Quantities sentence example

quantities
  • Gold is exported in large quantities from Australia.
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  • For large buildings where large quantities of hot water are used an independent boiler of suitable size should be installed.
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  • Wine is manufactured in large quantities, but the output is not sufficient to meet the home demand.
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  • Large quantities of fruits - apples, pears, quinces, peaches, nectarines, apricots, grapes and melons - were exported by special trains to central Europe, where the Turkestan crop was received a short time before the south European supplies ripened.
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  • The Suffolk beds have been worked since 1846; and immense quantities of coprolite have also been obtained from Essex, Norfolk and Cambridgeshire.
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  • The chemical symbols stand for quantities measured in grammes, and heat-evolution is reckoned as positive, heat-absorption as negative.
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  • He thus writes S+02=S02+7110o cal., which expresses the fact that the intrinsic energy of the quantities of sulphur and oxygen considered exceeds that of the sulphur dioxide derived from them by 71100 cal.
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  • One of the neighbouring mines, the Proprietary, is the richest in the world; gold is associated with the silver; large quantities of lead, good copper lodes, zinc and tin are also found.
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  • It is used chiefly in the manufacture of coarse sackcloth, cordage and hammocks, and is exported in large quantities.
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  • From the extreme south most of the merchantable timber had been cut, but immediately north of this there were still vast quantities of valuable long-leaf pine; in the marshes of the Delta was much cypress, the cotton-wood was nearly exhausted, and the gum was being used as a substitute for it; and on the rich upland soil were oak and red gum, also cotton-wood, hickory and maple.
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  • Large quantities of mineral water, sulphur, chalybeate and lithia, bottled at Meridian, Raymond and elsewhere, are sold annually.
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  • Aromatic and medicinal herbs, of which the state has several hundred distinct species, have been obtained in larger, quantities than from any other state in the Union.
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  • At the beginning of the 20th century a great number of minerals were found in the Piedmont Plateau and Mountain regions, but most of them in such small quantities as to be of little or no commercial value, and in 1902 the total value of the products of the mines and quarries was only $927,376; but in 1907 their value was $2,961,381, and in 1908, $2,145,947.
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  • To him belongs the merit of carrying out some of the earliest determinations of the quantities by weight in which acids saturate bases and bases acids, and of arriving at the conception that those amounts of different bases which can saturate the same quantity of a particular acid are equivalent to each other.
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  • He was thus led to conclude that chemistry is a branch of applied mathematics and to endeavour to trace a law according to which the quantities of different bases required to saturate a given acid formed an arithmetical, and the quantities of acids saturating a given base a geometrical, progression.
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  • Owing to the long line of coast and the numerous lakes, fishing forms an important industry, and large quantities of herrings, eels and lampreys are sent from Pomerania to other parts of Germany.
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  • The chief constituent of palm oil; also contained in greater or less quantities in human fat, olive oil, and other animal and vegetable fats.
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  • The blanched fronds are also sold in large quantities for the processions of Palm Sunday, and after they have received the blessing of the priest they are regarded throughout Spain as certain defences against lightning.
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  • Small quantities of quicksilver, sulphur and iron are obtained.
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  • Naphtha is also obtained, though in much smaller quantities, in Terek and Kuban, in Tiflis and Daghestan.
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  • In addition large quantities are shipped at Baku direct for the Volga and the Transcaspian port of Krasnovodsk.
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  • Derbyshire cheeses are exported or sent to London in considerable quantities; and cheese fairs are held in various parts of the county, as at Ashbourne and Derby.
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  • Ironstone is not extensively wrought, but, on account of the abundant supply of coal, large quantities are imported for smelting purposes.
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  • Derbyshire has always been mainly a mining and manufacturing county, though the rich land in the south formerly produced large quantities of corn.
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  • The low price of grain, which was imported in huge quantities from Sicily and other Roman provinces, operated to crush the small holder, at the same time as it made arable farming unremunerative.
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  • The quantities of these are relatively small, and, excepting rabbits from Australia, they show no general tendency to increase.
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  • Immense quantities are imported into Britain from Norway, Sweden and Prussia, under the names of "white Norway," "Christiania" and "Danzig deal."
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  • The town and neighbourhood have been long noted for their lime and cement, and large quantities of potters', pipe, fire and other kinds of clay are sent to Staffordshire and to foreign countries.
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  • Vineyards are cultivated by a German colony and large quantities of wine are made.
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  • Venetian beads are now sent in large quantities to the various colonies in Africa, and to India, Sumatra and Borneo.
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  • It is the chief seat of the glass pearl and imitation jewelry manufacture, and has also an important textile industry, and produces large quantities of hardware, papier mache and other paper goods.
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  • Using average prices paid for nitrogen, phosphoric acid and potash when bought in large quantities and in good forms, these ingredients, in a ton of cotton seed, amount to $9.00 worth of fertilizing material.
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  • Hull is the principal seat of the industry in Great Britain, and enormous quantities of Indian and Egyptian cotton seed are imported and worked up.
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  • The World's Commercial Cotton Crop. It is impossible to give an exact return of the total amount of cotton produced in the world, owing to the fact that in China, India and other eastern countries, in Mexico, Brazil, parts of the Russian empire, tropical Africa, &c., considerable - in some cases very large - quantities of cotton are made up locally into wearing apparel, &c., and escape all statistical record.
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  • Mexico.-Cotton is extensively grown in Mexico, and large quantities are used for home consumption.
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  • To-day a spinner who is asked to quote for deliveries of yarn for, say, the next six months, may obtain from a broker quotations for deliveries of the cotton that he needs, in quantities as he needs it, for the next six months, and upon these quotations he may base his own for yarn.
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  • Average Quantities of Raw Cotton imported Annually into the United Kingdom from the following Countries in the Periods 1896-1900 and 1901-1904.
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  • Tartaric acid, which is sometimes present in large quantities as an adulterant in commercial citric acid, may be detected in the presence of the latter, by the production of a precipitate of acid potassium tartrate when potassium acetate is added to a cold solution.
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  • This plain produces large quantities of indigo and opium, and is physically remarkable for the number of isolated conical hills which dot its surface.
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  • In minerals Manchuria is very rich: coal, gold, iron (as well as magnetic iron ore), and precious stones are found in large quantities.
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  • The indigo plant is grown in large quantities in the plain country to the north of Mukden, and is transported thence to the coast in carts, each of which carries rather more than a ton weight of the dye.
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  • The calorific power of Baku oil appears to be highest, while this oil is poorest in solid hydrocarbons, of which the American petroleums contain moderate quantities, and the Upper Burma oils the largest amount.
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  • Even prior to the discovery of petroleum in commercial quantities, a number of chemists had made determinations of the chemical composition of several different varieties, and these investigations, supplemented by those of a later date, show that petroleum consists of about 84% by weight of carbon with 12% of hydrogen, and varying proportions of sulphur, nitrogen and oxygen.
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  • Paraffins are found in all crude oils, and olefines in varying proportions in the majority, while acetylene has been found in Baku oil; members of the benzene group and its derivatives, notably benzene and toluene, occur in all petroleums. Naphthenes are the chief components of some oils, as already indicated, and occur in varying quantities in many others.
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  • Natural gas is found to consist mainly of the lower paraffins, with varying quantities of carbon dioxide, carbon monoxide, hydrogen, nitrogen and oxygen, in some cases also sulphuretted hydrogen and possibly ammonia.
