L sentence example

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  • Hofmann, who obtained it by saturating an alcoholic solution of ammonium sulphide with sulphur and mixing the product with an alcoholic solution of strychnine, considered the resulting product to be H2S3; while P. Sabatier by fractionating the crude product in vacuo obtained an oi l which boiled between 60° and 85° C. and possessed the composition H4S5.
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  • If h is the water heat at the lower temperature, h l the water heat at the higher temperature, and L the latent heat at the higher temperature, the heat supply per pound of steam is equal to h1 - h2+L1, which, from the steam tables, with the values of the temperatures given, is equal to 1013 B.Th.U.
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  • Such l i nes are primarily intended to supply quick means of passenger communication within the limits of cities, and are to be distinguished on the one hand from surface tramways, and on the other from those portions of trunk or other lines which lie within city boundaries, although the latter may incidentally do a local or intra-urban business.
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  • I also read Tibullus, Catullus, Propertius, Horace (with Dacier's and Torrentius's notes), Virgil, Ovid's Epistles, with l"leziriac's commentary, the Ars amandi and the Elegies; likewise the Augustus and Tiberius of Suetonius, and a Latin translation of Dion Cassius from the death of Julius Caesar to the death of Augustus.
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  • The first volume was expanded into three volumes, La Gaule romaine (1891), L' Invasion germanique et la fin de l'empire (1891)and La Monarchie franque(1 888), followed by three other volumes, L'Alleu et le domaine rural pendant l'epoque merovingienne (1889), Les Origines du systeme feodal: le benefice et le patronat..
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  • Isaac Artom was Cavour's secretary, L' Olper a counsellor of Mazzini.
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  • General View Oft 'Il Sll L 1 RUM i tiL LA I.
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  • The letter L indicates the position of the labellum; the large figures indicate the developed stamens; the italic figures show the position of the suppressed stamens.
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  • E Arabian Sea Ba Of G A L e Geological information incomplete Desert Deposits Quaternary Tertiary Mesozoic Palaeozoic Archaean and Metamorphic Younger Volcanic Rocks English Miles b iuHi iiiiuiiiiii after llargl,aua Geology The geology of Asia is so complex and over wide areas so little known that it is difficult to give a connected account of either the structure or the development of the continent, and only the broader features can be dealt with here.
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  • General du Teil, younger brother of the baron, had recently published a work, L' Usage de l'artillerie nouvelle; and it is now known that Bonaparte derived from this work and from those of Guibert and Bourcet that leading principle, concentration of effort against one point of the enemy's line, which he had advocated at Toulon and which he everywhere put in force in his campaigns.
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  • The little fly-sheet of Zorn l - for it is scarcely more - on the birds of the Hercynian Forest made its appearance at Pappenheim in 1745.
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  • The claim to that succession was made in 1845 by Des Murs for his Iconographie ornithologique, which, containing seventy-two plates by Prevot and Oudart l (the latter of whom had marvellously improved in his drawings since he worked with Vieillot), was completed in 1849.
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  • These terms were explained in his great work L' Organisation du regne animal, oiseaux, begun in 1855, to mean exactly the same as those applied by Merrem to his two primary divisions.
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  • The fibrous nervetissue is more dense in the higher differentiated, more loose and spongy in the lower organized 1P L forms; the cellular nerve-tissue is FIG.
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  • L A dames, ?
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  • Iivernesso TsalaApopl sa L
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  • Its consonants are k, g, ng, ch, j, n, t, d, n, p, b, m, y, r, l, w, s, h.
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  • Its Arabic title is Kitab ul'Ibar, wa diwan el Mubtada wa'l Khabar, fi ayyamul`Arab wa'l`Ajam wa'l Berber; that is, "The Book of Examples and the Collection of Origins and Information respecting the History of the Arabs, Foreigners and Berbers."
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  • Thus the pseudo-Democritus, who was reputed the author of the Physica et Mystica, which itself concludes each of its receipts with a magical formula, was believed to have travelled in Chaldaea, and to have had as his master Ostanes l the Mede, a name mentioned several times in the Leiden papyrus, and often by early Christian writers such as Tertullian, St Cyprian and St Augustine.
