.

00Further, 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.

00allotropic change to gamma iron which has a face-centred cubic lattice and is non-magnetic.

00The polarizability in cubic angstroms of a molecule in any particular orientation can then easily be calculated.

00About 60 million cubic meters of dome and crater wall traveled to the south as a debris avalanche and pyroclastic density currents.

00barium titanate has a cubic structure.

00It is extremely lightweight but is the third hardest material known to science, next to diamond and cubic boron nitride.

00One pound of liquid butane produces 6.4 cubic feet of gas.

00caesiumntrast with cesium chloride, sodium chloride forms a simple cubic structure.

00huge calderas erupted thousands of cubic miles of ash.

00capabilityre miniature computing devices the size of a few cubic millimeters and have sensing, processing and wireless networking capabilities.

00The density, about 0.2 grams per cubic centimeter, means it is a gas giant like Jupiter.

00portable compactor / Compaction Unit / Container 26.8 cubic meter compaction container.

00There are three common methods for resampling: nearest neighbor, bilinear interpolation, and cubic convolution.

00cubic meters of concrete waste will result by March 2006.

00cubic centimeters of water.

00cubic spline, yet, for a really smoothed out shape, this is the only way to go.

00cubic meters of illegal wood were seized.

00cubic zirconia, framing the pink stones.

00cubic centimeter would be nice.

00A very interesting example is Fe in the face centered cubic (fcc) phase.

00The program should return the type of local structure (face centered cubic, etc.) for each atom of the system.

00Which saw cubic rising he adds big safe cars which was a. Buy it the dollar you mail.

00cubic zirconia set at either end of the ' coil ' .

00The measuring volume of the F25 is one cubic decimeter; measuring uncertainty 250 nm at a scale resolution of 7.5 nm.

00A mini excavator working in the jacking shield, just ahead of the first pipe, removed 290 cubic meters of spoil.

00foote fields are estimated to contain recoverable reserves of 350 to 400 billion cubic feet.

00One gallon of aviation gasoline that has completely evaporated will form about 30 cubic feet of vapor at sea level.

00The town is supplied with gas by the local gasworks, at 4/7 per 1,000 cubic feet.

00grams per cubic centimeter (gm/cc ), so a cubic meter would weigh 19.2 tons.

00A cubic fourfold is called special if it contains a surface which is not homologous to a multiple of a plane section.

00Less radical plans turned out to be an increase in capacity to 74 cubic inches in the IoE form of the Js.

00The cylinders on the back are charged with 10 cubic feet of oxygen at a pressure of 18.000 lbs per square inch.

00In a formal garden you can also grow ivy into a cubic shape.

00To produce 1 kilogram of cereals takes from 0.4 to 3 cubic meters of water.

00In the 1939 eruption, lava of about 0.1 cubic kilometer flowed out.

00For the simple cubic lattice, all values of n will give Bragg peaks.

00There are several varieties in which the cubic non linearity is common to each.

00Samphire Hoe is a new piece of England created from 4.9 million cubic meters of chalk marl dug to create the Channel Tunnel.

00Cubic Transportation Systems, with WMATA, designed the two-year-old SmarTrip system, the nation's first mass transit Smart Card fare collection program.

00Millions of cubic meters of illegal wood were seized.

00metreowerful internal fan uses just 29 watts of power to circulate 460 cubic meters of air per hour.

00If ozone concentrations exceed 180 micrograms per cubic meter, they must inform the public and provide health advice.

00micrograms per cubic meter on average in smoking areas.

00After all, even a cubic micron of water contains about thirty billion molecules.

00Normal CD4 counts in adults range from around 500 to 1,500 cells per cubic millimeter of blood.

00Note: read mol dm -3 s -1 as " moles per cubic decimetre (or liter) per second " .

00The structure is a cubic close packing of equal spheres.

00In the dense center of the cluster, the star density can increase from 100 to 1000 per cubic parsec.

00PM10 50 micrograms per cubic meter or less, when expressed as the 99th percentile of daily maximum running 24 hour means.

00This occurs as cubic crystals of what is often referred to as Fool's Gold.

00Finite generalized tetrahedron groups with a cubic relator 2003/21 Vincent Schmitt.

00The fields are estimated to contain recoverable reserves of 350 to 400 billion cubic feet.

00reverberant room has a volume of 112 cubic meters and the outer walls are 215mm Accrington brick.

00The Cubic smooth option fits a smooth cubic spline to the data.

00Still longer needs the cubic spline, yet, for a really smoothed out shape, this is the only way to go.

00tenth of a cubic millimeter in size.

00tetrahedron groups with a cubic relator 2003/21 Vincent Schmitt.

00Above 120°C, barium titanate has a cubic structure.