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  • In France, the standard is 35° C. (Granier tester, equivalent to 98° F.), and according to their flashpoint, liquid hydrocarbons are divided into two classes (below and above 35° C.), considered differently in regard to quantities storable and other regulations.
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  • Sugar-cane, maize, tapioca and other similar products are grown, however, in smaller quantities.
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  • The market-gardening of the region called the Westland, between the Hague and the Hook of Holland, is remarkable, and large quantities of vegetables are exported to England.
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  • As the lye becomes absorbed, a condition indicated by the taste of the goods, additional quantities of lye of increasing strength are added.
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  • Great quantities of early potatoes and vegetables, together with flowers and fish, are sent to London and elsewhere.
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  • Then by solving these equations, regarding the six elements as unknown quantities, the values of the latter may be computed.
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  • Instead of the six ideal equations just described we have to combine a number of equations of various forms containing other quantities than the elements.
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  • Rice is grown in such quantities as to procure for Formosa, in former days, the title of the " granary of China "; and the sweet potato, taro, millet, barley, wheat and maize are also cultivated.
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  • Coal is also found in large quantities near Kelung and sulphur springs exist in the north of the island.
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  • Turning to the study of radioactivity, he noticed its association with the minerals which yield helium, and in support of the hypothesis that that gas is a disintegration-product of radium he proved in 1903 that it is continuously formed by the latter substance in quantities sufficiently great to be directly recognizable in the spectroscope.
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  • Lobsters and fish in considerable quantities are shipped from the city.
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  • Grain is shipped to and from Jersey City in large quantities, and in general the city is an important shipping port; being included, however, in the port of New York, no separate statistics are available.
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  • It is really not extraordinary that Isaac Hollandus was able to indicate the method of the preparation of the " philosopher's stone " from " adamic " or " virgin " earth, and its action when medicinally employed; that in the writings assigned to Roger Bacon, Raimon Lull, Basil Valentine and others are to be found the exact quantities of it to be used in transmutation; and that George Ripley, in the 15th century, had grounds for regarding its action as similar to that of a ferment.
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  • Hassenfratz and Adet, who assigned to each element a symbol, and to each compound a sign which should record the elements present and their relative quantities.
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  • Experimental conditions were thoroughly worked out; the necessity of working with hot or cold solutions was clearly emphasized; and the employment of small quantities of substances instead of the large amounts recommended by Klaproth was shown by him to give more consistent results.
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  • By taking ivth or 10th of these quantities, decinormal or centinormal solutions are obtained.
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  • The general procedure is to make a series of standard solutions containing definite quantities of the substance which it is desired to estimate; such a series will exhibit tints which deepen as the quantity of the substance is increased.
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  • Neumann, who, in 1831, deduced from observations on many carbonates (calcium, magnesium, ferrous, zinc, barium and lead) that stoichiometric quantities (equimolecular weights) of compounds possess the same heat capacity.
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  • He introduced the idea of comparing the refractivity of equimolecular quantities of different substances by multiplying the function (n-1)/d by the molecular weight (M) of the substance, and investigated the relations of chemical grouping to refractivity.
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  • - Fibre is obtained from the aloe plants, this industry being in the hands of women; ostriches are reared for the sake of their feathers, and large quantities of gum and resin are collected.
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  • Springfield is a trading and shipping centre for a prosperous agricultural region, and ships large quantities of bituminous coal from the immediate vicinity.
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  • In the town of Raymond is a large beet sugar manufactory, and in the vicinity great quantities of beets are grown by irrigation.
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  • The most notable gas discovery is that at Medicine Hat, which has wells with unlimited quantities.
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  • The Yenangyat oil-fields, which produce quantities of petroleum, are in the south of the district, and iron used to be worked in a small way.
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  • The existence of sulphuretted hydrogen in great quantities below loo fathoms, the extensive chemical precipitation of calcium carbonate, the stagnant nature of its deep waters, and the absence of deep-sea life are conditions which make it impossible to discuss it along with the physical and biological conditions of the Mediterranean proper.
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  • In the Tertiary region are found small quantities of iron ore and an indifferent brown coal.
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  • In some localities, especially in the " Florida parishes," small quantities of rosin and turpentine are taken from the long-leaf pine, but this industry was unimportant in Louisiana before 1908.
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  • Sawdust, slabs, stumps and large quantities of logs are wasted.
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  • Chromium and a number of other rare minerals are known to exist, but probably not in commercially available quantities.
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  • For building and miscellaneous purposes, in addition to the rare woods above named, there are cedars (used in great quantities for cigar boxes); the pine, found only in the W., where it gives its name to the Isle of Pines and the province of Pinar del Rio; various palms; oaks of varying hardness and colour, &c. The number of alimentary plants is extremely great.
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  • Bananas are grown particularly in the region about Nipe, Gibara and Baracoa, whence they are exported in large quantities, though there is a tendency to lessen their culture in these parts in favour of sugar.
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  • After the Ten Year's War seed of Mexican and United States tobaccos was in great demand to re-seed the ruined vegas, and was introduced in great quantities; and although by a later law the destruction of these exotic species was ordered, that destruction was in fact quite impossible.
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  • Of these all except points are quantities: lines involve lengths, planes involve areas, and cubic contents involve volumes.
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  • Also, as the Cartesian geometry shows, all the relations between points are expressible in terms of geometric quantities.
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  • The application of the theory of real numbers to physical quantities involves analogous considerations.
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  • The heading "Measurement of Dynamical Quantities" includes the topics units, measurements, and the constant of gravitation.
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  • The Greeks created the sciences of geometry and of number as applied to the measurement of continuous quantities.
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  • All these commodities are exported in considerable quantities, besides bitumen, which is obtained from a mine worked by a French III.
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  • Attar of roses is produced in large quantities both in European and Asiatic Turkey, and to aid in furthering the industry numerous rose plants are distributed gratuitously.
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  • Meanwhile kaime was being issued in great quantities (about 60,000 purses a month) and fell to a discount (December 1861) of 75%.
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  • The Zahran district lies four days west of Besha on the crest of the main range: the principal place is Makhwa, a large town and market, from which grain is exported in considerable quantities to Mecca.
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  • It is also the largest market for fresh-water fish in America, and handles large quantities of lumber and grain.
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  • The growth during the Civil War was partly due to the rapid development of the manufacturing interests of the city, which supplied large quantities of iron products and of clothing to the Federal government.
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  • It is limited to Disco Island, and perhaps to a small part of the Noursoak Peninsula, and the neighbouring country, and consists of numerous thin beds of sandstone, shale and coal - the sideritic shale containing immense quantities of leaves, stems, fruit, &c., as well as some insects, and the coal pieces of retinite.
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  • It might be expected that there should be a decrease in the Greenland seal fisheries, caused by the European and American sealers catching larger quantities every year, especially along the coasts of Newfoundland and Labrador, and so actually diminishing the number of the animals in the Greenland seas.
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  • Tracing, then, the quantities of oil given per 1,000 fish from year to year, they seemed to establish a connexion between the variation in " condition " of the fish, the variation in the inflow of Atlantic water, and the variation in the number of sunspots from year to year.
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  • Detailed study of the cod shoals also showed that their composition was continually changing: in some years the shoal is composed of younger or older fish than the average and with this latter variation there are changes in the quantities of oil yielded per t,000 fish.
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  • In the case of all these substances the quantities involved are so very small, and the difficulties of estimation are therefore so great, that the information we possess is by no means satisfactory.
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  • The quantities of oxygen and carbonic acid in the sea are nearly constant so far as we can determine.
