E sentence example

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  • What is most worthy of notice in this method is the management of the e subordinates in the pruning for fruit.

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  • During a small electric transfer through the cell, the external work done is Ee, where E is the electromotive force.

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  • The declaration is to the effect that the clergyman has not received the presentation in consideration of any sum of money, reward, gift, profit or benefit directly or indirectly given or promised by him or any one for him to any one; that he has not made any promise of resignation other than that allowed by the Clerical Resignation Bonds Act 1828; that he has not for any money or benefit procured the avoidance of the benefice; and that he has not been party to any agreement invalidated by sec. 3 sub-sec. 3 of the act which invalidates any agreement for the exercise of a right of patronage in favour or on the nomination of any particular person, and any agreement on the transfer of a right of patronage (a) for the retransfer of the right, or (b) for postponing payment of any part of the consideration for the transfer until a vacancy or for more than three months, or (c) for payment of interest until a vacancy or for more than three months, or (d) for any payment in respect of the date at which a vacancy occurs, or (e) for the resignation of a benefice in favour of any person.

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  • See C. Revillout, E tude hist.

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  • He was assisted by the consiglio speciale of 9 0 and the consiglio generale e speciale of 300, composed of nobles, while the capitano del popolo had also two councils composed of burghers, heads of the gilds, gonfalonieri of the companies, &c. The anziani had a council of 3 6 burghers, and then there was the parlamento or general assembly of the people, which met only on great occasions.

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  • During the first centuries both branches of the Church had used vestments substantially the same, developed from common originals; the alb, chasuble, stole and pallium were the equivalents of the anxItinov, e t fvoXcov, copapcov and 1 The rationale is worn only over the chasuble.

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  • It is shown in the article on Combinatorial Analysis that (w; 0,n) is the coefficient of a e z w in the ascending expansion of the fraction 1-a.

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  • Q 1 The Unreduced Generating Function Which Enumerates The Covariants Of Degrees 0, 0' In The Coefficients And Order E In The Variables.

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  • A full account of his literary activity and ecclesiastical troubles will be found in Abbe Albert Houtin's La Question biblique au XIX e siècle (Paris, 2nd ed., 1902) and La Question biblique au XX e siècle (Paris, 1906), but the latter especially is largely unfair to the conservatives and sadly lacking in religious feeling.

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  • From 1881 to 1884 his activity in Tunisia so raised the prestige of France that it drew from Gambetta the celebrated declaration, L'Anticldricalisme n'est pas un article d'exportation, and led to the e .?mption of Algeria from the application of the decrees concerning the religious orders.

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  • The Vivarais mountains and the northern Cevennes approach the right banks of the Rhone and Saone closely, and on that side send their waters by way of short torrents to those rivers; on the west side the streams a y e tributaries of the Loire, which rises at the foot of Mont Mezenc. A short distance to the south on the same side are the sources of the Allier and Lot.

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  • The suspended needle is, in the absence of disturbing causes, directed solely by the horizontal component of the earth's field of magnetic force H E, and therefore sets itself approximately north and south.

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  • The direction of the resultant field of force will then make, with that of H E, an angle 0, such that Hp/H E tan 0, and the suspended needle will be deflected through the same angle.

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  • The angle B is indicated by the position of the spot of light upon the scale, and the horizontal intensity of the earth's field H E is known; thus we can at once determine the value of H P, from which the magnetization I of the body under test may be calculated.

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  • The strength of the magnetizing current is regulated by adjusting the position of the sliding contact E upon the resistance D.F.

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  • The closed figure a c d e a is variously called a hysteresis curve or diagram or loop. The area f HdB enclosed by it represents the work done in carrying a cubic centimetre of the iron through the corresponding magnetic cycle; expressed in ergs this work is I HdB.

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  • The current passes through the rocking key K, which, when thrown over to the right, places a in contact with c and b with d, and when thrown over to the left, places a in contact with e and b with f.

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  • In the same circuit is also included the induction coil E, which is used for standardizing the galvanometer; this secondary coil is represented in the diagram by three turns of wire wound over a much longer primary coil.

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  • By means of the three-way switch C the battery current may be sent either into the primary of E, for the purpose of calibrating the galvanometer, or into the magnetizing coil of the ring under test.

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  • But though a formula of this type has no physical significance, and cannot be accepted as an equation to the actual curve of W and B, it is, nevertheless, the case that by making the index e =1.6, and assigning a suitable value to r t, a formula may be obtained giving an approximation to the truth which is sufficiently close for the ordinary purposes of electrical engineers, especially when the limiting value of B is neither very great nor very small.

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  • Let each of the effects A, B, C, D and E be called positive when it is such as is exhibited by moderately magnetized iron, and negative when its sense is opposite.

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  • A, D, E Several gaps remain to be filled, but the results so far recorded can leave no doubt that the five effects, varied as they may at first sight appear, are intimately connected with one another.

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  • If S is the area of the orbit described in time T by an electron of charge e, the moment of the equivalent magnet is M = eST; and the change in the value of M due to an external field H is shown to be OM = - He'S/47rm, m being the mass of the electron.

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  • E, Stage with twelve free somites; the telsonic carapace has not increased in size.

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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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  • E, Lateral view of the whole body and two 1st appendages, showing the fusion of the dorsal elements of the prosoma into a single plate, and of those of the opisthosoma into an imperfectly segmented plate continuous with that of the prosoma.

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  • How otherwise are we to explain such Hebraisms (or Syriacisms) as Evui pEEC rb g Xacov E ct ro (§ 9), ov elir€v.

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  • The more fragmentary recension gives the history of the childhood from the 5th to the 8th year, and is entitled LGyypa j sa roil) e yiov arov76Xov 7rEpi Tijs 7racScKCis avaUTpocbC7s Tou Kvpiov (Tischendorf, op. cit.

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  • There are many private schools in all the large cities, from the primary schools maintained by the church and various corporations and religious associations to schools of secondary and collegiate grades, such as the Protestant mission schools of Petropolis, Piracicaba, Juiz de Fora, Sao Paulo and Parana, the Lyceu de Artes e Officios (night school) of Rio de Janeiro, and the Mackenzie College of Sao Paulo.

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  • The In- stituto Historico e Geographico Brazileiro, though devoted chiefly to historical research, has rendered noteworthy service in its encouragement of geographical exploration and by its publication of various scientific memoirs.

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  • In 1586 Witherington plundered Bahia; E and i n 1591 Cavendish made an abortive attack on Santos; French in 1595 Lancaster attacked Olinda.

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  • Pietro e Cesareo, fronting upon it, is ensconced in.a temple of Rome and Augustus, part of the side wall of which, with engaged columns, is still visible.

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  • Mariano e Jacopo, a structure of the 12th century, with a façade, adorned with contemporary sculptures, partly restored in 1514-1550.

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  • The government was now reconstituted under the protection of the French agents; the balia was abolished, its very name having been rendered odious by the tyranny of Spain, and was replaced by a similar magistracy styled capitani del popolo e reggimento.

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  • In 1837 he founded the Panorama in imitation of the English Penny Magazine, and there and in Illustracdo he published the historical tales which were afterwards collected into Lendas e Narratives; in the same year he became royal librarian at the Ajuda Palace, which enabled him to continue his studies of the past.

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  • John the Scot was still E acquainted with Greek, seeing that he translated the work of the pseudo-Dionysius; and his speculative genius achieved the fusion of Christian doctrine and Neoplatonic thought in a system of quite remarkable metaphysical completeness.

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  • The grammatical forms are expressed, as in Turkish, by means of affixes modulated according to the high or low vowel power of the root or chief syllables of the word to which they are appended-the former being represented by e, o, S, ii, i l l, the latter by a, d, o, 6, u, it; the sounds e, i, i are regarded as neutral.

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  • Thus, to solve the equation ax e +bx+c = o, we consider, not merely the value of x for which ax 2 +bx+c is o, but the value of ax e +bx+c for every possible value of x.