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  • These early fortifications of the Acropolis, ascribed to the primitive non-hellenic Pelasgi, must be distinguished from the Pelasgicum or Pelargicum, which was in all prob ab i l i ty an encircling wall, built round the base of the g citadel and furnished with nine gates from which it derived the name of Enneapylon.
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  • In the centre was the Agora of Hippodamus; on the western margin of the Cantharus harbour extended the emporium, or Digma, the centre of commercial activity, flanked by a series of porticoes; at its northern end, near the entrance to the inner harbour, was another Agora, on the site of the modern market-place, and near it the µa?cp l OTOa, the corn depot of the state.
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  • We derived this substance from ethane by introducing a meth y l group; hence it may be termed " methylethane."
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  • In the formulae which follow we suppose 1 and l' to represent the latitudes, a and b the co-latitudes (90° - 1 or 90° - l'), and t the difference in longitude between them or the meridian distance, whilst D is the distance required.
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  • Thus, cos D - cos a cos b cos sin a sin b cos D = cos a cos b + sin a sin b cos t = sin 1 sin l' + cos 1 cos l cos t.
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  • Phison +barya L op felice Other Catalans are, Jahuda Cresques, a Jew of Barcelona, the supposed author of the famous Catalan map of the world (1375), Guglielmo Solerio (1384), Mecia de Viladestes (1413-1433) Gabriel de Valleseche (1439-1447) and Pietro Roselli, a pupil of Beccario of Genoa (1462).
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  • The works of this period are Les Philosophes Salaries, Machiavel juge des revolutions de notre temps (1849), La Federazione repubblicana (1851), La Filosofia della rivoluzione (1851), L' Italia dopo it colpo di Stato (1852), Histoire des revolutions, ou Guelfes et Gibelins (1858; Italian trans., 1871-1873).
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  • The formula is Fe n, Sn+, where n may vary from 5 to 16; usually it is Fe, S8 or Fe l s S12, the latter being also the composition of the artificially prepared compound.
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  • The dentition is i, c 1, p 4, m L total 42.
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  • The incisors tend to become latera l, the canines are enlarged, and the last upper molar is sub-quadrangular.
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  • If such a complex number is written (as usual) in the form x i e l +x 2 e 2 +...
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  • Also the "unit" e l (or e,) considered as a number of the system is merely a shortened form for the complex number (+I) ei +0e2+ +oen.
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  • The sum of two complex numbers x i e l +x 2 e 2 + ...
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  • The product of two complex numbers of the second order - namely, l e l +x 2 e 2 and y i e l +y 2 e 2, is in this case defined to mean the complex (x i y i - x 2 y 2)e i +(x i y 2 +x 2 y 1)e 2.
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  • Thus e1Xe1 = el, e 2 Xe 2 = - e l, e i X e 2 =e 2 X e 1 =e 2.
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  • With this definition it is usual to omit the first symbol e l, and to write i or A I - 1 instead of e 2.
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  • For a few months Mustafa was replaced on the throne; when he abdicated in L, favour of his nephew Murad IV.
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  • Thus, if L denote the heat corresponding with the chemical changes associated with unit electric transfer, Le will be the heat corresponding with an electric transfer e, and will also be equal to the change in internal energy of the cell.
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  • To the east of the Yablonoi border-range p l ateau: lies the lower terrace of the high plateau, reaching 2000 to 2500 ft.
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  • The l principal gold-mining regions in these tracts are the .
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  • It is this Wale ' circumstance that facilitated the rapid invasion of Siberia Wal er l by the Russian Cossacks and hunters; they followed the omm courses of the twin rivers in their advance towards the east, and discovered short portages which permitted them to transfer their boats from the system of the Ob to that of the Yenisei, and from the latter to that of the Lena, a tributary of which - the Aldan - brought them close to the Sea of Okhotsk.
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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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  • 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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  • Multiplying out the right-hand side and comparing coefficients X1 = (1)x1, X 2 = (2) x2+(12)x1, X3 = (3)x3+(21)x2x1+ (13)x1, X4 = (4) x 4+(31) x 3 x 1+(22) x 2+(212) x2x 1 +(14)x1, Pt P2 P3 P1 P2 P3 Xm=?i(m l m 2 m 3 ...)xmlxm2xm3..., the summation being for all partitions of m.
