O sentence example

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  • As he rose in the morning he prayed: " O God, grant that throughout this coming day I may be able to love my neighbour as myself."
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  • When distilled over lead oxide, it forms diphenylene oxide, (C 6 H 4) 2 O: and when heated with oxalic acid and concentrated sulphuric acid, it forms aurin, C19H1403.
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  • O CH 3, is prepared either by the above method or by the action of diazomethane on phenol, C6HSOH+CH2N2=N2+C6H5.
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  • O C 2 H 51 a liquid boiling at 172° C., may be obtained by similar methods.
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  • O Coch 3, a colourless liquid of boiling point 193° C., may be prepared by heating phenol with acetamide.
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  • About £1 4 o per acre was paid for the lease of the land, which after two years was restored to its owners re-soiled and levelled.
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  • The pseudo-coprolites of the Suffolk Crag have been estimated by Herapath to be as rich in phosphates as the true ichthyo-coprolites and saurio-coprolites of other formations, the proportion of P 2 O 5 contained varying between 12.5 and 37.25%, the average proportion, however, being 32 or 33%.
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  • The acid renders it available as a manure by converting the calcium phosphate, Ca 3 P 2 O 8, that it contains into the soluble monocalcium salt, CaH 4 P 2 O 8, or "superphosphate."
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  • He himself superintended all the preparations, visiting Darnley with Mary on the night of the crime, Sunday, 9th of February 1567, attending the queen on her return to Holyrood for the ball, and riding back to Kirk o' Field to carry out the crime.
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  • At present this otherwise excellent preparation is not standardized, but the suggestion has been made that it should be standardized to contain o 1% of colchicine.
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  • The yearly rainfall at these three places is 21 o, 16.
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  • From Garmat Ali, where the Tigris and Euphrates at present unite,' under the title of Shattel-Arab, the river sweeps on to Basra, Ex p o yds.
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  • Annaberg, together with the neighbouring suburb, Buchholz, is the chief seat of the braid and lace-making industry in Germany, introduced here by Barbara Uttmann in 1561, and further developed by Belgian refugees, who, driven from their country by the duke of Alva, settled here in 15 9 o.
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  • Constant use, increased friction (m o r e especially at high speeds), and damage to the rotator will alter an ascertained log error; head or following seas, strong winds, currents and tidal streams also FIG.
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  • In many cases it acts as a reducing agent (when used in the presence of acids); thus, permanganates are reduced to manganous salts, iodates are reduced with liberation of iodine, &c., 2KMnO 4 + 550 2 + 2H 2 0 = K 2 SO 4 + 2MnSO 4 + 2H 2 SO 4; 2K103+ 550 2 + 4H 2 O =1 3 + 2KHSO 4 + 3H2S04.
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  • Disulphuryl chloride, S 2 O 5 C1 2, corresponding to pyrosulphuric acid, is obtained by the action of sulphur trioxide on sulphur dichloride, phosphorus oxychloride, sulphuryl chloride or dry sodium chloride: 650 3- + 2POC1 3 = P 2 O 5 + 3S 2 O 5 C1 2; S2C12+ 5503 = S 2 0 5 C1 2 + 550 2; SO 3 + SO 2 C1 2 = S 2 0 5 C1 2; 2NaC1 + 3SO 3 = S 2 0 5 C1 2 -1 Na 2 SO 4.
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  • The average number of women to every 100 men in the Russian governments proper was 102.9; in Poland, 98.6; in Finland, 102.2; in Caucasia, 88.9; in Siberia, 93'7; and in Turkestan and Transcaspia, 83 o.
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  • ': opal e ° °o T A R ple ' ag a ',ap iJ,wl Karkinit A C K r B L Scale, English Miles D S E A 32 Stavropol P O L A PI A N L A s E Derbent ° I?
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  • 3 law schools, 4 veterinary institutes, 4 agricultural colleges, 2 mining institutes, 4 engineering institutes, 2 universities for women (93 o students at St Petersburg), 3 technical pedagogic schools, to technical institutes, I forestry and 1 topographical school.
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  • F o i Notwithstanding the efforts of the Poles and the Military Orders to exclude Russia from the shores of the Baltic and keep her in a state of isolation, she was coming slowly into closer relations with central and western Europe.
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  • 199,371 In the United States railway mileage now tends to increase at the rate of slightly over 5000 miles a year, which is about 2 ° o on the present main line mileage.