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  • The sum and product of two quaternions are defined by the formulae mi ase + F+lases = (a s + 133) es 2arer X ZO,es = Fiarfseres, where the products e,e, are further reduced according to the following multiplication table, in which, for example, the eo e1 e2 e3 second line is to be read eieo = e1, e 1 2 = - eo, e i e 2 = es, eie3 = - e2.

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  • Thus e 1 e 2 = - e2ei, and if q, q are any two quaternions, qq is generally different from q'q.

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  • The symbol e 0 behaves exactly like i in ordinary algebra; Hamilton writes I, i, j, k instead of eo, el, e2, es, and in this notation all the special rules of operation may he summed up by the equalities = - I.

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  • To multiply A 1 by a scalar, we apply the rule A = A1E = E (Eat) ea, and similarly for division by a scalar.

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  • If A 1 = X a i e i, B i = /if i e i, the distributive law of multiplication is preserved by assuming A1B1=E(a0 i 3)eiej; it follows that A 1 B 1 = - B 1 A 1, and that A l 2 = o.

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  • Every unit of the rth species which does not vanish is the product of r different units of the first species; two such units are independent unless they are permutations of the same set of primary units e i, in which case they are equal or opposite according to the usual rule employed in determinants.

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  • If E is any extensive unit, there is one other unit E', and only one, such that the (progressive) product EE' =- r.

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  • This unit is called the supplement of E, and denoted by IE.

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  • If, in the extensive calculus of the nth category, all the units (including i and the derived units E) are taken to be homologous instead of being distributed into species, we may regard it as a (2'-I)-tuple linear algebra, which, however, is not wholly associative.

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  • For instance, there are the symbols A, D, E used in the calculus of finite differences; Aronhold's symbolical method in the calculus of invariants; and the like.

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  • Thus we find Paciolus calling it l'Arte Magiore; ditta dal vulgo la Regula de la Cosa over Alghebra e Almucabala.

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  • In this they were completely successful, for they obtained general solutions for the equations ax by = c, xy = ax+by+c (since rediscovered by Leonhard Euler) and cy 2 = ax e + b.

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  • A particular case of the last equation, namely, y 2 = ax e + 1, sorely taxed the resources of modern algebraists.

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  • His travels and mercantile experience had led E t u eopre him to conclude that the Hindu methods of computing were in advance of those then in general use, and in 1202 he published his Liber Abaci, which treats of both algebra and arithmetic. In this work, which is of great historical interest, since it was published about two centuries before the art of printing was discovered, he adopts the Arabic notation for numbers, and solves many problems, both arithmetical and algebraical.

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  • At the focal point (E =o, n = o) all the secondary waves agree in phase, and the intensity is easily expressed, whatever be the form of the aperture.

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  • If the image of the line be =o, the intensity at any point E, n of the diffraction pattern may be represented by ?2a2t2 S A2f2 the same law as obtains for a luminous point when horizontal directions are alone considered.

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  • E is then the co-ordinate relatively to 0 of any focal point 0' for which the retardation is R; and the required result is obtained by simply integrating (5) with respect to from - cc to +oo.

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  • The linear width of the band (e) is the increment of which alters p by 27r, so that e =27r /tr.

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  • The integration of the several terms may then be effected by the formula e y dy =r(4+2)=(4 - i)(4-2)...

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  • Since the dimensions of T are supposed to be very small in com d parison with X, the factor dy (--) is sensibly constant; so that, if Z stand for the mean value of Z over the volume T, we may write TZ y d e T ?

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  • Its connexion with a is expressed by a =c4'/dr; so that TZ sin 05 e'(at - kr) 47b 2 where the factor e int is restored.

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  • His comedies give a truthful and interesting picture of 18th century society, especially his best comedy, the Alec rim e Mangerona, in which he treats of the fidalgo pobre, a type fixed by Gil Vicente and Francisco Manoel de Mello.

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  • His plays were published in the first two volumes of a collection entitled Theatro comico portuguez, which went through at least five editions in the 18th century, while the Alecrim e Mangerona appeared separately in some seven editions.

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  • The Hexaplar text of the LXX., as reduced by Origen into greater conformity with the Hebrew by the aid of subsequent Greek versions, was further the mother (d) of the Psalterium gallicanum - that is, of Jerome's second revision of the Psalter (385) by the aid of the Hexaplar text; this edition became current in Gaul and ultimately was taken into the Vulgate; (e) of the SyroHexaplar version (published by Bugati, 1820, and in facsimile from the famous Ambrosian MS. by Ceriani, Milan, 1874).

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  • Slippers (irepauKai) were adopted from the East by women; shoes (E e13a&ES) were worn by the poorer classes.

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  • His name survives in the town of Mopsuestia (M6 tov `E rria) and the spring of Mopsucrene.

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  • His Schiavitic e servaggio (Milan, 1868-1869) gave an account of the development and abolition of slavery and serfdom.

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  • Having been appointed assistant lecturer and afterwards full lecturer at the Ecole des Hautes Etudes, it was to the town of St Omer that he devoted his first lectures and his first important work, Histoire de la vile de Saint-Omer et de ses institutions jusqu'au XI V e siecle (1877).

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  • The substantive occurs in an inscription of the Arvalian brotherhood (Marini, Gli Atti e Monumenti de' fratelli Arvali, p. 639),but is frequent only in ecclesiastical Latin.

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  • E is a valve in the inlet pipe opening into the cylinder; and A the piston is perforated by one or more holes, each fitted with valves opening outwards on its upper surface.

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  • On raising the piston, the valve F remains closed and a vacuum tends to be created in the cylinder, but the pressure of the atmosphere forces the liquid up the tube D and it raises the valve E and passes into the cylinder.

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  • On reversing the motion the valve E closes and the liquid is forced through the valve F to the upper part of the cylinder.

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  • On raising the piston the liquid rises in the cylinder, the valve E opening and F remaining shut.

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  • On again F J J raising the piston the valve E opens ?g G admitting more liquid whilst F re- mains closed.

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  • The cartesian equation referred to the axis and directrix is y=c cosh (x/c) or y = Zc(e x / c +e x / c); other forms are s = c sinh (x/c) and y 2 =c 2 -1-s 2, being the arc measured from the vertex; the intrinsic equation is s = c tan The radius of curvature and normal are each equal to c sec t '.

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  • Referring the reader to the article Elasticity for the theoretical and to the Strength Of Materials far the practical aspects of this subject, we give here a table of the "modulus of elasticity," E (column 2), for millimetre and kilogramme.

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  • Taking the axis of x for an instant in the normal through a point on the surface H = constant, this makes u = o, = o; and in steady motion the equations reduce to dH/dv=2q-2wn = 2gco sin e, (4) where B is the angle between the stream line and vortex line; and this holds for their projection on any plane to which dv is drawn perpendicular.

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  • When the cylinder r =a is moved with velocity U and r =b with velocity U 1 along Ox, = U b e - a,1 r +0 cos 0 - U ib2 - 2 a, (r +Q 2 ') cos 0, = - U be a2 a2 (b 2 - r) sin 0 - Uib2 b1)a, (r - ¢2 sin 0; b and similarly, with velocity components V and V 1 along Oy a 2 b2 ?= Vb,_a,(r+r) sin g -Vi b, b2 a, (r+ 2) sin 0, (17) = V b, a2 a, (b2 r) cos 0+Vi b, b, a, (r- ¢ 2) cos h; (18) and then for the resultant motion z 2zz w= (U 2 + V2)b2a a2U+Vi +b a b a2 U z Vi -(U12+V12) b2 z a2b2 Ui +VIi b 2 - a 2 U1 +Vii b 2 - a 2 z The resultant impulse of the liquid on the cylinder is given by the component, over r=a (§ 36), X =f p4 cos 0.ad0 =7rpa 2 (U b z 2 + a 2 Uib.2bz a2); (20) and over r =b Xi= fp?

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  • Denoting the cross-section a of a filament by dS and its mass by dm, the quantity wdS/dm is called the vorticity; this is the same at all points of a filament, and it does not change during the motion; and the vorticity is given by w cos edS/dm, if dS is the oblique section of which the normal makes an angle e with the filament, while the aggregate vorticity of a mass M inside a surface S is M - l fw cos edS.