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  • Before the days of the "higher criticism" and the rise of the modern scientific views as to the origin of species, there was much discussion among the learned, and many ingenious and curious theories were advanced, as to the number of the animals and the space necessary for their reception, with elaborate calculations as to the subdivisions of the ark and the quantities of food, &c., required to be stored.
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  • It is clear that, when two opposite streams of ions move past each other, equivalent quantities are liberated at the two ends of the system.
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  • It seems that this reverse electromotive force of polarization is due to the deposit on the electrodes of minute quantities of the products of chemical decomposition.
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  • The latex of this tree flows less freely than that of Hevea brasiliensis, and the collection of large quantities of the latex is attended with considerable difficulty.
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  • A large number of plantations in British Malaya and Ceylon are now actively exporting increasing quantities of rubber.
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  • He receives both the wild rubber containing variable quantities of impurity and the purer plantation rubber, the latter, however, in much smaller amount.
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  • Agriculture is well developed and relatively large quantities of the principal cereals are produced.
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  • Large quantities of ground mica are used in the manufacture of wall-paper, and to produce a frosted effect on toys, stage scenery, &c. Powdered mica is also used in the manufacture of paints and paper, as a lubricant, and as an absorbent of nitro-glycerine and disinfectants.
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  • Let there be given n 2 quantities all a,2 a13 ��� aln a21 a22 a23 ��� a2n a3, a32 a33 ��� a3n and an, an 3 ��� ann and form from them a product of n quantities ala a2 0 a37 ...
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  • Y ...a n v, the summation being for all permutations of the n numbers, is called the determinant of the n 2 quantities.
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  • Further we find x=aX+a'Y+a"Z, y=bX z= cX+c'Y+ c"Z, and the problem is to express the nine coefficients in terms of three independent quantities.
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  • In general in space of n dimensions we have n substitutions similar to X l = a11x1 +a12x2 + � � � + ainxn, and we have to express the n 2 coefficients in terms of Zn(n - I)i independent quantities; which must be possible, because X1+X2+..."IL Xn =xi+x2 +x3 +...+4.
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  • There are then 2n(n-I) quantities b rs .
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  • We may therefore form an orthogonal transformation in association with every skew determinant which has its leading diagonal elements unity, for the Zn(n-I) quantities b are clearly arbitrary.
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  • Assuming then 01 to have the coefficients B1, B2,...B,, and f l the coefficients A 1, A21...A,n, we may equate coefficients of like powers of x in the identity, and obtain m+n homogeneous linear equations satisfied by the m+n quantities B1, 2, ...B n, A 1, A 2, ...A m.
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  • = 11(1 +�alxl+� g al x2+�3a1x3+...), the product on the right involving a factor for each of the quantities a l, a2, a3..., and u being arbitrary.
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  • Denote by brackets () and [] symmetric functions of the quantities p and a respectively.
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  • Taking the systems of quantities to be / al, a2, a3,...
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  • All symmetric functions are expressible in terms of the quantities ap g in a rational integral form; from this property they are termed elementary functions; further they are said to be single-unitary since each part of the partition denoting ap q involves but a single unit.
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  • The analogous formula appertaining to n systems of quantities which Vienna Transactions, t.
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  • The similar theorem for n systems of quantities can be at once written down.
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  • 1 exp(Adlo + vdol) = (1+/oD10+ v Doi +..�+ VQ +.�.)f; now, since the introduction of the new quantities 1.1., v results in the addition to the function (plglp2g2p3g3...) of the new terms A PI Pg1 (p 2q2 p 3g3���) +/ AP2Pg2 (p 1 g 1P343 ...)+/ Z3vg3 (p l g i p 2 g 2 ...)+ �, we find DP141(plqip2q2p3q3���) = (p 2 q 2 p 3 q 3���), and thence D P141 D P242 D P343 ��.
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  • Recalling the formulae above which connect s P4 and a m, we see that dP4 and Dp q are in co-relation with these quantities respectively, and may be said to be operations which correspond to the partitions (pq), (10 P 01 4) respectively.
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  • This fact is of extreme importance in the theory of algebraic forms, and is easily representable whatever be the number of the systems of quantities.
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  • We frequently meet with cogredient and contragedient quantities, and we have in general the following definitions:-(i) " If two equally numerous sets of quantities x, y, z,...
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  • + ���, Z = v16+v2%/+v3" +���, wherein it should be noticed that new quantities are expressed in terms of the old, as regards the latter set, and not vice versa."
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  • If u, a quantic in x, y, z, ..., be expressed in terms of new variables X, Y, Z ...; and if, n,, ..., be quantities contragredient to x, y, z, ...; there are found to exist functions of, n, ?, ..., and of the coefficients in u, which need, at most, be multiplied by powers of the modulus to be made equal to the same functions of E, H, Z, ...
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  • Again, if 0 is uneven =20+I, the condition is a 1 a 2 ...cr 241 II(a 1 +a 2)II(cr 1 +a 2 +(73)...II(a 1 +a 2 +...+ac) =0; and the degree, in the quantities a, is 20+1 + (42+1) +(21) �...-F(254)�1) =22°-1= 2e-1-1 Hence the lowest weight of a perpetuant is 2 0 - 1 -1, when 0 is >2.
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  • Remark, too, that we are in association with non-unitary symmetric functions of two systems of quantities which will be denoted by partitions in brackets ()a, ()b respectively.
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  • Large quantities of coal and tea are exported.
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  • Fourteen years later, when curule aedile, he distributed large quantities of grain among the citizens at a very low price.
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  • Bangor is one of the largest lumber depots in the United States, and also ships considerable quantities of ice.
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  • Large quantities of lac and tussur silk are gathered in the hilly tract.
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  • The water-supply of London is considered under that heading; it may be noted here that the Thames forms the chief source of supply for the metropolis, but apart from this the corporation of Oxford and two companies in the Staines district have powers to draw water from the river, though not in any large quantities.
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  • Mining is only of slight importance, small quantities of coal and iron-ore being extracted in the Alpine foothill region; graphite is found near Miihldorf.
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  • This ore, metallurgically, was not reckoned of much value, until immense quantities of it were discovered in Nevada and in Colorado (U.S.).
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  • "Pewter" (q.v.) may be said to be substantially an alloy of the same two metals, but small quantities of copper, antimony and zinc are frequently added.
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  • As a rule the soluble salts if taken in sufficient quantities produce acute poisoning, and the insoluble salts chronic plumbism.
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  • Agricultural products, fruit and wool from the surrounding country are shipped in considerable quantities.
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  • It contains considerable quantities of the alkaloid pseudaconitine, which is the most deadly poison known.
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  • It must be used with extreme care, and in small quantities, and it must not be used at all where cuts or cracks are present in the skin.
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  • 2 Clerk Maxwell employed German capitals to denote vector quantities.
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  • The presence of ordinary impurities usually tends to diminish the permeability, though, as will appear later, the addition of small quantities of certain other substances is sometimes advantageous.
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  • When nickel was added to the iron in increasing quantities the coercive force increased until the proportion of nickel reached 20%; then it diminished, and when the proportion of nickel was 32% the coercive force had fallen to the exceedingly low value of 0.5.
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  • The addition of silicon in small quantities considerably diminished permeability and increased coercive force; but when the proportion amounted to 2.5% the maximum permeability (µ =5100 for H =2) was greater than that of the nearly pure iron used for comparison, while the coercive force was only 0.9.
