How to use L in a sentence

l
  • 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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  • 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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  • 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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  • 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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  • 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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  • 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 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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  • 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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  • 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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  • 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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  • To represent the simplest perpetuant, of weight 7, we may take as base either A2B 1 B 2 or A l A 2 B2, and since Ai+Bi =o the former is equivalent to A 2 ArB 2 and the latter to A 2 B i B2; so that we have, (1 -f-aix) (1 + a2x).

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  • For the mean motion of the earth in one second in circular measure, we have n 8149' l o g.

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  • If m, and m 2 are the strengths of two poles, d the distance between them expressed in centimetres, and f the force in dynes, f=ml m2/d2 (I) The force is one of attraction or repulsion, according as the sign of the product m l m 2 is negative or positive.

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  • If P is the weight of the magnet, l the length of each of the two threads, 2a the distance between their upper points of attachment, and 2b that between the lower points, then, approximately, MH = P(ab/l) sin 0.

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  • The cardboard scale SS is placed above a wooden screen, having in it a narrow vertical slit which permits a beam of light from the lamp L to reach the mirror of the magnetometer M, whence it is reflected upon the scale.

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  • If H l and H2 be the values of 47rinll and 47ri' - 'Z/ l for the 2 2 same induction B, it can be shown that the true magnetizing force is H = H l - (H 2 - H 1).

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  • An iron bar shaped like an inverted L projects upwards from each of the yokes, the horizontal portions of the bars being parallel to the rods, and nearly meeting at a height of about 8 in.

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  • The strength of the induced current is - HScosO/L, where 0 is the inclination of the axis of the circuit to the direction of the field, and L the coefficient of self-induction; the resolved part of the magnetic moment in the direction of the field is equal to - HS 2 cos 2 6/L, and if there are n molecules in a unit of volume, their axes being distributed indifferently in all directions, the magnetization of the substance will be-3nHS 2 /L, and its susceptibility - 3S 2 /L (Maxwell, Electricity and Magnetism, § 838).

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  • L is the condition of outgrowth with gl, gill lamellae.

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  • PrGabp l, Rudiment of the appendage of the praegenital somite which disappears.

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  • And this is not strange seeing that of the former such abundant l See Porter in Hastings' Bible Did.

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  • It is one of the most favoured regions of English Miles 400 o L; Barcellos rd o?

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  • In Dean cemetery, partly laid out on the banks of the Water of Leith, and considered the most beautiful in the city (opened 1845), were interred Lords Cockburn, Jeffrey and Rutherford; " Christopher North," Professor Aytoun, Edward Forbes the naturalist, John Goodsir the anatomist; Sir William Allan, L Sam Bough, George Paul Chalmers, the painters; George Combe, the phrenologist; Playfair, the architect; Alexander Russel, editor of the Scotsman; Sir Archibald Alison, the historian; Captain John Grant, the last survivor of the old Peninsular Gordon Highlanders; Captain Charles Gray, of the Royal Marines, writer of Scottish songs; Lieutenant John Irving, of the Franklin expedition, whose remains were sent home many years after his death by Lieut.

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  • The political independence of Hungary was ultimately secured by the outbreak of the quarrel about investiture (1076), when L Geza I.

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  • One more attempt at compromise was made, General Count Lamberg l being sent to take command of all the troops, Slav or Magyar, in Hungary, with a view to arranging an armistice.

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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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  • Realism, more particularly of the Wundt type, is represented by Emericus Pauer, Az ethikai determinismus (" Ethical Determinism "), and Eugen Posch (Az idorb'l, " On Time ").

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  • His chief work, the Six livres de la Republique (Paris, 1576), which passed through several editions in his lifetime, that of 1583 having as an appendix L'A pologie de Rene Herpin (Bodin himself), was the first modern attempt to construct an elaborate system of political science.

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  • In the same way we regard log l 02, not as a new kind of number, but as an approximation.

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  • This suggests that we should write; la as a l l3; and we find that the use of fractional indices in this way satisfies the laws of integral indices.

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  • It should be observed that, by analogy with the definition of a fraction, a P l q mean (al/q)P, not (aP)llq.

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  • For graphical representation we select units of length L and M, not necessarily identical.