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  • The importance of the operator consists in the fact that taking any two operators of the system (I l, v; m, n); (Ill, v l : m l, n1), the operator equivalent to (I l, v; m, n) (111, v 1; ml, n1) - (i l l, v1; ml, n1) (/l, v; m, n), known as the " alternant " of the two operators, is also an operator of the same system.
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  • In this notation the fundamental relation is written (l + a i x +01Y) (I + a 2x+l32Y) (1 + a3x+133y)...
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  • If we restrict ourselves to this set of symbols we can uniquely pass from a product of real coefficients to the symbolic representations of such product, but we cannot, uniquely, from the symbols recover the real form, This is clear because we can write n-1 n-2 2 2n-3 3 a1a2 =a l a 2, a 1 a 2 = a 1 a2 while the same product of umbrae arises from n n-3 3 2n-3 3 aoa 3 = a l .a a 2 = a a 2 .
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  • We consider the quantic to have any n number of equivalent representations a- b n -c n So that a 1 -k a 2 = b l -k b 2 - c 1 -k c 2 = ...
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  • We write;L 22 = a 1 a 2 .b 1 n-2 b2s 3 n - 3 3 n-3 3 n-3 3 a 3 = a 1 a 2 .b 1 b 2 .c 1 c2, and so on whenever we require to represent a product of real coefficients symbolically; we then have a one-to-one correspondence between the products of real coefficients and their symbolic forms. If we have a function of degree s in the coefficients, we may select any s sets of umbrae for use, and having made a selection we may when only one quantic is under consideration at any time permute the sets of umbrae in any manner without altering the real significance of the symbolism.
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  • Such an expression as a l b 2 -a 2 b i, which is aa 2 ab 2 aa x 2 2 ax1' is usually written (ab) for brevity; in the same notation the determinant, whose rows are a l, a 2, a3; b2, b 2, b 3; c 1, c 2, c 3 respectively, is written (abc) and so on.
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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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  • A 1, A2 � Ai, A 1 A 2, A2 and then Ao = al Ai+2a1a2AIA2+a2 A2 - (a1A1+a2A2) 2 = a?, A l = (a 1 A 1 +a2A2) (al�l +a2�2) = aAa�, A 2 = (al�l +a2/-12) 2 = aM; so that A = aa l +2a A a u 152+aM5 2 = (aA6+a,e2)2; whence A1, A 2 become a A, a m, respectively and ?(S) = (a21+a,E2) 2; The practical result of the transformation is to change the umbrae a l, a 2 into the umbrae a s = a1A1 +a2A2, a � = a1/�1 + a21=2 respectively.
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  • For this reason the umbrae -a 2, a l are said to be cogredient to 5 1 and x 2.
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  • Since (ab) = a l b 2 -a 2 b l, that this may be the case each form must be linear; and if the forms be different (ab) is an invariant (simultaneous) of the two forms, its real expression being aob l -a l b 0.
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  • This will be recognized as the resultant of the two linear forms. If the two linear forms be identical, the umbral sets a l, a2; b l, b 2 are alternative, are ultimately put equal to one another and (ab) vanishes.
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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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  • First observe that with f x =a: = b z = ���,f1 = a l a z ', f 2 = a 2 az-', f x =f,x i +f 2 x i, we find (ab) - (a f) bx - (b f) ax.
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  • To exhibit any covariant as a function of uo, ul, a n = (aiy1+a2y2) n and transform it by the substitution fi y 1+f2 y where f l = aay 1, f2 = a2ay -1, x y - x y = X x thence f .
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  • Let a covariant of degree e in the variables, and of degree 8 in the coefficients (the weight of the leading coefficient being w and n8-2w = �), be Coxl -}- ec l l 1 x 2 -{-...
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  • For these two cases the perpetuants are enumerated by z 2 23 -z2' and l -z2.1-z3 respectively.
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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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  • For w = i the form is A i ai+Bib i, which we may write aob l -albo = ao(I) b -(I)abo; the remaining perpetuants, enumerated by z I - 2' have been set forth above.
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