Tri-, tetraand more complicated members are also known.
With ammonia they yield complex condensation products; acetone forming diand tri acetonamines (W.
Numerous di- and tri-sulphonic acids are known.
To fix a weighted point and a weighted plane in Euclidean space we require 8 scalars, and not the 12 scalars of a tri-quaternion.
The force which holds chemically dissimilar substances together (and also similar substances as is seen in di-, tri-, and poly-atomic molecules), was introduced by Hermann Boerhaave, and made more precise by Sir Isaac Newton.
If more than one compound be formed from the same two elements,, the difference is shown by prefixing such words as mono-, di-, tri-, sesqui-, per-, sub-, &c., to the last part of the name, or the suffixes -ous and -ic may be appended to the name of the first element.
The slag, in order that it may have such an excess of base that this will retain the phosphoric acid as fast as it is formed by the oxidation of the phosphorus of the pig iron, and prevent it from being re-deoxidized and re-absorbed by the iron, should, according to von Ehrenwerth's rule which is generally followed, contain enough lime to form approximately a tetra-calcic silicate, 4CaO,S10 2 with the silica which results from the oxidation of the silicon of the pig iron and tri-calcic phosphate, 3CaO,P205, with the phosphoric acid which forms. The danger of this " rephosphorization " is greatest at the end of the blow, when the recarburizing additions are made.
The chlorine is not completely precipitated by silver nitrate in nitric acid solution, the ionization apparently not proceeding to all the chlorine atoms. Thallic iodide, T11 3, is interesting on account of its isomorphism with rubidium and caesium tri-iodides, a resemblance which suggests the formula T11 (12) for the salt, in which the metal is obviously monovalent.
A collection of the various signs of the alphabet has shown thirty-two letters, four more than Arabic. De Slane, in his notes on the Berber historian Ibn Khaldun, shows the following points of similarity to the Semitic class: - its tri-literal roots, the inflections of the verb, the formation of derived verbs, the genders of the second and Arab districts to build mills for the Arabs.
It is obtained by condensing benzal chloride with mercury diphenyl (Kekule and Franchimont, Ber., 1872, 5, p. 907); from benzal chloride or benzotrichloride and zinc dust or aluminium chloride; from chloroform or carbon tetrachloride and benzene in the presence of aluminium chloride; and deamidating diand tri-aminotriphenylmethane with nitrous acid and alcohol (0.
Cyanogen iodide and iodine monoand tri-chloride effect similar decompositions with simultaneous liberation of iodine; sulphuric acid reacts slowly, forming nickel sulphate and liberating hydrogen and carbon monoxide.
Hospitals, orphanages, schools and an admirable college in Seoul have been founded, along with tri-lingual (Chinese, Korean and English) printing-presses; religious, historical and scientific works and much of the Bible have been translated into En-mun, and periodicals of an enlightened nature in the Korean script are also circulated.
Combebiac's tri-quaternions, which require the addition of quasi-scalars, independent of one another and of true scalars, and analogous to true scalars.
He arrives at the tri-quaternion as the suitable fundamental concept.
We believe that this tri-quaternion solution of the very interesting problem proposed by Combebiac is the best one.
(Note that the z here occurring is only required to ensure harmony with tri-quaternions of which our present biquaternions, as also octonions, are particular cases.) The point whose position vector is Vrq i is on the axis and may be called the centre of the bi-quaternion; it is the centre of a sphere of radius Srq i with reference to which the point and plane are in the proper quaternion sense polar reciprocals, that is, the position vector of the point relative to the centre is Srg i.
Putting 1 - n _ E we get Combebiac's tri-quaternion under the form Q= Ep+nq+wr.
Combebiac's tri-quaternion may be regarded from many simplifying points of view.
Thus, in place of his general tri-quaternion we might deal with products of an odd number of point-plane-scalars (of form, uq+wr) which are themselves point-plane-scalars; and products of an even number which are octonions; the quotient of two point-plane-scalars would be an octonion, of two octonions an octonion, of an octonion by a point-plane-scalar or the inverse a point-plane-scalar.