00The latest operation brings the total of oil removed from the wreck to over 670 cubic meters.

00trisecting an angle, namely a cubic equation.

00The primary structure is a glulam frame consisting of over 1,000 cubic meters of renewable European whitewood formed into paired columns and beams.

00Ironically, the Kenyon Cutting, east of the Newton Viaduct, yielded 750,000 cubic yards of material.

00Two solid looking silver vertical bridges rise on either side of the cubic zirconia, framing the pink stones.

00Victoria came on the phone and said they wanted cubic zirconium on the detailing, and a large Union Jack somewhere too.

00this view; for example, a cubic foot of air can be corn 0 hydrogen.

00The later expedition of the " Pola " discovered the " Rhodes Deep " (36Ã‚° 5' N., 28Ã‚° 36' E.), with a maximum depth of 2110 fathoms: this deep is closed to the south-east by a ridge running south-east, over which the depth is 1050 fathoms. Off the coast of Syria the " Pola "obtained four soundings of more than 1100 fathoms, and between Cyprus and the coast of Asia Minor only two over 550 fathoms. Murray gives the following figures for the areas and volumes of the Mediterranean at different depths: which gives a mean depth over all of 768 fathoms. The following table is due to Karstens: Kriimmel gives the total volume of the basin as 4,249,020 cubic kilometres or 1,019,400 cubic statute miles, and the mean depth as 782 fathoms. (See Ocean.) Meteorology.

00This 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.

00From this we deduce for the charge p per cubic centimetre (I/41r)Xio-5 (volt/cm 2), or 2.7 X 101 electrostatic units.

00The charge on an ion being 3.4 X 1010 Mache deduces for the ionic charge, I + or I_, per cubic metre 1800X3'4 X 10 -1 Ã‚° X Io 6, or o 6.

00On account of its cubic form the mineral was early known as "cube ore" (Ger., Witir felerz); the name pharmacosiderite, given by J.

00The 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.

00The 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.

00Titanium is often present, and occasionally the mineral contains magnesium, nickel, &c. It is always strongly magnetic. Magnetite crystallizes in the cubic system, usually in octahedra, less commonly in rhombic dodecahedra, and not infrequently in twins of the " spinel type " (fig.

00We see therefore that I cubic centimetre of a normal sodium carbonate solution will exactly neutralize 0.049 gramme of sulphuric acid, 0.0365 gramme of hydrochloric acid (i.e.

00For example, boracite forms pseudo-cubic crystals which become truly cubic at 265Ã‚°, with a distinct change in density; leucite behaves similarly at about 560Ã‚°.

00Hexachlorethane is trimorphous, forming rhombic, triclinic and cubic crystals; the successive changes occur at about 44Ã‚° and 71Ã‚°, and are attended by a decrease in density.

00telluric acid forms cubic and monoclinic crystals from a hot nitric acid solution, and ammonium fluosilicate gives cubic and hexagonal forms from aqueous solutions between 6Ã‚° and 13Ã‚°.

00The 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.

00we find that Di must be equal to p x g x for then t x (p x) 3 +, u (g x) 3, Hence, if px, qx be the linear factors of the Hessian 64, the cubic can be put into the form A(p x) 3 +Ã¯¿½(g x) 3 and immediately solved.

00The transformation to the normal form, by the solution of a cubic and a quadratic, therefore, supplies a solution of the quartic. If (XÃ¯¿½) is the modulus of the transformation by which a2 is reduced to 3 the normal form, i becomes (X /2) 4 i, and j, (Ap) 3 j; hence?

00The system of the quadratic and cubic, consisting of 15 forms, and that of two cubics, consisting of 26 forms, were obtained by Salmon and Clebsch; that of the cubic and quartic we owe to Sigmund Gundelfinger (Programm Stuttgart, 186 9, 1 -43); that of the quadratic and quintic to Winter (Programm Darmstadt, 1880); that of the quadratic and sextic to von Gall (Programm Lemgo, 3873); that of two quartics to Gordan (Math.

00The first difficulty to be overcome was the algebraical solution of cubic equations, the " irreducible case" (see Equation).

00One 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.

00It forms colourless, transparent rhombohedra, like those of Iceland spar; the angles are nearly equal to right angles, being 73Ã‚° 30', so that the crystals look like cubes: hence the name of "cubic saltpetre."

00Thus, 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.

00A "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.

00For a discussion of this type of wave, u = dt = - U¢ cos (x - Ut), and Ã‚° 4, x Za2 / cos t (x - Ut) dx pu2ax=p = 2p7r 2 U 2 a 2 /X (12) The energy per cubic centimetre on the average is 2 pif2 U2a2 / A2 (13) and the energy passing per second through I sq.