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  • A magnetizable substance was supposed to consist of an indefinite number of spherical particles, each containing equivalent quantities of the two fluids, which could move freely within a particle, but could never pass from one particle to another.
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  • It imports great quantities of wool from the Argentine and Australia, and is in regular communication with New York, London and the chief ports of the United Kingdom, Brazil and the far East.
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  • It is readily polymerized, small quantities of hydrochloric acid, zinc chloride, carbonyl chloride, &c. converting it, at ordinary temperatures, into paraldehyde, (C 2 H 4 0) 3, a liquid boiling at 124° C. and of specific gravity o�998 (15° C.).
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  • Formerly this coast region furnished large quantities of Brazil-wood (Caesalpinia echinata), and the river valleys have long been the principal source of Brazil's best cabinet-wood - rosewood (Dalbergia nigra), jacaranda (Machaeriumfirmum,Benth.),vinhatico (Plathymenia foliosa, Benth.), peroba (Aspidosperma peroba), cedro, &c. The exotic mangabeira (mango) is found everywhere along the coast, together with the bamboo, orange, lemon, banana, cashew, &c.
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  • In the Amazon valley fish is a principal article of food, and large quantities of pirarucu (Sudis gigas) are caught during the season of low water and prepared for storage or market by drying in the sun.
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  • Sugar-works were established, and considerable quantities of the produce exported to the mother country.
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  • Theconglomerates are true " banket " and are auriferous, but the gold has not been met with in payable quantities.
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  • Fish of excellent quality and in great quantities abound on the coast.
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  • The tea plant was first introduced in Natal in 1850, but little attention was paid to it until the failure of the coffee plantations about 1875, since when only small quantities of coffee have been produced.
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  • On the lower Umzimkulu, near Port Shepstone, marble is found in great quantities.
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  • Timber is also exported, being floated in large quantities down the Lule.
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  • The vomiting may take place every two or three days, enormous quantities of undigested food mixed with frothy, yeast-like mucous being thrown up. And whilst the stomach is slowly filling up again after one of these uncontrollable emptyings, sudden and violent movements of the individual may cause the fluid to give rise to audible "splashings."
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  • The rivers and lakes yield enormous quantities of fish, and leeches also are plentiful.
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  • Pigs are reared in large quantities all over the country, but the principal centres for distribution are Debreczen, Gyula, Bares, Szeged and Budapest.
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  • The device known as the method of least squares, for reducing numerous equations of condition to the number of unknown quantities to be determined, had been adopted as a practically convenient rule by Gauss and Legendre; but Laplace first treated it as a problem in probabilities, and proved by an intricate and difficult course of reasoning that it was also the most advantageous, the mean of the probabilities of error in the determination of the elements being thereby reduced to a minimum.
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  • The knowledge of these laws, however, does not imply the existence of a conception of negative quantities.
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  • The principal step in the modern development of algebra was the recognition of the meaning of negative quantities.
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  • This involved not only the geometrical interpretation of negative quantities, but also the idea of continuity; this latter, which is the basis of modern analysis, leading to two separate but allied developments, viz.
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  • We must count with something; and the successive somethings obtained by the addition of successive units are in fact numerical quantities, not numbers.
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  • When we are familiar with the treatment of quantities by equations, we may ignore the units and deal solely with numbers; and (ii.) (a) and (ii.) (b) may then, by the commutative law for multiplication, be regarded as identical.
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  • Expressed Equations.-The simplest forms of arithmetical equation arise out of abbreviated solutions of particular problems. In accordance with � 15, it is desirable that our statements should be statements of equality of quantities rather than of numbers; and it is convenient in the early stages to have a distinctive notation, e.g.
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  • Use of Letters in General Reasoning.-It may be assumed that the use of letters to denote quantities or numbers will first arise in dealing with equations, so that the letter used will in each case represent a definite quantity or number; such general statements as those of �� 15 and 16 being deferred to a later stage.
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  • For multiplication, for instance, we have the statement that, if P and Q are two quantities, containing respectively p and q of a particular unit, then p X Q = q X P; or the more abstract statement that p X q= q X p.
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  • (v.) Permutations and Combinations may be regarded as arithmetical recreations; they become important algebraically in reference to the binomial theroem (�� 41, 44)� (vi.) Surds and Approximate Logarithms. - From the arithmetical point of view, surds present a greater difficulty than negative quantities and fractional numbers.
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  • When, however, we come to the equation x 2 --- 5, where we are dealing with numbers, not with quantities, we have no concrete facts to assist us.
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  • While mensuration is concerned with the representation of geometrical magnitudes by numbers, graphics is concerned with the representation of numerical quantities by geometrical figures, and particularly by lengths.
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  • There are also cases in which graphics and mensuration are used jointly; a variable numerical quantity is represented by a graph, and the principles of mensuration are then applied to determine related numerical quantities.
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  • Let X and Y be the related quantities, their expressions in terms of selected units A and B being x and y, so that X=x.A, Y = y.
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  • Graphic representation thus rests on the principle that equal numerical quantities may be represented by equal lengths, and that a quantity mA may be represented by a length mL, where A and L are the respective units; and the science of graphics rests on the converse property that the quantity represented by pL is pA, i.e.
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  • The principles of arithmetical transformation follow from those stated in �� 15-18 by replacing X, A, B, m, M, x, n, a and p by any expressions involving or not involving the unknown quantity or number and representing positive numbers or (in the case of X, A, B and M) positive quantities.
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  • Negative quantities will have arisen in various ways, e.g.
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  • The occurrence of negative quantities does not, however, involve the conception of negative numbers.
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  • The graphic method, therefore, does not give any direct assistance towards the conception of negative numbers as operators, though it is useful for interpreting negative quantities as results.
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  • This led to a prolonged controversy on the nature of negative and imaginary quantities, which was ultimately settled in a very curious way.
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  • The progress of analytical geometry led to a geometrical interpretation both of negative and also of imaginary quantities; and when a " meaning " or, more properly, an interpretation, had thus been found for the symbols in question, a reconsideration of the old algebraic problem became inevitable, and the true solution, now so obvious, was eventually obtained.
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  • Evolution and involution are usually regarded as operations of ordinary algebra; this leads to a notation for powers and roots, and a theory of irrational algebraic quantities analogous to that of irrational numbers.
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  • From A Merely Formal Point Of View, We Have In The Barycentric Calculus A Set Of " Special Symbols Of Quantity " Or " Extraordinaries " A, B, C, &C., Which Combine With Each Other By Means Of Operations And Which Obey The Ordinary Rules, And With Ordinary Algebraic Quantities By Operations X And =, Also According To The Ordinary Rules, Except That Division By An Extraordinary Is Not Used.
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  • Thus every quaternion may be written in the form q = Sq+Vq, where either Sq or Vq may separately vanish; so that ordinary algebraic quantities (or scalars, as we shall call them) and pure vectors may each be regarded as special cases of quaternions.
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  • Associated with these new units there is a system of extensive quantities of the second species, represented by symbols of the type = Ei 121 [i=I, 2,...zn(n - I)].
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  • The outer and inner products of two extensive quantities A, B, are in many ways analogous to the quaternion symbols Vab and Sab respectively.
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  • As in quaternions, so in the extensive calculus, there are numerous formulae of transformation which enable us to deal with extensive quantities without expressing them in terms of the primary units.
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  • Only a few illustrations can be given here, Let a, b, c, d, e, be quantities of the first species in the fourth category; A, B, C ...
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    0
  • An n-tuple linear algebra (also called a complex number system) deals with quantities of the type A=/aiei derived from n special units e l, e 2 ...