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  • Some of his statues, now in the Louvre, are carved out of Sinaitic dolerite, and on the lap of one of them (statue E) is the plan of his palace, with the scale of measurement attached.

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  • In Nisan the Kalda prince, M e rodach (Marduk)-baladan, entered Babylon and baladan. ?

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  • It is found under the above name, OeaOiyc?7 'E eKtov, only in Cedrenus i.

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  • Higher education is imparted at the university (Istituto di studii superiori e di perfezionalnento), with 600 to 650 students; although only comprising the faculties of literature, medicine and natural science, it is, as regards the first-named faculty, one of the most important institutions in Italy.

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  • He was refused admittance to the palace, and the people began to shout "Popolo e liberta I" in opposition to the Medicean cry of "Palle, Palle !"

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  • Savonarola also proposed a court of appeal for criminal and political crimes tried by the Otto di guardia e balia; this too was agreed to, but the right of appeal was to be, not to a court as Savonarola suggested, but to the Greater Council, a fact which led to grave abuses, as judicial appeals became subject to party passions.

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  • On the 1st of September 1512 Retur e Medici G i ul i ano and Giovanni de' Medici, and their nephew (1512).

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  • The narrative was first printed at Pesaro in 1513, in what Apostolo Zeno calls lingua inculta e rozza.

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  • The Krajewski crusher has two such E steel rolls, with V-shaped corrugations extending longi tudinally across them.

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  • Felice e Fortunato was restored in A.D.

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  • These cells are f - - imbedded in the peri pheral parenchyma, E"- and lead into convo luted excretory tubes _ that form an anasto- - mosis opening to the exterior by a pore at the " hinder " end of the body.

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  • Outline of the ventral surface to show the external apertures and nervous system; a, rosette-organ; b, uterine pore; c, terminal sucker; e, vaginal pore; g, male gonopore; n, o, p, nervous system.

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  • According to Plato (Prot., 318 E), he endeavoured to communicate "prudence" (6130vXia) to his pupils, "which should fit them to manage their households, and to take part by word and deed in civic affairs."

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  • H, E, Egg-float and further enlarged J, detached egg of Culex.

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  • For Dante's connexion with Pisa, see Dante e i Pisani, by Giovanni Sforza (Pisa, 1873).

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  • The curved surfaces take the place of fl e the lens in fig.

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  • The sun shining, he fixed a round glass speculum (orbem e vitro) in a window-shutter, and then closing it the images of outside objects would be seen transmitted through the aperture on to the opposite wall, or better, a white paper screen suitably placed.

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  • A, Dorsal view showing the nervous system and digestive system; a, mouth; b, pharynx; c, d, e, gut; E, post-genital union of two limbs of gut; f, excretory pore; g, vaginal pore; h, j, k, brain and nerves; 1, dorsal nerves; m, ventral nerves; n, adoral sucker; o, posterior sucker; p, hooks on posterior sucker; r, vitello-intestinal duct.

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  • If the egg with its contained embryo falls into water E (All from Marshall and Hurst, after Thomas.) FIG.

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  • D, An adult redia, containing a daughter-redia, two almost mature cercariae, and germs. E, A free cercaria.

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  • It contains numerous illustrations; maps of the routes of the ancient aqueducts and the city of Rome in the time of Frontinus; a photographic reproduction of the only MS. (the Monte Cassino); several explanatory chapters, and a concise bibliography, in which special reference is made to P. d Tissot, E tude sur la condition des agrimensores (1879).

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  • The standard modern work on Savonarola is Pasquale Villari's, La Storia di Fra Girolamo Savonarola e de' suoi tempi (Florence, 1887) based on an exhaustive study of the original authorities and containing a number of new documents (English translation by Linda Villari, London, 1889).

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  • The ri entral tract was a lower plain, covered with loose ashes and e riarked by a few pools of hot and saline water.

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  • English also adopted the value of s for c in the 13th century before e, i and y.

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  • Gladstone justly regarded the refusal to remit a duty as being in effect an act of taxation, and Budget th e refore as an infringement of the rights of the House of'1860.

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  • His Storia critica di Spagna e della cultura spagnuola in ogni genere (2 vols., 1781-1784) was finally expanded into the Historia critica de Espana y de la cultura espanola (1783-1805), which, though it consists of twenty volumes, was left unfinished; had it been continued on the same scale, the work would have consisted of fifty volumes.

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  • This early Chinese manner, which lasted in the parent country down to the end of the 13th century, was characterized by a viril,e grace of line, a grave dignity of composition, striking simplicity of technique, and a strong but incomplete naturalistic ideal.

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  • As for his ivory-white, it distinctly surpasses the Chinese Ming Chen-yao in every quality except an indescribable intimacy of glaze and p&e which probably can never be obtained by either Japanese or European methods.

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  • The Siemens and Halske ozonizer, in form somewhat resembling the old laboratory instrument, is largely used in Germany; working with an alternating current transformed up to 650o volts, it has been found to give 280 grains or more of ozone per e.

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  • The next that deserve mention are the Giornale enciclopedico (1806) of Naples, followed by the Progresso delle scienze (1833-1848) and the Museo di scienze e letteratura of the same city, and the Giornale arcadico (1819) of Rome.

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  • He now began to fulfil the promise of his "Cimabue," and by such pictures as "Paolo e Francesca," "The Star of Bethlehem," "Jezebel and Ahab taking Possession of Naboth's Vineyard," "Michael Angelo musing over his Dying Servant," "A Girl feeding Peacocks," and "The Odalisque," all exhibited in 1861-1863, rose rapidly to the head of his profession.

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  • There is only one fairly reliable treatment, that by serum therapeutics, the injection of considerable quantities of serum of animals which have e?

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  • Alloys represented by points on Ee, when they begin to solidify, deposit crystals of lead and bismuth simultaneously; Ee is a eutectic line, as also are E'e and E"e.

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  • The alloy of the point e is the ternary eutectic; it deposits the three metals simultaneously during the whole period of its solidfication and solidifies at a constant temperature.

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  • An important event must be referred probably to the year 451, - the law of Pericles, by which citizenship (including the right to vote in the Ecclesia and to sit on paid juries) was restricted to those who could prove themselves the children of an Athenian father and mother (E d,u001v avroiv).

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  • If a small conducting body is charged with Q electrostatic units of electricity, and placed in any electric field at a point where the electric force has a value E, it will be subject to a mechanical force equal to QE dynes, tending to move it in the direction of the resultant electric force.

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  • In the same manner, if an electrified body carries a positive charge Q electrostatic units and is placed in an electric field at a place where the electric force or electromotive intensity has a value E units, it is urged in the direction of the electric force with a mechanical force equal to QE dynes.

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  • For by the definition of potential it follows that the electric force in any direction at any point is measured by the space rate of change of potential in that direction or E = + dVldx.

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  • But the charge is Q = 21rra, and therefore the capacity of the thin wire is given by C =1/2 log e llr (2).

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  • Accordingly for a given ellipsoid the surface density of free distribution of electricity on it is everywhere proportional to the the tangent e plane e att that point.

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  • In the extreme case when e=1, the prolate ellipsoid becomes a long thin rod, and then the capacity is given by C 1 = a/log e 2a/b (io), which is identical with the formula (2) already obtained.

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  • In the other extreme case the oblate spheroid becomes a circular disk when e = i, and then the capacity C2 = 2a17r.

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  • Hence the electric force E in the interspace 1dRccor the potential V at any point in the interspace is given by varies inversely E = as - the distance distance =A/R from or V the - axis.

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  • If we consider a length l of the cylinder, the charge Q on the inner cylinder is Q=27rR l ly, where v is the surface density, and by Coulomb's law v = E i /47r, where E 1 = A/R 1 is the force at the surface of the inner Ai cylinder.

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  • If S is the surface of each plate, and d their distance, then the electric force E in the space between them is E = es.

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  • One of the best methods for doing this is to charge the Ab l condenser by the known voltage of a battery, and then d e t erdischarge it through a galvanometer and repeat this minations.