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  • 1.9 8.8 Dutch Indies o 6 0.5 Siam 2..
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  • Po o 8 I 3 3.5 I I.
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  • The number of passengers (36) killed in train accidents in 1907 was equal to o 0759 per million passengers carried and o o024 per million kilometres travelled by passengers, or 0.1503 per million kilometres travelled by trains.
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  • In the United States a committee of the American Society of Civil Engineers, appointed to consider the question of rail manufacture in consequence of an increase in the number of rail-failures, issued an interim report in 1907 in which it suggested a range of carbon from 0-55 to 0-65% for the heaviest sections of Bessemer steel flange rails, with a phosphorus maximum of 0.085%; while the specifications of the American Society for Testing Materials, current at the same period, put the carbon limits at o 45 to 0-55%, and the phosphorus limit at o io.
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  • The relation between the b.h.p. and the torque on the driving-axle is 55 o B.H.P. =Tu., (9) It is usual with steam locomotives to regard the resistance R as including the frictional resistances between the cylinders and the driving-axle, so that the rate at which energy is expended in moving the train is expressed either by the product RV, or by the value of the indicated horse-power, the relation between them being 55 0 I.H.P. =RV (Io) or in terms of the torque 55 0 I.H.P.X€=RVe=TW (II) The individual factors of the product RV may have any value consistent with equation (to) and with certain practical conditions, so that for a given value of the I.H.P. R must decrease if V increases.
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  • D According to the Report, for the best results both H and h should be made as great as practicable, and then d= o 21D-l-o 16h, b=2d or o.
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  • - The combined engine and boiler efficiency has hitherto been taken to be o 06; actual values of the boiler efficiencies are given in Table XX.
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  • The figures in this column indicate that o 06 is a good average value to work with.
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  • Lines representing efficiency ratios of o 6, 0.5 and 0.4 are plotted on the diagram, so that the efficiency ratios corresponding to the various experiments plotted may be readily read off.
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  • This type has the advantage of economy in first construction, there being the minimum amount of material to be excavated, and no interference during construction with street traffic or subsurface structures; it has, however, the disadvantage of the cost of o p eration of lifts at the stations.
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  • ==Pagan Analogues== In ancient states common meals called sussitia (o - va - o - LTia) were instituted, particularly in the Doric states, e.g.
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  • In 18 3 o the respected missionary John Williams paid his first visit to Samoa.
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  • 2 His " priest," r o ' " priestess "; see Hommel, Rid-arabische Chrestomathie, p. 127; Ancient Hebrew Tradition, p. 278 foil.
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  • It arose from a spiritual movement in answer to the yearning of the heart: " O that Thou mightest rend the heavens and come down and the mountains quake at Thy presence !"
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  • "If thou art determined, O God, to destroy me," the unhappy Angevin exclaimed, "let my fall be gradual!"
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  • 16; presages recovery or death of patients); (4) the pelican (recalls its young to life by its own blood); (5) the owl (or nyktikorax; loves darkness and solitude); (6) the eagle (renews its youth by sunlight and bathing in a fountain); (7) the phoenix (revives from fire); (8) the hoopoe (redeems its parents from the ills of old age); (9) the wild ass (suffers no male besides itself); (1 o) the viper (born at the cost of both its parents' death); (I I) the serpent (sheds its skin; puts aside its venom before drinking; is afraid of man in a state of nudity; hides its head and abandons the rest of its body); (12) the ant (orderly and laborious; prevents stored grain from germinating; distinguishes wheat from barley on the stalk); (13) the sirens and onocentaurs (Isa.
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  • In 17 4 o he entered the army, and rumour had it that he was one of the favourites of the empress Elizabeth.
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  • Hess (18 4 o) were the first who systematically investigated thermochemical effects in solution, and arrived at conclusions from their experimental data which still possess validity.
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  • Amongst endothermic compounds may be noted hydriodic acid, HI, acetylene, C 2 H 2, nitrous oxide, N 2 O, nitric oxide, NO, azoimide, N 3 H, nitrogen trichloride, NC1 3.
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  • 1 1854 Elizabeth, daughter of Maximilian Joseph, duke of o avaria, who belonged to the younger and non-royal branch si f the house of Wittelsbach.
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  • The empress, who shared the o ~markabl beauty common to all her family, took little part V
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  • She built a castle of great beauty and magnificence, ti ailed the Achilleion, in the island of Corfu, where she often o fsided.