00L Ã‚° poiedx = a (y + I) average energy per cubic centimetre, (Is) a result first published by Lord Rayleigh (Phil.

00Iooi), who obtained cubic crystals from a supersaturated solution of sodium and aluminium sulphates below 20Ã‚°, higher temperatures giving monoclinic crystals.

00The 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.

00These values of p refer to a standard density of the air, of 534.22 grains per cubic foot, which is the density of dry air at sea-level in the latitude of Greenwich, at a temperature of 62Ã‚° F.

00In the measurement of the cubic inch it has been found that 2 the specific mass of the cubic inch of distilled water freed from air, and weighed in air against brass weights (= 8.13), at the temperature of 62Ã‚° F., and under an atmospheric pressure equal to 30 in.

00For the specific mass of the cubic decimetre of water at 4Ã‚° C., under an atmospheric pressure equal to 760 mm., Guillaume and Chappuis of the Comite International des Poids et Mesures at Paris (C.I.P.M.) have obtained 0.9999707 kg., which has been accepted by the committee.

00It crystallizes in the cubic system, and well-developed crystals are of common occurrence; the usual form is the cube or the cubo-octahedron (fig.).

00The 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.

00The crystals belong to the cubic system, generally assuming the form of the octahedron (fig.

00The cubic parabola (fig.

00S = 0.9944 00O 04T 0.000,0009 T 2 (Regnault Above 60Ã‚° To 200Ã‚° Corrd.) S =1.000 0.000,22 (T 60), (Bosscha Corrd.) The Addition Of The Cubic Term Below 20Ã‚° Is Intended To Represent The Somewhat More Rapid Change Near The Freezing Point.

00Silver iodide is dimorphous; at ordinary temperatures the stable form is hexagonal; on heating to about 138Ã‚° the colour changes from deep yellow to yellowish-white with the formation of cubic crystals.

00The next important work, founded on the Geometric, was Sir Isaac Newton's Enumeratio linearum tertii ordinis (1706), establishing a classification of cubic curves founded chiefly on the nature of their infinite branches, which was in some details completed by James Stirling (1692-1770), Patrick Murdoch (d.

00The 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.

00In 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.

00pÃ‚°r cubic foot, at oÃ‚° and 760 mm.

00The final book presents the solution of cubic and quartic equations.

00This is the case for all objects that involve the solution of a cubic or quartic polynomial.

00This occurs as cubic crystals of what is often referred to as Fool 's Gold.

00The smaller reverberant room has a volume of 112 cubic meters and the outer walls are 215mm Accrington brick.

00The second stage smoothes these oscillations by performing a least squares cubic spline fit to the data.

00The program uses a fast 2D cubic spline method to create data to give the appearance of a smoothed set of results.

00Solution method: The analyzed function is approximated first by a cubic spline interpolant, then the Fourier coefficients of the latter are constructed.

00It can spot a fragment only a tenth of a cubic millimeter in size.

00Including manual indexing of a cubic cell, labeling HKLs and showing peak splitting when going from cubic to tetragonal cells.

00The cations are arranged into a face centered cubic structure with the anions occupying the tetrahedral sites.

00He also considered the equation associated with the problem of trisecting an angle, namely a cubic equation.

00There are no high active or medium active liquors in store and only 1.5 cubic meters of unconditioned intermediate level waste.

00Part of the appeal of cubic zirconia jewelry is its remarkable ability to look exactly like real diamond jewelry.

00Member Profile: L.M. Jewelry Ltd. is one of the UK 's leading importers of diamond and cubic zirconia set jewelry.

00Average range covered is about 250 to 350 cubic feet.

00For 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.

00For example, paper recycling saves over three cubic yards of landfill space for every ton of paper made from recycled materials.

00Glaciers, which weigh approximately one ton per cubic meter, place pressure on the Earth's surface.

00Cape 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.

00Cubic zirconias may not be allowed for your engagement ring, but for bridal jewelry it may just do the trick.

00In keeping with the geometric patterns and shapes, cubic or square shapes were used in shower curtains.

00Fill power is the number of cubic inches per single ounce of down.

00For instance, the highest and rarest quality of down has approximately 750 cubic inches per ounce.

00The average fill power is around 500 to 550 cubic inches per ounce.

00When 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.

00The following online calculators make it simple to sit at the computer and get the number of cubic feet of mulch you need.

00This 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.

00You now have the number of cubic feet of mulch you need.

00Divide 40 by 12 = 3.3 cubic feet of mulch needed.

00That box contains approximately 2.5 cubic yards of mulch, or about equal to 6 cubic yards of traditional wood mulch.

00Pine needle mulch comes in round or square bales, sized from 3 to 6 cubic feet.

00Many necklaces are items of fine jewelry, using superior metals and precious stones or diamonds, and others utilize more affordable materials such as cubic zirconia.