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  • This applies also to quaternions, but not to extensive quantities, nor is it true for linear algebras in general.
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  • Franciscus Vieta (Francois Viete) named it Specious Arithmetic, on account of the species of the quantities involved, which he represented symbolically by the various letters of the alphabet.
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  • The unknown he terms arithmos, the number, and in solutions he marks it by the final s; he explains the generation of powers, the rules for multiplication and division of simple quantities, but he does not treat of the addition, subtraction, multiplication and division of compound quantities.
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  • Clearer ideas of imaginary quantities and the " irreducible case " were subsequently published by Bombelli, in a work of which the dedication is dated 1572, though the book was not published until 1579.
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  • Michael Stifel and Johann Scheubelius (Scheybl) (1494-1570) flourished in Germany, and although unacquainted with the work of Cardan and Tartalea, their writings are noteworthy for their perspicuity and the introduction of a more complete symbolism for quantities and operations.
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  • It includes the properties of numbers; extraction of roots of arithmetical and algebraical quantities, solutions of simple and quadratic equations, and a fairly complete account of surds.
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  • He denotes quantities by the letters of the alphabet, retaining the vowels for the unknown and the consonants for the knowns; he introduced the vinculum and among others the terms coefficient, affirmative, negative, pure and adfected equations.
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  • He follows Vieta in assigning the vowels to the unknown quantities and the consonants to the knowns, but instead of using capitals, as with Vieta, he employed the small letters; equality he denoted by Recorde's symbol, and he introduced the signs > and < for greater than and less than.
    0
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  • His notation is based primarily on that of Harriot; but he differs from that writer in retaining the first letters of the alphabet for the known quantities and the final letters for the unknowns.
    0
    0
  • The geometrical interpretation of imaginary quantities had a far-reaching influence on the development of symbolic algebras.
    0
    0
  • In the applications with which we are concerned, t, n are very small quantities; and we may take P = x yn - At the same time dS may be identified with dxdy, and in the de nominator p may be treated as constant and equal to f.
    0
    0
  • To get an idea of the magnitudes of the quantities involved, let us take the case of an aperture of 1 in., about that of the pupil of the eye.
    0
    0
  • The path of a ray from the wave-surface A 0 B 0 to the point A is changed; but in virtue of the minimum property the change may be neglected in calculating the optical distance,as it influences the result by quantities of the second order only in the changes of refrangibility.
    0
    0
  • (b2V2 + n2) (a2 - b 2) = - z It will now be convenient to introduce the quantities a l, a 2', 7731 which express the rotations of the elements of the medium round axes parallel to those of co-ordinates, in accordance with the equations Ty - 1 = dz ' 3= - dy 2 = dx - In terms of these we obtain from (7), by differentiation and subtraction, (b 2 v 2 + n 2) 7,3 = 0 (b 2 0 2 +n 2) .r i = dZ/dy (b 2 v 2 +n 2)', , 2 = - dZ/dx The first of equations (9) gives 3 = 0 (10) For al we have ?1= 47rb2, f dy e Y tkr dx dy dz
    0
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  • The Geestlande comprise the suburban districts encircling the city on the north and west; the Marschlande includes various islands in the Elbe and the fertile tract of land lying between the northern and southern arms of the Elbe, and with its pastures and market gardens supplying Hamburg with large quantities of country produce.
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  • The surrounding country is very fertile and produces large quantities of rice, as well as Indian corn, tobacco, sugar, coffee and a great variety of fruits.
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  • Mieres is the chief town of a mountainous, fertile and well-wooded region in which coal, iron, and copper are extensively mined and sulphur and cinnabar are obtained in smaller quantities.
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    0
  • The conglomerate bands and quartzites contain large quantities of iron pyrites deposited subsequent to their formation, that in the conglomerates containing the gold.
    0
    0
  • The gold is found in minute particles arid in the richest ores the metal is rarely in visible quantities before treatment.
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    0
  • Salt is obtainable from the many pans in the plateaus, notably in the Zout(salt)pansberg, and was formerly manufactured in considerable quantities.
    0
    0
  • Shaft furnace smelting is confined to those parts of the world where charcoal can still be obtained in large quantities at moderate prices.
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  • It exports iodine and immense quantities of nitrate of soda obtained from the desert region of the province.
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  • In addition to the mining, the district produces large quantities of wool.
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  • On its thoroughness depends the removal of small quantities of products other than the nitrates, for instance, some sulphates and products from impurities contained in the original cellulose.
    0
    0
  • In the neighbourhood large quantities of fruit are grown, including apples, pears, plums, gooseberries, and strawberries.
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  • In addition to goods thus conveyed, enormous quantities of timber are floated down the Elbe; the Ix.
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  • Brandy is produced in large quantities.
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  • It has a strong and characteristic odour, and a hot sweetish taste, is soluble in ten parts of water, and in all proportions in alcohol, and dissolves bromine, iodine, and, in small quantities, sulphur and phosphorus, also the volatile oils, most fatty and resinous substances, guncotton, caoutchouc and certain of the vegetable alkaloids.
    0
    0
  • Wheat, barley, oats, rye, maize, flax, hemp and tobacco are grown in large quantities, and the products of the vineyards are of a good quality.
    0
    0
  • The number of cod is still further reduced by the trade carried on in roe, large quantities of which are used in France as groundbait in the sardine fishery, while it also forms an article of human food.
    0
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  • The fishery is also carried on along the coast of Norfolk and Suffolk, where great quantities of the fish are caught with hook and line, and conveyed to market alive in "well-boats" specially built for this traffic. Such boats have been in use since the beginning of the '8th century.
    0
    0
  • Sugarcane, tobacco, maguey, cotton, in small quantities, and fruits are also produced.
    0
    0
  • Temperance in the use of alcohol has followed the demonstration not only of its unimportance as a food or tonic, but also of its harmfulness, save in very small quantities.
    0
    0
  • The coinage had not only been seriously debased during the closing years of the Tokugawa regime, but large quantities of paper currency had been issued and circulated, both by many of the feudal lords, and by the central government itself, as a temporary expedient for filling an impoverished exchequer.
    0
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  • In the burntofferings of male kine to Isis, the carcase of the steer, after evisceration, was filled with fine bread, honey, raisins, figs, frankincense, myrrh and other aromatics, and thus stuffed was roasted, being basted all the while by pouring over it large quantities of sweet oil, and then eaten with great festivity.
    0
    0
  • The enormous quantities of Roman coins may be accounted for by consideration of the well-known practice of the Romans to make these imperishable monuments subservient towards perpetuating the memory, not only of their conquests, but also of those public works which were the natural result of their successes in remote parts of the world.
    0
    0
  • Wooden or steel buckets, holding from 35 to 200 gallons, are employed only for temporary or auxiliary service or for small quantities of water in shallow shafts.
    0
    0
  • In mining operations explosives are used on a large scale and the powder gases contain large quantities of the very poisonous gas, carbon monoxide, a small percentage of which may cause death, and even a minute percentage of which in the air will seriously affect the health.
    0
    0
  • The efficiency of such ventilating furnaces is low, and they cannot safely be used in mines producing fire-damp. They are sometimes the cause of underground fires, and they are always a source of danger when by any chance the ventilating current becomes reversed, in which case the products of combustion, containing large quantities of carbon dioxide, will be drawn into the mine to the serious danger of the men.
    0
    0
  • To guard against explosions from this cause it is necessary to use explosives in moderate quantities and to see that the blast-holes are properly placed, so that the danger of blown-out shots may be lessened.