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  • On compulsion he stood in their midst and said: " O God, king of the universe, since these who stand with me are thy people and the besieged are thy priests, I pray thee that thou hearken not to those against these, nor accomplish what these entreat against those."
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  • His soldiers sacked the upper city and killed 6 3 o persons - men, women and children.
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  • Its north-eastern extremity, Cape Sidero, is distant about 1 z o m.
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  • Borings show that the thickness of this group varies from 35 o ft.
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  • Projecting into these sounds and between the estuaries of rivers flowing into them are extensive tracts of swamp land - the best known of these is Dismal Swamp, which lies mostly in Virginia and is about 3 o m.
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  • Although the state of North Carolina owns 70.3% of the stock (besides this Craven county holds 7.7%; Lenoir, 2.8%; and Pamlico county, 1.13%), the state casts only 35 o votes to the 700 of the private stockholders.
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  • 1 The vowels, which are ten in number (a a e e i i o o u u), were, as usual in the Semitic languages, indicated only partially by the use of consonants as vowel-letters 2 and by means of certain diacritical points, so long as Syriac remained a living language.
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  • But the second syllable of the same word shows Syriac siding with Hebrew against Arabic. Again the primitive a of Arabic is in the older (Nestorian) pronunciation of Syriac maintained, while in Jacobite Syriac and in Hebrew it passes into o: thus Ar.
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  • They reach through Extension Afghanistan and Baluchistan to the eastern districts of o ofge: Persia, and along the coast of Makran to that of Arabia.
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  • There is also a corresponding diffusion o f Japanese and Chinese forms along this zone, these being most numer - ous in the eastern Himalaya, and less frequent in the west.
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  • Some misunderstanding has been caused by the confusion of Edom (cis) and Aram (o,·) in viii.
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  • Amongst these glycerides may be mentioned the following: Tristearin - C 3 H 5 (O C1 8 H350)3.
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  • C 3 H 5 (O C i cH 31 0) 3.
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  • Thus in cows' butter, tributyrin, C 3 H 5 (O C 4 H 7 0) 3, and the analogous glycerides of other readily volatile acids closely resembling butyric acid, are present in small quantity; the production of these acids on saponification and distillation with dilute sulphuric acid is utilized as a test of a purity of butter as sold.
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  • Triacetin, C 3 H 5 (O C 2 H 3 0) 3, is apparently contained in cod-liver oil.
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  • Even to the present day the legend has 1 It is probable that the story of the piercing of his feet is a subsequent invention to explain the name, or is due to a false etymology (from oih&o), 01St rovs in reality meaning the "wise" (from oTSa), chiefly in reference to his having solved the riddle, the syllable - irovs having no significance.
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  • It is an oxide of iron having the formula Fe 3 O 4, corresponding with 72.4% of metal, whence its great value as an ore.
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  • It may be regarded as a ferroso-ferric oxide, FeO.Fe 2 O 3, or as iron ferrate, Fe"Fe 2 '0 4.
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  • Closely related to magnetite is the rare volcanic mineral from Vesuvius, called magnoferrite, or magnesioferrite, with the formula MgFe 2 O 4; and with this may be mentioned a mineral from Jakobsberg, in Vermland, Sweden, called jakobsite, containing MnFe204.
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  • Of prize sheep at the centenary show the largest average daily gain was o.
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  • - P l e u r o c e r i d a e.
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  • A=D= -_-- - - ---Island =r= b = o =ir- monument by James Edward Kelly to General Fitz John Porter; a cottage hospital (1886); a United States naval hospital (1891); a home for aged and indigent women (1877); and the Chase home for children (1877).
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  • The characteristic conveyances on the canals of Venice - which take the place of cabs in other cities - are the gondolas, flat-bottomed boats, some 3 o ft.
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  • Their chief towns were Massieville or Manchester (17 9 o) and Chillicothe (1796).
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  • Frau Holda; others, like the Welsh Pwck, the Lancashire boggarts or the more widely found Jack-o'-Lantern (Will o' the Wisp), are sprites who do no jmore harm than leading the wanderer astray.
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  • On 21 referenda, io being questions of license, the ratio of actual to registered voters ranged on the latter from 57.00 to 75.38% (mean 67.15), and on other referenda from 75.6 3 t o 33.4 0 (mean 61.39), - the mean for all, 64.18.