00Big Heart Gold Bunny Necklace: This 14K gold necklace features a hollow heart lined with cubic zirconia and a solid bunny logo on the upper ridge.

00Tiered Heart Gold Rabbit: This necklace features a tiered drop down of cubic zirconia hearts with a gold rabbit logo in between.

00Playmate of the Year: This white gold necklace showcases dozens of cubic zirconia stones affixed to the white gold rabbit head logo.

00If you can't afford the pricier versions of the pink gemstones, there are many alternatives from cubic zirconia to less pricey topaz rings.

00Some styles include a choice of diamond or cubic zirconia.

00Tanzanite Cubic Zirconica: This synthetic gemstone is available in many colors to replicate the wide range of hues of natural gemstones.

00Tanzanite cubic zirconica has recently become available and can be found at a variety of gemstone suppliers.

00Gemstone stimulants such as cubic zirconia are a good alternative.

00Cubic zirconia: This affordable looks shines and evokes the bold but classy feel of Chanel.

00Many of these are Chanel knockoffs, such as the star shaped earrings studded with cubic zirconia gems.

00Overstock Jeweler offers a variety of designer inspired jewelry items, including cubic zirconia pieces that have classy look like that of Chanel.

00Smaller families often use some of the spaces on the pendant for the mother's birthstone, for a pearl, diamond, or cubic zirconia.

00Rock crystal or even man made stones such as cubic zirconia make perfect alternatives.

00In some cases, they include pave cubic zirconias for a bit of extra life.

00It's a 38 centimeter chain with the typical Chanel logo at the end, studded in pave cubic zirconias.

00Stones: Diamonds are popular on palm trees, but more affordable jewelry may use cubic zirconia (CZ) or other simulated gemstones.

00Emitations: Emitations has a pendant and cocktail ring featuring a spider with a silver and pave cubic zirconia head and legs, with a dyed black pearl body.

00Show your love by giving that someone special a cubic zirconia journey circle pendant.

00There are even versions featuring cubic zirconia accents.

00Almost Diamonds.com has a variety of journey pendants accented with cubic zirconia.

00New Outlet.com has several journey pendants accented with cubic zirconia.

00Macy's has a wide selection of cubic zirconia jewelry.

00They feature pendants such as the CRISLU Cubic Zirconia Circle Pendant and the Sterling Silver Cubic Zirconia Pendant.

00Pearl and cubic zirconia sterling silver stud earrings can be the perfect complement to any outfit.

00A popular combination seen in stud earrings is pearls and cubic zirconia.

00Cubic zirconia adds all the sparkle of a diamond without the high price tag.

00They feature a 10 mm faux white pearl and three cubic zirconia accents set in rhodium plated sterling silver.

00Often 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.

00Kohl's has the Silvertone Simulated Pearl with Cubic Zirconia Stud Earrings.

00Each earring has a 12 mm faux white pearl surrounded by a wreath of cubic zirconias.

00Day Trips: Backpacks for day trips are designed to hold supplies for a single day, and typically have capacities ranging from 2000 to 3000 cubic inches.

00Overnight Trips: When preparing for an overnight camping trip, the best selection is a backpack with a capacity ranging from just over 3000 cubic inches to 4000 cubic inches.

00Depending on what you plan to carry, you should look for a pack with a capacity ranging from 4000 to 5000 cubic inches.

00The LX - This camper measures 113" by 38" and has 26 cubic feet of storage space.

00Its storage space is reduced to 16 cubic feet.

00It holds up to 20 cubic feet of camping essentials and has an optional luggage rack.

00It provides six cubic feet of storage room.

00Sharp's mini has a half-pint of capacity, and the most recent variations of the new classic are only about fourteen cubic inches.

00Small and compact ovens typically can hold 0.5 to 0.8 cubic feet.

00Regular sized microwaves can hold 1.0 to 2.0 cubic feet of food.

00Larger models, including convection-oven microwave combinations, have a capacity of 2.2 cubic feet or greater.

00GE produces countertop models ranging from 0.8 to 2.0 cubic feet with wattage ratings of 800 to 1200.

00Sharp offers inexpensive and compact models that have a capacity of 0.8 cubic feet and wattage rating of 800, costing less than $100.

00Their higher end models include a capacity of 2.0 cubic feet and cost upwards of $800.

00Kenmore microwaves can hold 1.5 to 2.0 cubic feet and cost $200 to $800.

00CFM is cubic feet (of air flow) per minute, and this number is what you need your dehumidifier to be able to process.

00The oven has a .7 cubic foot capacity and can accommodate up to six slices of bread.

00Upright freezers classified as small models typically range from just over one cubic foot to just over eight cubic feet.

00Sub-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.

00