    0
    0
  • Where large quantities of fire-damp are present, safety-lamps of approved pattern must be used and carefully inspected daily.
    0
    0
  • The quarry mines on the top of the hill near Tawmaw produce enormous quantities, but the quality is not so good.
    0
    0
  • England takes by far the greatest share of Burma's rice, though large quantities are also consumed in Germany, while France, Italy, Belgium and Holland also consume a considerable amount.
    0
    0
  • A high silica-content tends towards both hardness and chemical stability, and this can be further increased by the addition of small proportions of boric acid; in larger quantities, however, the latter constituent produces the opposite effect.
    0
    0
  • When a suitable temperature for the fusion of the particular glass in question has been attained, the mixture of raw materials is introduced in comparatively small quantities at a time.
    0
    0
  • - Sheet-glass is almost wholly a soda-lime-silicate glass, containing only small quantities of iron, alumina and other impurities.
    0
    0
  • For the production of coloured sheet-glass, however, the employment of pot furnaces is still almost universal, probably because the quantities of glass required of any one tint are insufficient to employ even a small tank furnace continuously; the exact control of the colour is also more readily attained with the smaller bulk of glass which has to be dealt with in pots.
    0
    0
  • Oxides of iron and manganese can only be used in glass manufacture in comparatively small quantities for the purpose of colouring or neutralizing colour in glass, and their introduction would not be a matter of sufficient importance to be specially recorded.
    0
    0
  • The vessels of later date which have been found in considerable quantities, principally in the coast towns and islands of the Mediterranean, are amphorae and alabastra, also decorated with zigzag lines.
    0
    0
  • Thenceforward the manufacture continued to grow in importance; glass vessels were made in large quantities, as well as glass for windows.
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    0
  • Marineus Siculus, writing early in the 16th century, says that the best glass was made at Barcelona; and Gaspar Baneiros, in his Chronographia, published in 1562, states that the glass made at Barcelona was almost equal to that of Venice and that large quantities were exported.
    0
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  • About 1350 considerable quantities of colourless flat glass were supplied by John Alemayn of Chiddingfold for glazing the windows in St George's chapel, Windsor, and in the chapel of St Stephen, Westminster.
    0
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  • They also collect honey in large quantities.
    0
    0
  • Large quantities of grain are shipped in lighters to Braila.
    0
    0
  • This theorem was published in 1643, at the end of his treatise De motu gravium projectorum, and it was confirmed by the experiments of Raffaello Magiotti on the quantities of water discharged from different ajutages under different pressures (1648).
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  • Unfortunately, however, the confusion engendered by a defective organization has long been a byword among the people; there is no printed catalogue, quantities of books are buried in packingcases and unavailable, the collection of foreign books is very poor, hardly any new works being purchased, and the building itself is quite inadequate and far from safe; but the site of a new one has now been purchased and the plans are agreed upon, so that eventually the whole collection will be transferred to more suitable quarters.
    0
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  • These latter pass to automatic weighing machines, which drop them, in quantities of 1 cwt., into wooden boxes of uniform measurement, made to contain that weight; and the boxes are then conveyed to the storehouse, ready for sale.
    0
    0
  • Quantities of raw and refined cane and beet sugar in tons avoirdupois imported into the United Kingdom in 1870 and in 1875, and yearly from 1880 to 1901 inclusive, with the consumption per head of the population in lb and the price per cwt.
    0
    0
  • The quantities for India have been computed from information furnished by the India office, and publications made under authority of the secretary of state and the commercial intelligence department of the Indian government.
    0
    0
  • The addition of small quantities of lime, especially in a caustic form, to stiff greasy clays makes them much more porous and pliable.
    0
    0
  • This is generally effected by adding the calculated amount of potassium chloride (of which immense quantities are obtained as a by-product in the Stassfurt salt industry) dissolved in hot water to a saturated boiling solution of sodium nitrate; the common salt, which separates on boiling down the solution, is removed from the hot solution, and on cooling the potassium nitrate crystallizes out and is separated and dried.
    0
    0
  • Wall-saltpetre or lime saltpetre, calcium nitrate, Ca(N03)2, is found as an efflorescence on the walls of stables; it is now manufactured in large quantities by fixing atmospheric nitrogen, i.e.
    0
    0
  • In making cigars by the hand, the operator rolls together a sufficient quantity of material to form the filling of one cigar, and experience enables him or her to select very uniform quantities.
    0
    0
  • Cheroots come principally from Manila, but there are now large quantities imported into the United Kingdom from the East Indies and Burma.
    0
    0
  • Traces of ancient workings were found in several places, but the ores did not contain gold in paying quantities.
    0
    0
  • Large quantities of timber are floated down the Ilz.
    0
    0
  • The main objection to the Hempel is the retention of liquid in the beads, and the consequent inapplicability to the distillation of small quantities.
    0
    0
  • For efficiency the operation must be conducted with small quantities; caking may be prevented by mixing the substance with sand or powdered pumice, or, better, with iron filings, which also renders the decomposition more regular by increasing the conductivity of the mass.
    0
    0
  • The southern half of the province, that portion south of the Yangtsze Kiang, forms part of the Nan-shan, or hilly belt of the south-eastern provinces, and produces, besides cotton, coal and iron ore, large quantities of green tea.
    0
    0
  • Solingen is one of the chief seats of the German iron and steel industry, its speciality consisting in all kinds of cutlery, Solingen sword-blades have been celebrated for centuries, and are widely used outside Germany, while bayonets, knives, scissors, surgical instruments, files, steel frames and the like are also produced in enormous quantities.
    0
    0
  • Silver and gold are produced, but they are not known to exist in any large quantities.
    0
    0
  • Lead is of frequent occurrence, and indeed the area through which copper, silver, lead, tin and zinc are distributed in sufficient quantities to make mining answer, comprises at least 80,000 sq.
    0
    0
  • Sugar, cotton, Indian corn, beans and considerable quantities of wheat are grown, but agriculture is largely hampered by the uncertainty of the rainfall.
    0
    0
  • The wine of the neighbourhood, which resembles port, is shipped in large quantities from Barcelona; and the district furnishes fine roses and strawberries for the Barcelona market.
    0
    0
  • There are also present small quantities of arsenic and antimony, and zinc is found generally as a mere trace, but sometimes reaching to 6%.
    0
    0
  • From that time forward the Arita factories turned out large quantities of porcelain profusely decorated with blue under the glaze and colored enamels over it.
    0
    0
  • A ware of which considerable quantities have found their way westward of late years in the Awcfji-yaki, so called from the island of Awaji where it is manufactured in the village of Iga.
    0
    0
  • It is produced now in considerable quantities, but the modern ware falls far short of its predecessor.
    0
    0
  • Every year large quantities of porcelain and faience are sent from the provinces to the capital to receive surface decoration, and in wealth of design as well as carefulness of execution the results are praiseworthy.
    0
    0
  • They still manufacture quantities of tea and coffee sets, and dinner or dessert services of red-and-gold porcelain for foreign markets; but about 1885 some of them made zealous and patient efforts to revert to the processes that won so much fame for the old Kutaniyaki, with its grand combinations of rich, lustrous, soft-toned glazes.
    0
    0
  • The mineral wealth of Saxe-Coburg-Gotha is insignificant, small quantities of coal, lignite, ironstone and millstone being annually raised.