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  • Of the foreign-born population these elements constituted respectively 35.6, 24 o, 7.6, 7 o, 6.7 and 5.3%.
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  • (1 75318 3 o), an educated prince who shared the tastes and friendships of his mother, Caroline, became landgrave.
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  • Generally, while there is a relative poverty of zoological groups, there is a great wealth of species within the group. Of gammarids, there are as many as 300 species, and those living at great depths (33 o to 380 fathoms) tend to assume abyssal characters similar to those displayed by the deep-sea fauna of the ocean.
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  • I 3 Good middling Texas I o Good middling Upland I o Indian Cottons Fine Tinnevelly Fine Bhaunagar Fine Amraoti Fine Broach.
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  • The seed is dropped from a planter, five or six seeds in a single line, at regular intervals i o to 1 2 in.
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  • A field is gone over carefully, and perhaps some 5 o of the best plants selected; a second examination in the field reduces these perhaps to one half, and each plant is numbered.
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  • Thus if a person holds futures for 10,000 bales which stood at 5.20 on the last settlement day and now stand at 5.30, and in the course of the previous week has sold 5000 bales of " futures " at 5.1 o, he receives 10,000 X - i ce o d.
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  • If either party is dissatisfied with the award, he may appeal to an appeals committee on paying 3:o: which is refunded to him by the other party if the appeal be upheld.
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  • For drilling the deeper wells, the derrick, on account of the length of the " string " of drilling tools, is usually at least 7 o ft.
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  • A change of the Hebrew text seems necessary; possibly we should read S1p $t"', "low is the voice," instead of 51p$ o'p', "he rises up at the voice."
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  • Inland the Malays live by M o e, o preference on the banks of rivers, building houses on piles some feet from the ground, and planting groves of coco-nut, betel-nut, sugar-palm and fruit-trees around their dwellings.
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  • It possesses the five vowels a, i, u, e, o, both short and long, and one pure diphthong, au.
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  • Of the total area 54.8% is occupied by arable land, 7% by meadows, 5.7% by pasturages, 1.2% by gardens, o.
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  • Potassium ruthenium cyanide, K4Ru(CN) 6.3H 2 O, formed when potassium ruthenate is boiled with a solution of potassium cyanide, crystallizes in colourless plates which are soluble in water.
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  • An opportunity of retaliating on the nobility was afforded him by the arrival (1 o 1) of ambassadors from Mithradates VI.
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  • 8 6 CO 3 5 O // 3 Xanthone.
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  • Again, in nitrous oxide we have a compound of 8 parts by weight of oxygen and 14 of nitrogen; in nitric oxide a compound of 16 or 8 X 2 parts of oxygen and 1 4 of nitrogen; in nitrous anhydride a compound of 24 or 8 X 3 parts of oxygen and 14 of nitrogen; in nitric peroxide a compound of 3 2 or 8 X 4 parts of oxygen and 14 of nitrogen; and lastly, in nitric anhydride a compound of 4 o or 8 X 5 parts of oxygen and 14 of nitrogen.
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  • When nitric peroxide, N204, is converted into gas, it decomposes, and at about 180° C. its vapour entirely consists of molecules of the composition N02; while at temperatures between this and o C. it consists of a mixture in different proportions of the two kinds of molecules, N 2 O 4 and N02.
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  • It is often convenient to regard compounds as formed upon certain types; alcohol, for example, may be said to be a compound formed upon the water type, that is to say, a compound formed from water by displacing one of the atoms of hydrogen by the group of elements C 2 H 5, thus - H C2H5 O H O H Water Alcohol.
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  • Inorganic Chemistry Inorganic chemistry is concerned with the descriptive study o f the elements and their compounds, except those of carbon.
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  • Compounds containing the group - CH: O are known as aldehydes (q.v.), while the group >C: O (sometimes termed the carbonyl or keto group) characterizes the ketones (q.v.).
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  • 1.2 or 1.6, named ortho- (o), 1.3 or 1.5, named meta- (m), and 1.4, named para- compounds (p).
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  • The specific heat of indium is o 057; and the atomic heats corresponding to the atomic weights 38, 76 and 114 are 3.2, 4.3, 6.5.
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  • 6 1.86 3.01 o 88 1.03 Since at the boiling-point under atmospheric pressure liquids are in corresponding states, the additive nature of the critical coefficient should also be presented by boiling-points.