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  • The resultant electric force E at that point is then obtained by differentiating V, since E = - dV/dx, and E is in the direction in which V diminishes fastest.

    0
    0
  • Hence if dS and dS' are the areas of the ends, and +E and - E' the oppositely directed electric forces at the ends of the tube, the surface integral of normal force on the flux over the tube is EdS - E'dS' (20), and this by the theorem already given is equal to zero, since the tube includes no 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
  • Let E be the resultant electric force at any point in the field.

    0
    0
  • Then bearing in mind that a= (I/4x1-)dV/dn, and p =-(1/4xr)VV, we have finally E 2 c/v=2 f f v.-dS+ 2J J J Vp dv.

    0
    0
  • The resultant force due to these two pointcharges must then be in the direction CP, and its value E is the vector sum of the two forces along AP and BP due to the two point-charges.

    0
    0
  • The application of the first law leads immediately to the equation, II=E - E,+W, .

    0
    0
  • It follows from the first law that the intrinsic energy of a substance in a given state must always be the same, or that the change of E in any transformation must depend only on the initial and final states, and not on the path or process.

    0
    0
  • Applying the above equation to a gas obeying the law pv=RT, for which the work done in isothermal expansion from a volume i to a volume r is W=RT loger, whence dW=R log e rdt, he deduced the expression for the heat absorbed by a gas in isothermal expansion H=R log er/F'(t).

    0
    0
  • The same result follows if the work W =RT log e ?'

    0
    0
  • Dividing by (0' - e"), and writing dp/do and dL/do for the limiting values of !the ratios (p' - p")/(o' - o") and (L' - L")/(o' - o"), we obtain the important relations s' - s"+dL/do= (v" - v')dp/do=L/o,..

    0
    0
  • If, starting from E, the same amount of heat h is restored at constant pressure, we should arrive at the point F on the adiabatic through B, since the substance has been transformed from B to F by a reversible path without loss or gain of heat on the whole.

    0
    0
  • Since the amounts of heat supplied at constant pressure from E to F and from E to C are in the limit proportional to the expansions EF and EC which they produce, the ratio S/s is equal to the ratio ECÆF.

    0
    0
  • The amount of heat absorbed in any small change of state, as from E to G in fig.

    0
    0
  • Since the two expressions (9) are the partial differential-coefficients of a single function E of the independent variables v and 0, we shall obtain the same result, namely d 2 E/d0dv, if we differentiate the first with respect to v and the second with respect to 0.

    0
    0
  • Since dE=dH - pdv, we have evidently for the variation of the total heat from the second expression (8), dF=d(E + pv) =dH+vdp=Sde - (Odv/de - v)dp .

    0
    0
  • Observing that F is a function of the co-ordinates expressing the state of the substance, we obtain for the variation of S with pressure at constant temperature, dS/dp (0 const) '=' 2 F/dedp =-0d 2 v/d0 2 (p const) (12) If the heat supplied to a substance which is expanding reversibly and doing external work, pdv, is equal to the external work done, the intrinsic energy, E, remains constant.

    0
    0
  • The heat absorbed in isothermal expansion from vo to v at a temperature 0 is equal to the work done by equation (8) (since d0 =o, and 0(dp/d0)dv =pdv), and both are given by the expression RO log e (v/vo).

    0
    0
  • The energy E and the total heat F are functions of the temperature only, by equations (9) and (I I), and their variations take the form dE = sdO, d F = Sd0.

    0
    0
  • If we also assume that they are constant with respect to temperature (which does not necessarily follow from the characteristic equation, but is generally assumed, and appears from Regnault's experiments to be approximately the case for simple gases), the expressions for the change of energy or total heat from 00 to 0 may be written E - Eo = s(0 - 0 0), F - Fo = S(0-00).

    0
    0
  • If we assume that s is a linear function of 0, s= so(I +aO), the adiabatic equation takes the form, s 0 log e OW +aso(0 - Oo) +R loge(v/vo) =o

    0
    0
  • In passing B it does work, p"v", on the fluid in front, and carries its energy, E"+ U", with it out of the space AB.

    0
    0
  • The expression for the change of intrinsic energy E between any given limits poOo to po is readily found by substituting these values of the specific heats in equations (II) or (13), and integrating between the given limits.

    0
    0
  • If the tube is a perfect non-conductor, and if there are no eddies or frictional dissipation, the state of the substance at any point of the tube as to E, p, and v, is represented by the adiabatic or isentropic path, dE= -pdv.

    0
    0
  • The intrinsic energy, E, is similarly represented by the area DZ'Vd under the adiabatic to the right of the isometric Dd.

    0
    0
  • The increment of this area (or the decrement of the negative area E--04) at constant temperature represents the external work obtainable from the substance in isothermal expansion, in the same way that the decrement of the intrinsic energy represents the work done in adiabatic expansion.

    0
    0
  • Rose the third day, A, B, D, E (F omits " the third day " being a theological creed; the translation of C is uncertain).

    0
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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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  • The substance whose volume is to be determined is placed in the cup PE, and the tube PC is immersed in the vessel of mercury D, until the mercury reaches the mark P. The plate E is then placed on the cup, and the tube PC raised until the surface of the mercury in the tube stands at M, that in the vessel D being at C, and the height MC is measured.

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  • Had he not been hampered by the 0 Otranto., Var 19 E Glasgow yMONMOUTH Good Hope 5.55 Sun Set 6.45 p.m.

    0
    0
  • The masters he had to serve were the dieci di liberta e pace, who, though subordinate to the signoria, exercised a separate control over the departments of war and the interior.

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    0
  • On the 6th of December 1506 his plan was approved by the signoria, and a special ministry, called the nove di ordinanza e militia, was appointed.

    0
    0
  • But no such suggestion occurs in the Basis Astronomiae of Peter Horrebow (Copenhagen, 1735), which contains the only works of Roemer that re e o main to us.

    0
    0
  • The reading micrometers e, f also serve to measure, independently, the separation of the segments, by scales attached to the slides; such measurements can be employed as a check on those made by the screws.

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  • In 1876 a statue of Servetus was erected by Don Pedro Gonsalez de Velasco in front of his Instituto Antropologico at Madrid; in 1903 an expiatory block was erected at Champel; in 1907 a statue was erected in Paris (Place de la Mairie du XIV e Arrondissement); another is at Aramnese; another was prepared (1910) for erection at Vienne.

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  • Amongst the most widely distributed of the I E?t Xoirpocs - on the threshold.

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    0
  • In the tropical and subtropical belts of the Atlantic and Indian Oceans south of the equator the salinity diminishes rapidly from the surface downwards, and at 500 fathoms reaches a minimum of 34.3 or 34.4 p e r mille; after that it increases again to 800 fathoms, where it is almost 34.7 or 34.8, and this salinity holds good to the bottom, even to the greatest depths, as was first shown by the " Gauss " and afterwards by the " Planet " between Durban and Ceylon.

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  • Makaroff, The Yermak in the Ice (in Russian) (St Petersburg, 1901); The Norwegian North Atlantic Expedition (on the " Voringen "), 1876-1878 (Christiania, 1880-1900); Expeditions scientifiques du " Travailleur " et du " Talisman," 1880-1883 (Paris, 1891 et seq.); Die Ergebnisse der Plankton-Expedition, 1889 (Kiel, 1892 et seq.); Resultats des campagnes scientifiques accomplies sur son yacht par Albert I e ' Prince Souverain de Monaco (Monaco, from 1889); The Danish " Ingolf " Expedition, 1806 (Copenhagen, 1900); Prof. Luksch, Expeditionen S.M.

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  • In the same year appeared his two great metaphysical works, De la Causa,Principio, ed Uno, and De l'Infinito, Universo, e Mondi; in the year following the Eroici Furori and Cabala del Cavallo Pegaseo.

    0
    0
  • The ratio p is given by e"` e, where e= 2.718; µ is the coefficient of friction and 0 the angle, measured in radians,, subtended by the arc of contact between the rope and the wheel.