    0
    0
  • Iron goods and machinery, glass, earthenware, chemicals and wooden articles, including large quantities of toys, are produced; and various branches of textile industry are carried on.
    0
    0
  • The fruit is eaten in great quantities in the southern states of America,.
    0
    0
  • The mineral wealth of Baden is not great; but iron, coal, zinc and lead of excellent quality are produced, and silver, copper, gold, cobalt, vitriol and sulphur are obtained in small quantities.
    0
    0
  • Apples are grown in such quantities as to entitle the county to the title applied to it, the orchard of Ireland.
    0
    0
  • His manner of life was simple in the extreme; his diet consisted chiefly of bread and milk and large quantities of coffee.
    0
    0
  • A special branch is the making of scythes and sickles which are exported in large quantities.
    0
    0
  • The production of ozone in small quantities during electrolysis, and by the so-called silent discharge, has long been known, and the Siemens induction tube has been developed for use industrially.
    0
    0
  • The terms trinomial, quadrinomial, multinomial, &c., are applied to expressions composed similarly of three, four or many quantities.
    0
    0
  • The exports include copper and silver and their ores, nitrate of soda, borax, guano and other minerals in small quantities.
    0
    0
  • Hilversum manufactures large quantities of floor-cloths and horse-blankets.
    0
    0
  • There is only one fairly reliable treatment, that by serum therapeutics, the injection of considerable quantities of serum of animals which have e?
    0
    0
  • They are all more or less poisonous, paralysing their prey before, or during the act of swallowing; the poison-fangs standing so far back in the mouth, these snakes cannot easily inflict wounds with them on man; moreover, the poison is not very strong and not available in large quantities.
    0
    0
  • The electrical conductivity of a metal is often very much decreased by alloying with it even small quantities of another metal.
    0
    0
  • Chromium also, in comparatively small quantities, is taking its place as a constituent of steel axles and tires, and in the manufacture of tool-steel.
    0
    0
  • Titanium is alloyed in small quantities with aluminium for use in naval architecture.
    0
    0
  • Given internally in small quantities and in sufficient dilution, alcohol causes dilatation of;he gastric blood-vessels, increased secretion of gastric juice, and greater activity in the movements of the muscular layers in the wall of the stomach.
    0
    0
  • The raised temperature appears to facilitate the oxidation of the substance, so that quantities may be taken and completely utilized which would completely intoxicate the individual had his temperature been normal.
    0
    0
  • This experiment proves that when a charged body acts by induction on an insulated conductor it causes an electrical separation to take place; electricity of opposite sign is drawn to the side nearest the inducing body, and that of like sign is repelled to the remote side, and these quantities are equal in amount.
    0
    0
  • The electric density on the sphere being uniform, the quantities of electricity on these areas are proportional to the areas, and if the electric force varies inversely as the square of the distance, the forces exerted by these two surface charges at the point in question are proportional to the solid angle of the little cone.
    0
    0
  • - The third leading fact in electrostatics is that positive and negative electricity are always created in equal quantities, and that for every charge, say, of positive electricity on one conductor there must exist on some other bodies an equal total charge of negative electricity.
    0
    0
  • Every tube of electric force must therefore begin and end on electrified surfaces of opposite sign, and the quantities of positive and negative electricity on its two ends are equal, since the force E just outside an electrified surface is normal to it and equal to a/41r, where a is the surface density; and since we have just proved that for the ends of a tube of force EdS = E 1 dS', it follows that adS = a'dS', or Q = Q', where Q and Q' are the quantities of electricity on the ends of the tube of force.
    0
    0
  • (I) in which E 0 represents the quantity of energy originally present in the body, and all the quantities are supposed, as usual, to be expressed in mechanical units.
    0
    0
  • This equation is generally true for any series of transformations, provided that we regard H and W as representing the algebraic sums of all the quantities of heat supplied to, and of work done by the body, heat taken from the body or work done on the body being reckoned negative in the summation.
    0
    0
  • The significance of relation (I) is best appreciated by considering the graphic representation of quantities of heat and energy on a work-diagram.
    0
    0
  • The area ABCD, representing the work, W, per cycle, is the difference (H' - H") of the quantities of heat absorbed and rejected at the temperatures 0 and 0".
    0
    0
  • Finally, the substance is reconverted into the first state at the temperature 0", completing the cycle by the abstraction of a quantity of heat By the application of the first law, the difference of the quantities of heat absorbed and evolved in the cycle must be equal to the work represented by the area of the cycle, which is equal to (p' - p") (v" - v') in the limit when the difference of pressure is small.
    0
    0
  • Changes of entropy must be calculated in terms of quantities of heat, and must be interpreted in a similar manner.
    0
    0
  • Large quantities of timber are imported from Canada and Norway; coal, iron, manufactured goods and agricultural produce are the chief exports.
    0
    0
  • The surrounding district produces quantities of wheat and fruits for export, and much excellent wine is made.
    0
    0
  • Gold has a characteristic yellow colour, which is, however, notably affected by small quantities of other metals; thus the tint is sensibly lowered by small quantities of silver, and heightened by copper.
    0
    0
  • The presence of minute quantities of cadmium, lead, bismuth, antimony, arsenic, tin, tellurium and zinc renders gold brittle, 2 ' 0 15th part of one of the three metals first named being sufficient to produce that quality.
    0
    0
  • Skey showed that in substances which contain small quantities of gold the precious metal may be removed by the solvent action of iodine or bromine in water.
    0
    0
  • In solution minute quantities of gold may be detected by the formation of " purple of Cassius," a bluish-purple precipitate thrown down by a mixture of ferric and stannous chlorides.
    0
    0
  • It is, however, probable that the North-Western Territory will continue to yield gold in important quantities for some time to come.
    0
    0
  • Gold and Zinc.-When present in small quantities zinc renders gold TABLE II.-Gold brittle, but it may be added to gold in larger quantities without destroying the ductility of the precious metal; Peligot proved that a triple alloy of gold, copper and zinc, which contains 5.8% of the lastnamed, is perfectly ductile.
    0
    0
  • - Small quantities of iridium do not destroy the ductility of gold, but this is probably because the metal is only disseminated through the mass, and not alloyed, as it falls to the bottom of the crucible in which the gold is fused.
    0
    0
  • The potassium salt is obtained by crystallizing equivalent quantities of potassium and auric chlorides.
    0
    0
  • The " cradle " is a simple appliance for treating somewhat larger quantities, and consists essentially of a box, mounted on rockers, and provided with a perforated bottom of sheet iron in which the " pay dirt " is placed.
    0
    0
  • The bullion left in the retorts is then melted in black-lead crucibles, with the addition of small quantities of suitable fluxes, e.g.
    0
    0
  • Thus Strabo states that in his time a process was employed for refining and purifying gold in large quantities by cementing or burning it with an aluminous earth, which, by destroying the silver, left the gold in a state of purity.
    0
    0
  • The Carpathian system is richer in metallic ores than any other mountain system of Europe, and contains large quantities of gold, silver, copper, iron, lead, coal, petroleum, salt, zinc, &c., besides a great variety of useful mineral.
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  • The place is surrounded by extensive vineyards and orchards, all well watered by canals led from the river, and producing great quantities of fruit for exportation to Russia.
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  • It has manufactures of cloth, leather, chemicals and optical instruments; large quantities of beetroot sugar are produced in the neighbourhood; and there is a considerable transit trade on the Elbe.
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  • In 1798 the town mills were converted into a woollen manufactory, which up to recent times produced large quantities of cloth, and the serge manufacture was introduced early in the 19th century.