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  • The principal chromophores are the azo, -N = N -, azoxy, = N 2 O, nitro, - N02, nitroso, - NO, and carbonyl, = CO, groups.
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  • Hantzsch explains the transformation of the colourless acid into red salts, which on standing yield more stable, colourless salts, by the following scheme: N R.0N O H R CA O R'CC NO 2Na 2 O?
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  • In the case of sodium dihydrogen phosphate, NaH 2 PO 4 H 2 O, a stable rhombic form is obtained from warm solutions, while a different, unstable, rhombic form is obtained from cold solutions.
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  • I o.
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  • The chief of these ministers is denoted 6 E7rl r&o' 7r pay µarwv, and he corresponds to the vizier of the later East.
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  • A distinguished philosopher or man of letters would find them bidding f o r his presence, and most of the great names are p ?
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  • Thus the French survey commission of 1828 fixed the proportion of black to white at one and a half times the angle of slope; while in Austria, where steep mountains constitute an important feature, solid black has been reserved for a slope of 80°, the proportion of black to white varying from 80:o (for 50) to 8: 72 (for 5°).
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  • The introduction of additional diacritical marks, such as - and used to express quantity, and the diaeresis, as in ai, to express consecutive vowels, which are to be pronounced separately, may prove of service, as also such letters as a, o and ii, to be pronounced as in German, and in lieu of the French ai, eu or u.
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  • One of the most distinguished among them was Thales of Miletus (6 4 o -543 B.C.), the founder of the Ionian school of philosophy, whose pupil, Anaximander (611-546 B.C.) is credited by Eratosthenes with having designed the first map of the world.
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  • 111111111161111111111? ?I?ri1111111___?????o??
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  • _? ?w?lan F?,o i o a p oba - ?
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  • So that in the view of Barnabas the Messianic reign still belongs to ounros o auov.
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  • In 616 it was taken by Chosroes, king of Persia; and in 6 4 o by the Arabians, under `Amr, after a siege that lasted fourteen months, during which Heraclius, the emperor of Constantinople, did not send a single ship to its assistance.
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  • The assignats had now become totally valueless - the abolition of the "maximum" the previous year (1795) had produced no effect, and, though, by various payments into the treasury, the total number had been reduced to about 24,000,000,000 francs, their face-value was about 3 o to I of coin.
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  • The state bureau of agriculture in 1903 estimated that of the total area 14.9 millions of acres were timber land, 5.7 millions pasture and marsh, and 5 o millions cultivated farm land.
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  • The calcium salt, CaN 2 O 2.4H 2 O, formed by the action of calcium chloride on the silver salt in the presence of a small quantity of nitric acid, is a lustrous crystalline powder, almost insoluble in water but readily soluble in dilute acids.
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  • If a is a cardinal number, then ad-i #o.
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  • But the definition of the cardinal number of a class applies when the class is not finite, and it can be proved that there are different infinite cardinal numbers, and that there is a least infinite cardinal, now usually denoted by o where to is the Hebrew letter aleph.
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  • This last number exemplifies the fact that one signed real number, such as o, may be correlated to many of the n cardinals, such as 2.
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  • ?MasalCa; o o ?novo Uskiib, y fi a S E A Trnovo° L ?
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  • ` Li A7 t y, ., / ..Tachlno _ 1LlAm t o us J ° a ?
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  • 0,Leuca Santa 0 lf G.of Chander li r tiaid arPash o 1 SEA OF KQUIn ?
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  • The new sultan's reign marked, if not the beginning, at least the high tide Aba-ui-Aziz, o f that course of improvident and unrestrained 1861-1876.
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  • The Kurds, the constant oppressors of that people, had received official recognition and almost complete immunity from the control o f the civil law by being formed into a Y g eo Y manry frontier-guard known as the Hamidian cavalry.
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  • Peary and Astrup, as already indicated, crossed in 1892 the northern part of the inland ice between 78° and 82° N., o reaching a height of about 8000 ft., and deter mined the northern termination of the icecovering.
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  • This island, which is separated by Waigat Strait from the Nugsuak peninsula, is o lofty, and has an area of 3005 sq.
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  • To this period also belongs the massive rampart, over o ft.
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  • Of the 60 °,o that penetrates only about onethird actually heats up the surface of the land or sea and the rest is absorbed by the atmosphere.
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  • 18.14%, S=0.96%, O = 22.66%, which points to the formula C720H1134N218S50241, corresponding to the molecular weight 16,954.