    0
    0
  • To maintain e µe constant, compensation for variation of µ is made by inversely varying 0.

    0
    0
  • The pulley E is driven from an axle of the carriage.

    0
    0
  • Rheydt is an ancient place, but its industrial importar e is of very recent growth, and it only received municipal rights in 1856.

    0
    0
  • If the system is supposed to obey the conservation of energy and to move solely under its own internal forces, the changes in the co-ordinates and momenta can be found from the Hamiltonian equations aE aE qr = 49 - 1 57., gr where q r denotes dg r ldt, &c., and E is the total energy expressed as a function of pi, qi,.

    0
    0
  • Let the whole energy E of the system be supposed equal to Ei+E2, where E2 is of the form E2 = ?

    0
    0
  • If each of the fractions (3) is put equal to i/4h, it is readily found, from the first property of the normal state, that, of the s molecules of the first kind, a number sal (h3m3 /13)e hm (u2+v2+w2)dudvdw (4) Velocities.

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  • The number of molecules of the first kind of gas, whose components of velocity lie within the ranges between u and u+du, v and v+dv, w and w+dw, will, by formula (5), be v?l (h 3 m 3 /7 3)e hm (u2+v2+w2)dudvdw (9) per unit volume.

    0
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  • Thus the contribution to the total impulsive pressure exerted on the area dS in time dt from this cause is mu X udtdS X (11 3 m 3 /,r 3)e hm (u2+v2+w2 )dudvdw (I o) The total pressure exerted in bringing the centres of gravity of all the colliding molecules to rest normally to the boundary is obtained by first integrating this expression with respect to u, v, w, the limits being all values for which collisions are possible (namely from - co too for u, and from - oo to + oo for v and w), and then summing for all kinds of molecules in the gas.

    0
    0
  • This is equivalent to a steady pressure p i per unit area where +0 pi - zfff v J 1 (h3m3/ir3)e hm(u2+v2+w2)mu2dudvdw.

    0
    0
  • The equation of energy is dQ=dE+pdv, (17) expressing that the total energy dQ is used partly in increasing the internal energy of the gas, and partly in expanding the gas against the pressure p. If we take p = RNT/v from equation (14) and substitute for E from equation (16), this last equation becomes dQ 2 (n +3)RNdT +RNTdv (18) which may be taken as the general equation of calorimetry, for a gas which accurately obeys equation (14).

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  • Between 1903 and E 1909 the revenue increased from £51,000 to £102,000.

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    0
  • The A reprieve till the end of 1892 followed, funds having Question of been raised through the efforts of Bishop Tucker E vacuation, by the Church Missionary Society and friends.

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    0
  • Weil, Etudes sur l'antiquite grecque (1900), and C. Giarratani, Tirteo e i suoi carmi (1905).

    0
    0
  • The rocking-bar consists of a carrier a fixed to the cradle, a rockingbar d pivoted to the carrier at e, a sight bar f carrying the sights and sighting telescope.

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  • If we might accept the various theories mentioned above, Balaam would appear in one source of J as an Edomite, in another as an Ammonite; in E as a native of the south of Judah or' possibly as an Aramaean; in the tradition followed by the Priestly Code probably as a Midianite.

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  • The chief significance of the Balaam narratives for the history of the religion of Israel is the recognition by J and E of the genuine inspiration of a non-Hebrew prophet.

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  • To the more strictly exegetical lectures the names E nyncmtc, 4-07-Amara, i nynTuca, O o€t, were sometimes applied.

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    0
  • Then MA'B'N is a right trapezium, whose area is equal to that of Cabd; and it is related to the latter in such a way that, if any two lines parallel to AC and BD meet AB, CD, MN, A'B', in E, G, P, E', and F, H, Q, F', respectively, the area of the piece PE'F'Q of the right trapezium 'B.

    0
    0
  • In E'; the case of a parallelogram, the equivalent right,, trapezium is a rectangle; in the case of a triangle, Al it is a right-angled triangle.

    0
    0
  • Then, if we take ordinates Kb, Lg, Mc, Nd, Pf, equal to B'B, GG', C'C, D'D, FF', the figure abgcdfe will be the equivalent trapezoid, and any ordinate drawn from the base to the a LM N P e X top of this trapezoid will be equal to the portion of this ordinate (produced) which falls within the original figure.

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    0
  • Let E and F be two magnitudes so related that whenever F has any value (within certain limits) E has a definite corresponding value.

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    0
  • The corresponding solid figure, in its most general form, is such as would be constructed to represent the relation of a magnitude E to two magnitudes F and G of which it is a function; it would stand on a plane base, and be comprised within a cylindrical boundary whose cross-section might be of any shape.

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    0
  • This value of 0 is the same for all parabolas which pass through D and E and have their axes at right angles to KL.

    0
    0
  • The integration with regard to y may similarly (in the particular example) be replaced by the operation ak(I+3E'-+3E'2+E'3), where E' denotes the change of y into y + k.

    0
    0
  • The result of performipg both operations, in order to obtain the volume, is the result of the operation denoted by the product of these two expressions; and in this product the powers of E and of E' may be dealt with according to algebraical laws.

    0
    0
  • The fact that C 1 does not give the true area is due to the fact that in passing from one extremity of the top of any strip to the other extremity the tangent to the trapezette E, _- changes its direction.

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  • Among the incidental operations are (a) the valuation of the bullion by weighing and assaying it; (b) " rating" the bullion, or calculating the amount of copper to be added to make up the standard alloy; (c) recovering the values from ground-up crucibles, ashes and floor sweepings (the Mint " sweep "); (d) assaying the melted bars; (e) " pyxing " the finished coin or selecting specimens to be weighed and assayed; (f) " telling " or counting the coin.

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  • This is done by the little crank B on the axle of the fly-wheel, acting through the rod C, and the bent lever D, which forms a toggle-joint at E with the vertical piece of metal below it.

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    0
  • While the coin is being moved the hanger D is held firmly by the forceps E to prevent the pan from being pushed sideways.

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    0
  • In ethics Gioja follows Bentham generally, and his large treatise Del merito e delle recompense (1818) is a clear and systematic view of social ethics from the utilitarian principle.

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  • That layer C A E presses against and pushes forward the next layer and so on.

    0
    0
  • As AB returns from EF towards CD the layer of air next to it follows it as if it D E F were pulled back by AB.

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    0
  • Let E be the bulk modulus of elasticity, defined as increase of pressure = decrease of volume per unit volume where the pressure increase is so small that this ratio is constant, w the small increase of pressure, and - (dy/dx) the volume decrease, then E=e/(- dy/dx) or w Æ= - dy/dx (I) This gives the relation between pressure excess and displacement.

    0
    0
  • If the velocity U is so chosen that E - poU 2 = o, then X = o, or the wave travels on through the action of the internal forces only, unchanged in form and with velocity U = (E/p).

    0
    0
  • It may be noted that the elasticity E is only constant for small volume changes or for small values of dy/dx.

    0
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  • When the value of dyldx is not very small E is no longer constant, but is rather greater in compression and rather less in extension than -yP. This can be seen by considering that the relation between p and is given by a curve and not by a straight line.

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  • At the instant that the original wave reaches F the wave from E has travelled to a circle of radius very nearly equal to EF-not quite, as S is not quite in the plane of the rails.

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    0
  • Taking the successive key-notes D, A, E, B, it is found that besides small and negligible differences, each introduces a new sharp, and so we get the five sharps, C, D, F, G, A, represented nearly by the black keys.

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  • If we take the new note B flat as key-note, another note, E flat, is required.

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    0
  • E flat as key-note introduces another flat, and so on, each flat not quite coinciding with a sharp but at a very small interval from it.

    0
    0
  • In works on sound it is usual to adopt Helmholtz's notation, in which the octave from bass to middle C is written c d e f g a b c'.

    0
    0
  • The octave above is c' d'e' f' g' a' b' c".

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  • The simplest form of wave, so far as our sensation goes - that is, the one giving rise to a pure tone - is, we have every reason to suppose, one in which the displacement is represented by a harmonic curve or a curve of sines, y=a sin m(x - e).