When Su = o, (I + 2wu) () (1 + zwu) -1 is an operator which shifts (without further change) the tri - quaternion operand an amount given by u in direction and distance.
Similar phenomena are exhibited in the electrolysis of solutions of antimony tribromide and tri-iodide, the product obtained from the tribromide having a specific gravity of 5.4, and containing 18-20% of antimony tribromide, whilst that from the tri-iodide has a specific gravity of 5.2-5.8 and contains about 22% of hydriodic acid and antimony tri-iodide.
Boron sulphide B 2 S 3 can be obtained by the direct union of the two elements at a white heat or from the tri-iodide and sulphur at 44 0 ° C., but is most conveniently prepared by heating a mixture of the trioxide and carbon in a stream of carbon bisulphide vapour.
Molybdenum combines with the halogen elements in varying proportions, forming with chlorine a di-, tri-, tetraand penta-chloride, and similar compounds with bromine and iodine.
Among these was Judah IJayyuj of Cordova, the father of modern Hebrew grammar, who first established the principle of tri-literal roots.
Catasetinae, with three tropical American genera, two of which, Cataselurn and Cycnoches, have dior tri-morphic flowers.
Citric acid, being tribasic, forms either acid monometallic, acid dimetallic or neutral trimetallic salts; thus, mono-, diand tri-potassium and sodium citrates are known.
The city has a fine natural park (Central Park) of about 30 acres; and Clyffeside Park (maintained by a private corporation), of about 75 acres, just east of the city, is a pleasure resort and a meeting-ground (with a casino seating 3000 people) for the Tri-State "Chautauqua" (for certain parts of Kentucky, Ohio and West Virginia).
Group III.: B, trivalent; Al, trivalent, but possibly also tetra-or penta-valent; Ga, divalent and trivalent; In, mono-, diand tri-valent; Tl, monovalent and trivalent..
Group VI.: 0, usually divalent, but tetravalent and possibly hexavalent in oxonium and other salts; S, Se, Te, di-, tetraand hexa-valent; Cr, di-, triand hexa-valent; Mo, W, di-, tri-, tetra-, pentaand hexa-valent.
Group VIII.: Fe, Co, divalent and trivalent; Ni, divalent; Os, Ru, hexavalent and octavalent; Pd, Pt, divalent and tetravalent; Ir, tri-, tetraand hexa-valent.
In the same way it may be shown that three tri-substitution, three tetra-substitution, one penta-substitution, and one hexa-substitution derivative are possible.
Of the tri-substitution derivatives, 1.2.3.-compounds are known as " adjacent " or " vicinal " (v), the 1.2.4 as " asymmetrical " (as), the 1.3.5 as " symmetrical " (s), of the tetrasubstitution derivatives, 184.108.40.206-compounds are known as " adjacent," 220.127.116.11 as " asymmetrical," and 18.104.22.168 as " symmetrical."
Thus in the tri-substitution derivatives six isomers, and no more, are possible when two of the substituents are alike; for instance, six diaminobenzoic acids, C 6 H 3 (NH 2) 2 000H, are known; when all are unlike ten isomers are possible; thus, ten oxytoluic acids, C 6 H 3 -CH 3.
The orientation of higher substitution derivatives is determined by considering the diand tri-substitution compounds into which they can be transformed.
By further substitution of orthoand para-diderivatives, in general the same tri-derivative [1.2.4] is formed (Ann., 1878, 192, p. 219); meta - compounds yield [1.3.41 and [1.2.
3 1 tri-derivatives, except in such cases as when both substituent groups are strongly acid, e.g.
Kane; methylethyl ketone and methyl-n-propyl ketone suffer similar condensations to s-triethylbenzene and s-tri-n-propylbenzene respectively.
Potassium chlorate and hydrochloric acid oxidize phenol, salicylic acid (o-oxybenzoic acid), and gallic acid ([2.3.4] trioxybenzoic acid) to tri chlorpyroracemic acid (isotrichlorglyceric acid), CC13 C(OH)2 C02H, a substance also obtained from trichloracetonitrile, CC1 3 CO CN, by hydrolysis.