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  • Battle of In this battle the French numbered about 20,000 with Corunna, 4 o guns; the British 15,000 with 9 very light guns.
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  • Hamburg has comparatively few secular buildings of great architectural interest, but first among them is the new Rathaus, a huge German Renaissance building, constructed of sandstone in 1886-1897, richly adorned with sculptures and with a spire 33 o ft.
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  • In i i i o Hamburg, with Holstein, passed into the hands of Adolph I., count of Schauenburg, and it is with the building of the Neustadt (the present parish .of St Nicholas) by his grandson, Adolph III.
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  • The mean result of the best determinations shows that when a current of one ampere is passed for one second, a mass of silver is deposited equal to o ooi i 18 gramme.
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  • Kohlrausch has prepared water of which the conductivity compared with that of mercury was only o 4 oX 11 at 18° C. Even here some little impurity was present, and the conductivity of chemically pure water was estimated by thermodynamic reasoning as o 36X1011 at 18° C. As we shall see later, the conductivity of very dilute salt solutions is proportional to the concentration, so that it is probable that, in most cases, practically all the current is carried by the salt.
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  • The hydrogen at the cathode is developed by the secondary action 2Na+2H 2 O =2NaOH+H2.
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  • Thus, diminishing the concentration of the cadmium iodine solution from normal to one-twentieth normal changes the transport number from I 12 to o 64.
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  • The mean values of k for other common acids were - formic, 0.0000214; acetic, o 0000180; monochloracetic, 0.0.0155; dichloracetic, 0.051; trichloracetic, 1.21; propionic, 0.0000134.
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  • If we take as an example a concentration cell in which silver plates are placed in solutions of silver nitrate, one of which is ten times as strong as the other, this equation gives E = o 060 X Io 8 C.G.S.
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  • The result is that a high electromotive force is set up, which has been calculated as o.
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  • These formulae are supported by many considerations, especially by the selective CH 2 OH CH20H CH OH CH OH C C H O
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  • 5 o dwelling north and north-east of London, rivals and neighbours of the Catuvellauni.
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  • If ozone is passed into a solution of rubber in chloroform the caoutchouc combines with a molecule of ozone forming a compound of the empirical composition C 5 H 8 O 8.
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  • The form of the name Hadrumetum varied much in antiquity; the Greeks called it ASpbµns, 'ASpbµnros, 'ASpa o rns, ASpaµn-ros: the Romans Adrumetum, Adrimetum, Hadrumetum, Hadrymetum, &c.; inscriptions and coins gave Hadrumetum.
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  • _ .?, Niliols +?'?khu r i Ay?, N ?0° n 9 L j Khailar Scale, r :25,000,000 English Miles o iao 0 ' N,kgt hydrographical network is very imperfectly known, especially in the uninhabited hilly tracts.'
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  • Of the total in 1897, 81.4% were Russians, 8.3% Turko-Tatars, 5% Mongols and o 6% " indigenous " races, i.e.
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  • The last-named form is in the female o 36 mm.
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  • Its value is therefore O n and we have the identity D.0 = A n or D It can now be proved that the first minor of the adjoint determinant, say B rs is equal to An-2a�.
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  • =x� = o is the only solution; but if A vanishes the equations can be satisfied by a system of values other than zeros.
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  • Resultants.-When we are given k homogeneous equations in k variables or k non-homogeneous equations in k - i variables, the equations being independent, it is always possible to derive from them a single equation R = o, where in R the variables do not appear.
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  • If three equations, each of the second degree, in three variables be given, we have merely to eliminate the six products x, 2, z 2, yz, zx, xy from the six equations u = v = w = o = oy = = 0; if we apply the same process :to thesedz equations each of degree three, we obtain similarly a determinant of order 21, but thereafter the process fails.
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  • = = o, and have in consequence a vanishing resultant.
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  • It is definied as having four elements, and is written the coefficient of a0 o a1 a2 2 ...
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  • The operators ko.ki.k2 aoaai+alaa2+��., a00a i +2a11, 2 +��� are seen to be (I, o; 1, I) and (I, I; I, I) respectively.
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  • Since dp4+(-)P+T1(p +q qi 1)!dd4, the solutions of the partial differential equation d P4 =o are the single bipart forms, omitting s P4, and we have seen that the solutions of p4 = o are those monomial functions in which the part pq is absent.
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  • Instead of a single quantic we may have several f(ao, a1, a2...; x1, x2), 4 (b o, b1, b2,...; x1, x2), ...