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  • If we put this in the form y=a sin (x - e), we see that y=o, for x =e, e +aX, e+2A, e+;X, and so on, that y is + from x=e to x=e+iX, - from e+zX to e+?A, and so on, and that it alternates between the values+a and - a.

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  • If now the curve moves along unchanged in form in the direction ABC with uniform velocity U, the epoch e =OA at any time t will be Ut, so that the value of y may be represented as 2 y=a sin T (x - Ut).

    0
    0
  • It is therefore W m = (E 1 U) 27rUa/A = 27rnpUa.

    0
    0
  • If w is the total pressure excess, and if y is the total displacement at x, then w = E Xchange of volume _original volume = - Edy/dx.

    0
    0
  • At the nodes A, B, C, D, E there is no displacement, but there are maximum volume and pressure changes.

    0
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  • If U is the velocity of sound in a gas at pressure P with density p, and if waves of length X and frequency N are propagated through it, then the distanc?e l between the dust-heaps is 2 = N - zN Vyp' where y is the ratio of the two specific heats.

    0
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  • Under Britishrule Colombo has shared in the prosperity brought to the island by the successive industri e s of coffee and teaplanting.

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    0
  • For steel E =28,000,000 to 30,000,000, or on the average about twelve times its value for concrete.

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  • If it revolves about a vertical axis d its centre of gravity must always lie in that axis; if it rolls the centre of gravity must always lie over the e abutment.

    0
    0
  • With medium or moderately hard steel all rivet holes should be drilled, or punched e in.

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  • As the loads move over the girder, the points C, D, E describe the parabolas M1, M2, M3 i the middle ordinates of which are 4W 1 1, 4W 2 1, and 4W3l.

    0
    0
  • If these are first drawn it is easy, for any position of the loads, to draw the lines B'C, B'D, B'E, and to find the sum of the intercepts which is the total bending moment under a load.

    0
    0
  • Let w e be the load per ft.

    0
    0
  • Then w e may be termed the uniform load per ft.

    0
    0
  • But it is not difficult to find w e, approximately enough for practical purposes, very simply.

    0
    0
  • From these equations a value of W e can be obtained.

    0
    0
  • Hence the moment of the load on Am at C is wy0m, and the moment of a uniform load over any portion of the girder is w X the area of the influence curve Ip' G' E ' under that portion.

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  • If the load is in the bay D'E' and is carried by a rail girder which distributes it to cross girders at D'E', the part of the influence line under this bay is altered.

    0
    0
  • The loads at D', E, due to unit weight on the rail girder are (p-n)/p and n/p. The reaction at B' is {(p- n)xi+n(xi+p)}' /pi.

    0
    0
  • Then the deviation y= DE of the neutral axis of the bent beam at any point D from the axis OX is given by the relation d 2 y Ml dx 2 = EI' where M is the bending moment and I the amount of inertia of the beam at D, and E is the coefficient of elasticity.

    0
    0
  • Let E be the effective elasticity of the aether; then E = pc t, where p is its density, and c the velocity of light which is 3 X 10 10 cm./sec. If = A cos" (t - x/c) is the linear vibration, the stress is E dE/dx; and the total energy, which is twice the kinetic energy Zp(d/dt) 2 dx, is 2pn2A2 per cm., which is thus equal to 1.8 ergs as above.

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  • Encouraged by this pleasing symptom of orthodoxy the bishops, instead of first attempting to put their own dilapidated house in order, at once proceeded to institute pr e osecutions for heresy against all and sundry.

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  • He entered the Celestine order and came into prominence during the pontificate of his uncle, Gregory XII., by whom he was appointed bishop of Siena, papal treasurer, protonotary, cardinal-priest of St Marco e St Clemente, and later cardinal-priest of Sta Maria in Trastevere.

    0
    0
  • Also the velocity v at the end of the arc is given by (87) ve = u e sec 0 cos n.

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  • After a certain discount for friction and the recoil of the gun, the net work realized by the powder-gas as the shot advances AM is represented by the area Acpm, and this is equated to the kinetic energy e of the shot, in foot-tons, (I) e d2 I + p, a in which the factor 4(k 2 /d 2)tan 2 S represents the fraction due to the rotation of the shot, of diameter d and axial radius of gyration k, and S represents the angle of the rifling; this factor may be ignored in the subsequent calculations as small, less than I %.

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  • Arbogast's rule of the last and the last but one; in fact, taking the value of a to be unity, and, understanding this letter in each term, the rule gives b; c, b2; d, bc, b; e, bd, c, b c, b, &c., which, if b, c, d, e, &c., denote I, 2, 3, 4, &c., respectively, are the partitions of 1, 2, 3, 4, &c., respectively.

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  • A, B, C, D, E, F, Terminals to which standard cell or voltages to be tested are attached.

    0
    0
  • Considering the imprisonment of the ostracod body within the valves, it is more surprising that the Asteropidae and Cypridinidae should have a pair of compound and sometimes large eyes, in addition to the e median organ at the base of I the " frontal tentacle," than 6 that other members of the group should be limited to P that median organ of sight, or have no eyes at all.

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  • Somewhat later than " J," another writer, commonly referred to as " E," from his preference for the name Elohim (" God ") rather than " Jehovah," living apparently in the northern kingdom, wrote down the traditions of the past as they were current in northern Israel, in a style resembling generally that of " J," but not quite as bright and vivid, and marked by small differences of expression and representation.

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  • The first traces of " E " are found in the life of Abraham, in parts of Gen.

    0
    0
  • For this purpose he selected extracts from the two narratives, " J " and " E," and combined them together into a single narrative, introducing in some places additions of his own.

    0
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  • Certainly the publication E of his Einleitung (Introduction to the Old Testament), in 1780-1783, is a landmark in the history of Old Testament criticism.

    0
    0
  • These three classes he distinguished as 5(=Bcati 7 Krt), e (=ebayyeXtov) and a (= euroQroXos).

    0
    0
  • The corrections of s e are important, as they are based (according to a note by that scribe, at the end of Esther) on an early copy which had been corrected by, Pamphilus, the disciple of Origen, friend of Eusebius and founder of a library at Caesarea.

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  • The relations of s e to Pamphilus are studied by Bousset in " Textkritische Studien zum N.T."

    0
    0
  • L, von Soden e 56, containing the Gospels; cod.

    0
    0
  • Palatinus (e) of the 5th century at Vienna, both of which are imperfect, especially k, which, however, is far the superior in quality; in the Acts and Catholic epistles by cod.

    0
    0
  • Thus in arithmetical calculations if the base is not expressed it is understood to be io, so that log m denotes log n m; but in analytical formulae it is understood to be e.

    0
    0
  • The two systems of logarithms for which extensive tables have been calculated are the Napierian, or hyperbolic, or natural system, of which the base is e, and the Briggian, or decimal, or common system, of which the base is io; and we see that the logarithms in the latter system may be deduced from those in the former by multiplication by the constant multiplier /loge io, which is called the modulus of the common system of logarithms.

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  • The quantity denoted by e is the series, I I I+ I + i.2 +1.2.3+1.2.3.4 + the numerical value of which is, 2.71828 18284 59 0 45 2 353 6 02874.

    0
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  • The mathematical function log x or log x is one of the small group of transcendental functions, consisting only of the circular functions (direct and inverse) sin x, cos x, &c., arc sin x or sin-' x,&c., log x and e x which are universally treated in analysis as known functions.

    0
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  • It is customary, therefore, to denote the exponential function by e x, and the result ex = I +x+x2/2 !

    0
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  • Napier's logarithms are not the logarithms now termed Napierian or hyperbolic, that is to say, logarithms to the base e where e= 2.7182818 ...; the relation between N (a sine) and L its logarithm, as defined in the Canonis Descriptio, being N=10 7 e L/Ip7, so that (ignoring the factors re, the effect of which is to render sines and logarithms integral to 7 figures), the base is C".