The action of chlorine upon diand tri-oxybenzenes has been carefully investigated by Th.
Of the tri-derivatives the symmetrical compounds boil at the lowest temperature, the asymmetric next, and the vicinal at the highest.
The nitro group has a very important action mainly on account of the readiness with which it can be introduced into the molecule, but its effect is much less than that of the azo group. The colour produced is generally yellow, which, in accordance with a general rule, is intensified with an increase in the number of groups; compare, for example, mono-, diand tri-nitrobenzene.
In correspondence with the tri-regional differentiation of the body in its external configuration, the coelom (body-cavity, perivisceral cavity) is divided into three portions completely separated from one another by septa: - (I) proboscis-coelom, or first body-cavity; (2) the collar-coelom, or second body-cavity; (3) truncal coelom, or third body-cavity.
The mean values of the relative coagulative powers of sulphates of mono-, di-, and tri-valent metals have been shown experimentally to be approximately in the ratios 1 :35:1023.
I t may, however, be pointed out that Brachiopods seem to belong to that class of animal which commences life as a larva with three segments, and that tri-segmented larvae have been found now in several of the larger groups.
Hence the name of the sub-class signifying tri-lobed, a condition realized also in the Xiphosurous Arachnids.
Appendages of 1st pair.tri-segmented, chelate; of 2nd pair chelate, with their basal segments subserving mastication; of 3rd, 4th, 5th and 6th pairs similar in form and function, except that in recent and Carboniferous forms the basal segments of the 3rd and 4th are provided with sterno-coxal (maxillary) lobes, those of the 4th pair meeting in the middle line and underlying the mouth.
The same The Tri- spirit of hostility to the peasantry breathed through partitum.
The separatist movement was strongest in the south, where the Rumans were in touch with their kinsmen in Walachia and Moldavia, the Serbs with their brethren in Servia, and the Croats intent on reasserting the independence of the" Tri-une Kingdom."
He not only refused to obey, but on the 5th of June convoked to Agram the Croatian national diet, of which the first act was to declare the independence of the Tri-une Kingdom.
This particular product was insoluble in a mixture of ether and alcohol, and its composition could be expressed by the term tri-nitrocellulose.
The reaction proceeds in several stages, mono-, diand finally tri-nitrate being produced, the final stage requiring sulphuric acid as a dehydrator.
Heated above its melting point it polymerizes to di-cyandiamide (CN2H2)2, which at 150° C. is transformed into the polymer n-tri-cyantriamide or melamine (CN 2 H 2) 3, the mass solidifying.
By passing chloroform vapour over the heated dioxide the tetradiand tri-chlorides are formed, together with the free metal and a gaseous hydride, TiH 4 (Renz, Ber., 1906, 39, p. 2 49).
Cannizzaro, Ann., 1865, 1 34, p. 128), but diand tri-benzylamines are simultaneously formed.
It chanced that there existed on the polished surface of a cliff at Behistun in western Persia a tri-lingual inscription which, according to Diodorus, had been made by Queen Semiramis of Nineveh, but which, as is now known, was really the work of King Darius.
It gives origin to three classes of salts: M'H 2 PO 4 or M"H 4 P 2 0 8; M' 2 HPO 4 or M"HP04, M'3P04, M" 3 P 2 0 8 or M"'PO 4, wherein ll',M",M"' denote a mono-, di-, and tri-valent metal.
They still had a Bank Note Reporter to print, and soon got the printing of a tri-weekly paper, the Constitutionalist, the organ of some lottery dealers.
The diand tri-methyl derivatives are found in the fusel oil obtained by fermentation of beetroot sugar.
Iodine dissolves in an aqueous solution of the salt to form a dark brown liquid, which on evaporation over sulphuric acid gives black acicular crystals of the tri-iodide, K1 3.
The lower incisors have long tapering roots, but not of persistent growth; and are straight, directed somewhat forwards, with awlshaped, tri-lobed crowns.
Hydrobromic acid at 185°-190°C. converts it into diand tri-bromaniline.