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  • For a single quantic of the first order (ab) is the symbol of a function of the coefficients which vanishes identically; thus (ab) =a1b2-a2bl= aw l -a1ao=0 and, indeed, from a remark made above we see that (ab) remains unchanged by interchange of a and b; but (ab), = -(ba), and these two facts necessitate (ab) = o.
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  • If m > n there are n +1 transvectants corresponding to the values o, t, 2,...
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  • +na" -laan -a a O = na laao + (n 1)a 2aa1 +�..
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  • If 0 be the degree of an invariant j - aj aj a; oj =a ° a a o +al aa l +...
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  • On the one hand, assuming the quartic to have the form 4xix 2, we find i=j=o, and on the other hand, assuming i=j=o, we find that the quartic must have the form a o xi+4a 1 xix 2 which proves the proposition.
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  • We will write the cubic covariant (f, i) 2 =j, and then remark that the result, (f,j) 3 = o, can be readily established.
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  • When C vanishes j has the form j = pxg x, and (f,j) 3 = (ap) 2 (aq)ax = o.
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  • Remark.-The invariant C is a numerical multiple of the resultant of the covariants i and j, and if C = o, p is the common factor of i and j.
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  • Observe that, if we subject any symmetric function the diminishing process, it becomes ao 1 - P2 (p2p3...)� Next consider the solutions of 0=o o which are of degree 0 and weight w.
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  • Again, 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.
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  • Forms.-Taking the two forms to be a o xi + pa l x i 1x2+p(p-1)a2xr2x2-I-...
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  • 1 Ab' Establishing The Ground Forms Of Degrees Order (I, O; I), (O, I; I), (I, I; O), Viz: The Linear Forms Themselves And Their Jacobian J Ab.
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  • 1 Z2' The First Perpetuant Is The Last Seminvariant Written, Viz.: A O (B O B 2 3B O B 3) A L (Bi 2B0B2), Or, In Partition Notation, Ao(21) B (1)A(2)B; And, In This Form, It Is At Once Seen To Satisfy The Partial Differential Equation.
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  • (2A2+2l�1+1)a(2�2+1)b For the case 0=5, 0' =3, the condition is o 1 T 1 T 2 T 3 (a 1 + r)(r 1 + r 2)(o +T 3) =A1B3+AiB2B3=0.
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  • Galena (q.v.), the principal lead ore, has a world-wide distribution, and is always contaminated with silver sulphide, the proportion of noble metal varying from about o of or less to o 3%, and in rare cases coming up to 2 or i %.
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  • Such slags contain S10 2 =3033%, Fe(Mn)O =27-50%, Ca(Mg, Ba)O =12-28%, and retain less than 1% lead and I oz.
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  • A third addition becomes necessary to remove the rest of the silver, when the lead will assay only o I oz.
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  • The desilverized lead, which retains o 6-0.7% zinc, has to be refined before it is suited for industrial use.
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  • Its breaking strain is very small: a wire 1 o th in.
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  • A hydrated oxide, 2PbO H 2 O, is obtained when a solution of the monoxide in potash is treated with carbon dioxide.
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  • O, which, in turn, when boiled with a solution of boric acid, gives PbB407.4H20.
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  • Vertical section to show the ovules o, attached to the parietes.
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  • For the mean motion of the earth in one second in circular measure, we have n 8149' l o g.
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  • (9) At the point where a line of force intersects the perpendicular bisector of the axis r=r'=r o, say, and cos 0 - cos 0 obviously =l/r o, l being FIG.
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  • From the equation K=(µ - I)/47r, it follows that the magnetic susceptibility of a vacuum (where µ = I) is o, that of a diamagnetic substance (where, u I) is positive.
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  • Demagnetizing Force.-It has already been mentioned that when a ferromagnetic body is placed in a magnetic field, the resultant magnetic force H, at a point within the body, is compounded of the force H o, due to the external field, and of another force, Hi, arising from the induced magnetization of the body.
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  • Since H, generally tends to oppose the external force, thus making H less than H o, it may be called the demagnetizing force.
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  • An important instance in which the calculation can be made is that of an elongated ellipsoid of revolution placed in a uniform field H o, with its axis of revolution parallel to the lines of force.
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  • 3 +t 47fK o, Whence H Ho Ho (33) _ 3 __ 3 3r 47rK /1+2 and B =µH- + 2 Ho.