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  • If 1 denotes the logarithm to base e (that is, the so-called "Napierian " or hyperbolic logarithm) and L denotes, as above, " Napier's " logarithm, the connexion between 1 and L is expressed by L = r o 7 loge 10 7 - 10 7 / or e t = I 07e-L/Ia7 Napier's work (which will henceforth in this article be referred to as the Descriptio) immediately on its appearance in 1614 attracted the attention of perhaps the two most eminent English mathematicians then living - Edward Wright and Henry Briggs.

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  • Napier gives logarithms to base e ', Byrgius gives antilogarithms to base (I.coo')='a.

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  • In the same year (1620) Napier's Descriptio (1614) and Constructio (1619) were reprinted by Bartholomew Vincent at Lyons and issued together.5 Napier calculated no logarithms of numbers, and, as already stated, the logarithms invented by him were not to base e.

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  • The first logarithms to the base e were published by John Speidell in his New Logarithmes (London, 1619), which contains hYPerbolic log sines, tangents and secants for every minute of the quadrant to 5 places of decimals.

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  • Also, although logarithms have been spoken of as to the base e, &c., it is to be noticed that neither Napier nor Briggs, nor any of their successors till long afterwards, had any idea of connecting logarithms with exponents.

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  • Since loge(I +x) =x-2x 2 -3x 3 - 4x4+&c., we have, by changing the sign of x, log e (I - x) _ - x - zx 2 - 3x 3 - x 4 - &c.; whence g 1 +x to=2(x+ix'+1x5+&c.), e l - x and, therefore, replacing x by p +q, log e q =2 p +q +3 () 3T ?

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  • If a= logg = - log (1-10)' 81 (1) c = 10g 80 = log 1 +sr, 126 (8) e =10g1 o = log 1 +1000 then log 2=7a-2b+3c, log 3=IIa-3b+5c, log 5=16a-4b +7c, and log 7 =2(39a - IOb+17c - d) or=19a-4b+8c +e, and we have the equation of condition, a-2b+c=d+2e.

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  • By means of these formulae Adams calculated the values of log e 2, log e 3, log e s, and loge?

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  • The logarithm is then obtained by use of the formula d l d2 l d3 2 log e (x+d) = log e x-f- - x2+3 x3 - &c., in which of course the object is to render dlx as small as possible.

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  • In recent years the science of vegetable palaeontology has been given the distinct name of Palaeobotany, so that " palaeontology e' among biologists mainly refers to zoology; but historically the two cannot be disconnected.

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  • Even when seen in minute features only he recognized them as constant progressive characters or " chronologic varieties " in 3b --i C D E F G H I -14-21 -I-31 1 - I - 41 contrast with contemporaneous or " geographic varieties," which he considered inconstant and of slight systematic value.

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  • Tullii Ciceronis de republica quae supersunt appeared at Rome in 1822; Scriptorum veterum nova collectio, e vaticanis codicibus edita in 1825-1838; Classici scriptores e vaticanis codicibus editi in 1828-1838; Spicilegium romanum in 1839-1844; and Patrum nova bibliotheca in 1845-1853.

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  • E - H shows the formation of the myonemes and the flagellar border (flagellum) of the undulating membrane, by means of a greatly elongated nuclear-spindle.

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  • Luzio, whose account in Profili e bozzetti storici (Milan, 1906) gives the latest information on the subject, has demolished Amante's arguments.

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  • With the exception of his description of the French Revolution, which was chiefly a political manifesto, all his early works refer to the middle ages - De La feodalite, des institutions de Saint Louis et de l'influence de la legislation de ce prince (1822); La Germanic au vin e et au ix' siecle, sa conversion au christianisme, et son introduction dans la societe civilisee de l'Europe occidentale (1834); Essai sur la formation territoriale et politique de la France depuis la fin du xi e siècle jusqu'et la fin du xv e (1836); all of these are rough sketches showing only the outlines of the subject.

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  • The E the Bta, ovos and the are also forbidden to contract a second marriage.

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  • Mercati, Studi e testi (Rome, 1901) to be the proces verbal of an actual discussion held under Justinian at Constantinople in 527.

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  • The h L lower Mississippi receives no large tributary from the T e ower east, but two important ones come from the west; the Mississippi Arkansas drainage area being a little less than that River.

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  • That to the west is surrounded by a semicircular colonnade, leaving an open "paradise" (E) between it and the wall of the church.

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  • Facing the west are the stables (e), ox-sheds (f), goatstables (g), piggeries (h), sheep-folds (i), together with the servants' and labourers' quarters (h).

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  • In the plan before us this apartment (E) opens from the south cloister walk, adjoining the refectory.

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  • The church here is of the Cistercian t e YP with a short chancel of two squares, and transepts with three eastward chapels to each, divided by solid walls (222).

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  • The theorem for angle-bisection which Vieta used was not that of Archimedes, but that which would now appear in the form I - cos 0 = 2 sin e 20.

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  • In this way the notches d, e of the hinder part of the mantle-skirt of Anodonta are in the siphonate forms converted into two separate holes, the edges of the mantle being elsewhere fused together along this hinder margin.

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  • The current of water enters into the sub-pallial space at the spot marked e in fig.

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  • If we take another section nearer the hinder margin of the foot, we get the arrangement A e l..

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  • It must, however, be distinctly borne in mind that there is a fundamental difference between the eye of Vertebrates and of all other groups in the fact that in the Vertebrata the retinal body is itself a part of the central nervous system, and not a separate C E k e FIG.

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  • In the following stemma M and N are "mixed" or "conflated" MSS., being formed by the blending of readings from the "pure" or "unmixed" codices A, B and D, E respectively.

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  • Thus the Roman letters E and F are liable to be confused in capital script, but not in cursive (e, f), C, G, in capitals, c, e in the cursive writing called Caroline minuscule, c, t, in the angular cursive of the 13th century and later.

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  • The master and his scholars were called Peripatetics (ol Ert Tov 7reptlredrov), certainly from meeting, like other philosophical schools, in a walk (7repL7raros), and perhaps also, on the authority of Hermippus of Smyrna, from walking and talking there, like Protagora s s and his followers as described in Plato's Protagoras (314 E, 315 e).

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  • Then follows the treatment of oligarchy, democracy, commonwealth and tyranny, and of the various powers of government (0), and independent investigation of revolution, and of the means of preserving states (E), and a further treatment of democracy and oligarchy, and of the different offices of the state (Z), and finally a return to the discussion of the right form of constitution (II, 0).

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  • But 0 and Z are a group interrupted by E, and H and 0 are another group unconnected with the previous group and with E, and are also distinguished in style by avoiding hiatus.

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  • Finally the group (0, Z), the book (E) and the group (II, 0), though unconnected with one another, are all connected though imperfectly with " the first discourses " (A,B,F).

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  • It divides (chap. 8) evidences (7r1aTEts) into two kinds (I) evidence from arguments, actions and men (ai j s v E air&v Tcev Xhywv cal Twv 7rpit aw cal TWV avOpcoirwv); (2) adventitious evidences (ai S' iIriOETOtTOLs X yo,u vots cal Tois rpm-To/lb/0a).

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  • For The Sake Of Greater Generality, The Days Of The Week Are Denoted By The First Seven Letters Of The Alphabet, A, B, C, D, E, F, G, Which Are Placed In The Calendar Beside The Days Of The Year, So That A Stands Opposite The First Day Of January, B Opposite The Second, And So On To G, Which Stands Opposite The Seventh; After Which A Returns To The Eighth, And So On Through The 365 Days Of The Year.

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  • Now If One Of The Days Of The Week, Sunday For Example, Is Represented By E, Monday Will Be Represented By F, Tuesday By G, Wednesday By A, And So On; And Every Sunday Through The Year Will Have The Same Character E, Every Monday F, And So With Regard To The Rest.

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  • The Fourth Year Was Bissextile, And The Dominical Letters Were F, E; The Following Year D, And So On.