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  • Grain and fruit are grown in large quantities, and much coal is mined in the vicinity of Kirksville.
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  • The hypothesis that the state was steady, so that interchanges arising from convection and collisions of the molecules produced no aggregate result, enabled him to interpret the new constants involved in this law of distribution, in terms of the temperature and its spacial differential coefficients, and thence to express the components of the kinetic stress at each point in the medium in terms of these quantities.
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  • In later memoirs Reynolds followed up this subject by proceeding to establish definitions of the velocity and the momentum and the energy at an element of volume of the molecular medium, with the precision necessary in order that the dynamical equations of the medium in bulk, based in the usual manner on these quantities alone, without directly considering thermal stresses, shall be strictly valid - a discussion in which the relation of ordinary molar mechanics to the more complete molecular theory is involved.
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  • None of them, in point of fact, has held its ground, and even his proposal to denote unknown quantities by the vowels A, E, I, 0, u, Y - the consonants B, c, &c., being reserved for general known quantities - has not been taken up. In this denotation he followed, perhaps, some older contemporaries, as Ramus, who designated the points in geometrical figures by vowels, making use of consonants, R, S, T, &c., only when these were exhausted.
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  • This does not mean, what is often alleged, that nobody before him had ever thought of choosing symbols different from numerals, such as the letters of the alphabet, to denote the quantities of arithmetic, but that he made a general custom of what until his time had been only an exceptional attempt.
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  • On the other hand, Vieta was well skilled in most modern artifices, aiming at a simplification of equations by the substitution of new quantities having a certain connexion with the primitive unknown quantities.
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  • It may be that the study of such sums, which he found in the works of Diophantus, prompted him to lay it down as a principle that quantities occurring in an equation ought to be homogeneous, all of them lines, or surfaces, or solids, or supersolidsan equation between mere numbers being inadmissible.
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  • Lead and zinc are mined in much smaller quantities, alum and sulphur are also.
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  • Small quantities are occasionally met with in iron pyrites, and hence tellurium is found with selenium in the flue dust, or chamber deposits of sulphuric acid works.
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  • Large quantities of small fruits, particularly of strawberries, raspberries and blackberries, are produced, the southern portion of Sussex county being particularly favourable for strawberry culture.
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  • Larger quantities of deposit may be conveniently collected by means of the dredge, which can be worked in any depth and brings up large stones, concretionary nodules or fossils, of the existence of which a sounding-tube could give no indication.
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  • Sir John Murray finds the source of the phosphoric acid to be the decomposition of large quantities of animal matter, and he illustrates this by the well-known circumstance of the death of vast shoals of fish when warm Gulf-Stream water displaces the cold current which usually extends to the American coast.
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  • 5 cc. per litre at o C. while as a matter of fact the amount absorbed approaches 50 cc. The form of combination is unstable and apparently variable, so that the quantities of free carbonic acid, bicarbonate and normal carbonate are liable to alter.
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  • Australia possesses fields of great value, principally in the south-east (New South Wales and Victoria), and in New Zealand considerable quantities of coal and lignite are raised, chiefly in South Island.
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  • The props used are preferably of small oak or English larch, but large quantities of fir props, cut to the right length, are also imported from the north of Europe.
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  • The danger of explosion when gas exists in very small quantities is greatly increased by the presence of coal dust.
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  • In all British coal-mines, when gas in dangerous quantities has appeared within three months, and in all places that are dry and dusty, blasting is prohibited, except with Safety ex= c, „ permitted explosives, whose composition and pro perties have been examined at the testing station at the Royal Arsenal, Woolwich.
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  • This residue consists of sodium, potassium and lithium chlorides, with small quantities of caesium and rubidium chlorides.
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  • The methods which can be and have been employed from time to time for the formation of acetylene in small quantities are exceedingly numerous.
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  • It can be kept unaltered in dry air, but the smallest trace of moisture in the atmosphere leads to the evolution of minute quantities of acetylene and gives it a distinctive odour.
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  • The purity of the carbide entirely depends on the purity of the material used in its manufacture, and before this fact had been fully grasped by manufacturers, and only the purest material obtainable employed, it contained notable quantities of compounds which during its decomposition by water yielded a somewhat high pro portion of impurities in the acetylene generated from it.
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  • The formation of hydrogen is caused by small traces of metallic calcium occasionally found free in the carbide, and cases have been known where this was present in such quantities that the evolved gas contained nearly 20% of hydrogen.
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  • In Shan-hwa Fu coal is also found, but not in such quantities as in the places above named.
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  • Iron and silver also exist in small quantities in different parts of the province, and hot and warm springs are very common at the foot of the hills along the northern and western edges of the province.
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  • Fruits and vegetables are also grown in large quantities.
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  • Most of the large Texas rivers have deposited great quantities of silt along their lower courses on the Coastal Plain, where the current is often sluggish and the banks are periodically overflowed.
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  • Other minerals found in small quantities are copper, lead, zinc, iron ores, manganese ores and tin.
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  • It is by the help of numbers that concrete quantities are practically measured and calculated.
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  • The attempt to apply numerical methods to the comparison of geometrical quantities led to the doctrine of incommensurables, and to that of the infinite divisibility of space.
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  • " In the same way, a theory that some particular substance, say water, is homogeneous and continuous may be a good working theory up to a certain point, but may fail when we come to deal with quantities so minute or so attenuated that their heterogeneity of structure comes into prominence.
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  • This and the difficulty of obtaining accurate experimental results fully account for the differences inter se in the values of the quantities calculated.
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  • The cultivated products include coffee, the Coco-nut palm, tobacco, sugar-cane, cotton, vanilla, sorghum, earthnuts, sesame, maize, rice, beans, peas, bananas (in large quantities), yams, manioc and hemp. Animal products are ivory, hides, tortoiseshell and pearls.
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  • Large quantities of rice are imported from German East Africa.
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  • Small quantities of ebony and sandal-wood are exported.
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  • Oats is the principal crop, but rye, potatoes and flax are also grown in considerable quantities.
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  • Salt is also found in large quantities; but mining and quarrying are not practised on a large scale; only lead, lignite and asphalt being worked.
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  • Large quantities of benzoin are used as incense.
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  • Gold has been found in small quantities in Middlesex, Norfolk and Plymouth counties.
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  • Though cod is much the most important fish (in 1905 fresh cod were valued at $991,679, and salted cod at $696,928), haddock (fresh, $1,051,910; salted, $17,194), mackerel (value in 1905, including horse mackerel, $970,876), herring (fresh, $266,699; salted, $114,997), pollock ($267,927), hake ($258,438), halibut ($218,232), and many other varieties are taken in great quantities.
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  • From 1861-91 methylated spirits prepared in this way were allowed to be sold by retail in Great Britain in small quantities for domestic purposes such as cleaning, heating and lighting; but use in large quantities, or in manufacture, was only possible under special authority and under excise supervision.
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  • Alcohol was used in Germany for many years before the World War in increasing quantities as a source of heat, but its application for light and power started about 1887.
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  • Foodstuffs could not be grown in the United Kingdom at sufficiently low prices, nor in sufficient quantities, to produce alcohol commercially and on a large scale.
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  • Investigations started in 1920 by the British Government, in connexion with the production of alcohol for power purposes, have shown, however, that there are large areas of suitable land in the British Empire where the cost of production would be comparatively low, and where it might be possible to grow vegetable substances in excess of food requirements, and in sufficient quantities to produce alcohol for local consumption to replace expensive petrol.