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  • In such cases H i = o and H =Ho.
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  • If a hollow sphere 7 of which the outer radius is R and the inner radius r is placed in a uniform field Ho, the field inside will also be uniform and in the same direction as Ho, and its value will be approximately 3 i - R 3 For a cylinder placed with its axis at right angles to the lines of force, 2 = Ho (41) 2 +4(-2)(i - R2) These expressions show that the thicker the screen and the greater its permeability o, the more effectual will be the shielding action.
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  • The value of the constant / 7 ranges in different metals from about o ooI to 0.04; in soft iron and steel it is said to be generally not far from 0.002.
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  • Working with two different specimens, he found that the hysteresis loss in ergs per cubic centimetre (W) was fairly represented by o 00125B 1 6 and o o0101B 1 ' 6 respectively, the maximum induction ranging from about 300 to 3000.
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  • Thin sheet iron o 367 mm.
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  • Since the demagnetizing factor was o 052, the strongest field due to the coil was about 1340; but though arrangements were pro vided for cooling the apparatus by means of o ice, great difficulty was experienced owing to heating.
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  • The coercive force at 764° 5 is stated to have been little more than o 1 C.G.S.
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  • Induction curves of an annealed soft-iron ring were taken first at a temperature of 15° C., and afterwards when the ring was immersed in liquid air, the magnetizing force ranging from about o'8 to 22.
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  • The aluminium-iron attained its greatest permeability in a field of o 5, about that of the earth's force, when its value was 9000, this being more than twice the maximum permeability of the Swedish iron.
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  • Its hysteresis-loss for B =9000 was o 236 per pound.
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  • It was, however, found that the behaviour of this alloy was in part due to a layer of pure iron (" ferrite ") averaging o 1 mm.
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  • Assuming that for water o 8X 10 - 6, his value of for oxygen at 15° C. reduces to 0 .
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  • At 0° C., o 174 X '06.
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  • If V is the volume of a ball, H the strength of the field at its centre, and re its apparent susceptibility, the force in the direction x is f= K'VH X dH/dx; and if K',, and are the apparent susceptibilities of the same ball in air and in liquid oxygen, K' Q -K'o is equal to the difference between the susceptibilities of the two media.
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  • As the temperature was raised up to 273°, gradually fell to-9.38 X 10 -6, rising suddenly when fusion occurred to - o 37X 10 -6, at which value it remained constant when the fluid metal was further heated.
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  • The mass of each is about 3 7 1 o T th part of that of a hydrogen atom, and with each is indissolubly associated a charge of negative electricity equal to about 3.1 Xio '° C.G.S.
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  • Whilst the chances are in favour of some one homoplastic coincidence or structural agreement occurring between some member or other of a large group a and some member or other of a large group b, the matter is very different 2 a o FIG.
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  • The segmentation of the prosoma and the form of the appendages bear a homoplastic similarity to the head, pro-, meso-, and meta-thorax of a Hexapod with mandibles, maxillary palps and three pairs of walking legs; while the opistho io i e d c b o a S' S" 2 I VT V S IV III II I Opisthosoma Prosoma FIG.
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  • These esters on hydrolysis yield the free acids, which readily decompose, with loss of carbon dioxide and formation of an aldehyde, R /Crri /Crri Oc< +�Cl � CH � [[Cooc H - O I ?Ch Cooc H 0c Ch�Cooh - Co +Chrr I Cho]].
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  • Its specific gravity is 0.8009 (o C.).
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  • Potash alum, K 2 SO 4 �Al 2 (SO 4)a�24H 2 O, crystallizes in regular octahedra and is very soluble in water.
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  • Sodium alum, Na 2 SO 4 �Al 2 (S04) 3 �24H 2 O, occurs in nature as the mineral mendozite.
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  • Chrome alum, K 2 SO 4 �Cr 2 (SO 4) 3.24H 2 O, appears chiefly as a by-product in the manufacture of alizarin, and as a product of the reaction in bichromate batteries.
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  • It is one of the most favoured regions of English Miles 400 o L; Barcellos rd o?
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  • 9 eneZd He .aop elo P-or o Alegre VP P'S Continuatio Southward ul (Same Scale) G 46° na, Sao own Para Blumenau 4d
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  • There were 155 of these factories in 1895, but in 1905 only 108 were in operation, with 715,000 spindles, and about 37, 00 o operatives.
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