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  • In Order To Investigate A Formula For The Epact, Let Us Make E=The True Epact Of The Given Year; J =The Julian Epact, That Is To Say, The Number The Epact Would Have Been If The Julian Year Had Been Still In Use And The Lunar Cycle Had Been Exact;, S =The Correction Depending On The Solar Year; M =The Correction Depending On The Lunar Cycle; Then The Equation Of The Epact Will Be E=J S M; So That E Will Be Known When The Numbers J, S, And M Are Determined.

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  • But P Can Never Be Less Than I Nor 1 Less Than 4, And In Both Cases E =23.

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  • P= 54 E 1=57 E, Or (57 E) 7 R' By Substituting One Or Other Of These Values Of P And 1, According A; The Case May Be, In The Formula P = P (L L), We Shall Have P, Orthe Number Of Days From The 21St Of March To Easter Sunday.

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  • As in Bories's instrument, a series of 9 weights, each of the form shown at E, serves to extend the scale FIG.

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  • D, E, F, Trochosphere stage, D fp, Pore in the foot (belonging mf, The mantle-flap or limbus to the pedal gland?).

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  • E, The Trochosphere passing to the Veliger stage, dorsal view showing the formation of the primitive shell-sac.

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  • E, The cap of small cells has increased in number by repeated formation of pellucid cells in the same way, and by division of those first formed.

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  • One of the most noteworthy schools of the city is the Lycen de Artes e Officios, located on Rua 13 de Maio, opposite the operahouse; it dates from 1858 and has been the means of giving instruction to a multitude of clerks, artisans and others, through its night classes.

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  • In 1822 it was raised to the rank of a city, and in 1841, as a reward for its loyalty in revolutionary wars of that province, it was distinguished by the title of Leal e valorosa (loyal and valorous).

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  • Dormice a r e small arboreal rodents, with long hairy tails, large eyes and ears, and short fore-limbs, ranging over Europe, Asia and Africa.

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  • They hay e large heads, projecting incisors, no ears, almost functionless eyes and moderately long tails; the skin, with the exception of a few hairs on the body and frinr-es on the feet, being naked.

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  • These congresses have been supplemented by national congresses in ' See Annuaire du mouvement pacifaste pour l'anne'e 1910, published by the Bureau International de la Paix, at Bern.

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  • C. Pickering discovered in the structure of the star E Puppis a series of lines which showed a remarkable similarity to that of hydrogen having the same root.

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  • Assuming for a moment the change to be one of density and leaving out of account the pressure shift, the cases (e) and (f) point to the fact that it is the closeness of packing of similar molecules which is effective, e.g.

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  • He further supposed that, while this independent vital series of C is sometimes of this simple kind, at other times it is complicated by the addition of a dependent vital series in E, by which, in his fondness for too general and farfetched explanations, he endeavoured to explain conscious action and thought.

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  • It is curious that Avenarius should have brought forward this artificial hypothesis as the natural view of the world, without reflecting that on the one hand the majority of mankind believes that the environment (R) exists, has existed, and will exist, without being a counterpart of any living being as central part (C); and that on the other hand it is so far from being natural to man to believe that sensation and thought (E) are different from, and merely dependent on, his body (C), that throughout the Homeric poems, though soul is required for other purposes, all thinking as well as sensation is regarded as a purely bodily operation.

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  • They may have found in some places a soil already prepared by more ancient tenets which had been preserved in spite of th'e persecution of the official Church, and handed down from the period of primitive Christianity.

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  • E is due to transient induction in horizontal soft iron unsymmetrically placed with regard to the compass.

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  • C is compensated by permanent magnets athwartships and horizontal; D by masses of soft iron on both sides of the compass, and generally in the form of cast-iron spheres, with their centres in the same horizontal plane as the needles; E is usually too small to require correction; A is fortunately rarely of any value, as it cannot be corrected.

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  • The superintendent, who is a naval officer, has to investigate the magnetic character of the ships, to point out the most suitable positions for the compasses when a ship is designed, and subsequently to keep himself informed of their behaviour from the tin g e of the ship's first trial.

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  • Until the accession of Adrian IV., however, there had been considerable periods of tran- German quillity, years even of unbroken peace and alliance E with the Germanic power.

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  • As head of the state department he soon came into conflict with Adams. His hatred of France made it impossible for him to sympathize with the president's efforts to settle the differences with that country on a peaceabl e basis.

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  • The vowel sounds ai, oi, ui have become e, o, u; and a, o, u before the finals d and n are now et, o, ii.

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  • This indicates the appearance of a new compound, which should exist pure at E, the next maximum, and, led by these considerations, Roozeboom discovered and isolated a previously unknown hydrate, Fe 2 C1 6 7 H 2 0.

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  • The residual liquid would thus become richer in B, and the tem perature and composition would pass along the curve till E, the eutectic point, was reached.

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  • The conditions may then remain those of equilibrium along the curve f E, but before reaching f the solution may become supersaturated with B and deposit B crystals spontaneously.

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  • The two courts are divided by the main buildings of the monastery, including the church, the sanctuary (A), divided from B, the monks' choir, by a screen with two altars, the smaller cloister to the south (S) surrounded by the chapter-house (E), the refectory (X) - these buildings occupying their normal position - and the chapel of Pontgibaud (K).

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  • As an historian he published Origines de l'institution des intendants de provinces (1884), which is the authoritative study on the intendants; Etudes historiques sur les X VI e et X VIP siecles en France (1886); Histoire de Richelieu (2 vols., 1888); and Histoire de la Troisieme Republique (1904, &c.), the standard history of contemporary France.

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  • From about 1864 he occupied himself almost exclusively with spectrum analysis, both of stars (Catalogo delle stelle di cui si e determinato lo spettro luminoso, Paris, 1867, 8vo; "Sugli spettri prismatici delle stelle fisse," two parts, 1868, in the Atti della Soc. Ital.) and of the sun (Le Soleil, Paris, 1870, 8vo; 2nd ed., 1877).

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  • No doubt the Phoenicians had their legends and myths to account for the origin of man and the universe; to some extent these would Myth R e!,, o logy have resembled the ideas embodied in the book of and Genesis.

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  • For physiognomy of disease, besides the usual medical handbooks, see Cabuchet, Essai sur l'expression de la face dans les maladies (Paris, 1801); Mantegazza, Physiology of Pain (1893), and Polli, Saggio di fisiognomonia e potognomonia (1837).

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  • The two achromatic lenses, C and D, bring the rays to a focus on the plane surface of the large lens, E, forming an image there.

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  • From the large lens, E, the rays pass through the open air for a considerable distance, depending upon how much the mast has been raised, to the lower optical system.

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  • The name " Hebrew " is derived, through the Greek `E$3paios, from `ibhray, the Aramaic equivalent of the Old Testament word `ibhri, denoting the people who commonly spoke of themselves as Israel or Children of Israel from the name of their common ancestor (see JEws).

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  • The Order of St Maurice and St Lazarus (SS Maurizio e Lazzaro), is a combination of two ancient orders.

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  • The exact relation of gonidia and hyphae has been investigated e specially by Bornet and also by Hedlund, and very considerable differences have been shown to exist in different genera.

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  • In 1764 he published his brief but justly celebrated treatise Dei Delitti e delle Pene (" On Crimes and Punishments").

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  • These are usually divided into three groups, the Central (the watershed between the two passes named), the Western or French, and the Eastern or Italian; in the following lists the initials " C," " W," and " E " show to which group each peak and pass belongs.

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  • In the East the festival is known as the avitXi t ' cs, "taking up," or E rtcrco oµELn, a term first used in the Cappadocian church, and of which the meaning has been disputed, but which probably signifies the feast "of completed salvation."

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  • The bit of wood e must be gently withdrawn, care being taken that the bud adheres wholly to the bark or shield, FIG.

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  • Fig 36, b and c, are examples of the former, and d, e, f of the latter.

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  • Abraham Bennet, the inventor of the gold leaf electro e described a doubler or machine for multiplying Bennet'.

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  • The pins E, F rise out of the back of the fixed plates A and C, at unequal distances from the axis.

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  • The piece K is parallel to G H, and both of them are furnished at their ends with small pieces of flexible wire that they may touch the pins E, F in certain points of their revolution.

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