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  • Graphic representation thus rests on the principle that equal numerical quantities may be represented by equal lengths, and that a quantity mA may be represented by a length mL, where A and L are the respective units; and the science of graphics rests on the converse property that the quantity represented by pL is pA, i.e.

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  • Hence the successive remainders are successively smaller multiples of L, but still integral multiples, so that the series of quotients k, s, t,.

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  • Now suppose that the formula (2) has been established for every power of A+a up to the (n-i)th inclusive, so that (ii_ I) = (n- I) (r), (y I) = (n -1) (r _ l).

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  • The values of the first ten of Bernoulli's numbers are B1= t, B2= 1, B3 =412, B4 =30, B5 =6 = 6 9 1 B7 = l, B =3 =4 4 fl, IV.

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  • We want to express (23/13) 3 in the form a l b, where b is nearly equal to i.

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  • We know that log l oN(I+9) = log l oN+log 10 (I+0), and inspection of a table of logarithms shows that, when 0 is small, log 10 (I+B);s approximately equal to X0, where X is a certain constant, whose value is.

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  • Taking any number n to be represented by a point on a line at distance nL from a fixed point 0, where L is a unit of length, we start with a series of points representing the integers I, 2, 3,.

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  • Complex numbers are conveniently treated in connexion not only with the theory of equations but also with analytical trigonometry, which suggests the graphic representation of a+b,l - by a line of length (a 2 +b 2)i drawn in a direction different from that of the line along which real numbers are represented.

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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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  • The extreme discrepancy is that between the waves which travel through the outermost parts of the object-glass at L and L'; so that if we adopt the above standard of resolution, the question is where must P be situated in order that the relative retardation of the rays PL and PL' may on their arrival at B amount to a wave-length (X).

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  • Martha, L' Art etrusque, gives reproductions of the most important monuments.

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  • Either to the 10th or the 11th century must be referred the name of another Arabian physician who has also attained the position of a classic, Abu'l Qasiin or Abulcasis, of El-Zahra, near Cordova, in Spain.

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  • In December 1721 his father died, leaving him property (rather more than four thousand 'l y res a year), which was soon increased by a pension of half the amount from the regent.

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  • Shortly after this they came to London and settled in Holborn near L i ncoln's Inn, where they remained for more than fifty years.

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  • A stope is that portion of the working assigned to a party of miners, and the block of ground is usually A s /u//, ?l'?//?

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  • Two of these (UBI, L B 15) were attached to the Austrian submarine force.

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  • The general conformation of the Hindu Kush system south of the Khawak, no less than such fragmentary evidence of its rock composition as at present exists to the north, points to l its construction under the same conditions of upheaval and subsequent denudation as are common to the western o Himalaya and the whole of the trans-Indus borderland.

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  • Wohler, Ann., 1856, 97, p. 266; 1857, 102, p. 382); by heating silica with magnesium in the presence of zinc (L.

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  • On many maps it is marked as the Bahr-el-Arab, a designation also used as an alternative name for the Lol l another tributary of the Ghazal, which eventually unites with the Bahr-el-Homr. The Bahr-el-Homr in its lower reaches was in 1906 completely blocked by sudd, and then brought no water into the Bahr-el-Ghazal.

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  • The Takruri possess jagged throwing knives, which are said to have been brought from their original home in the L i pper Congo regions.

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  • For the liquid filling the interior of a rotating elliptic cylinder of cross section x2/a2+y2/b2 = 1, /(4) = m l (x 2 / a2 - - y2 /b 2) (5) with V21G1' =-2R =-2 m 1 (I / a2 + 21b2), 214 = m l (x2 / a2 + y2 / b2) - IR(x2+y2) = I R (x2 - y2) (a 2 - b2)/(a2+b2), cp 1 = Rxy (a 2 - b2)/(a2 +b2), w1 = cb1 +% Pli = - IiR(x +yi)2(a2b2)/(a2+b2).

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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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  • The continuity is secured if the liquid between two ellipsoids X and X 11 moving with the velocity U and 15 1 of equation (II), is squeezed out or sucked in across the plane x=o at a rate equal to the integral flow of the velocity I across the annular area a l.

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  • Thus for m =2, the spheres are orthogonal, and it can be verified that a13 a2 3 aY3 i f /' = ZU (I - 13 - 7.2 3 + 3) ' (8) where a l, a2, a =a l a 2 /J (a 1 2 +a 2 2) is the radius of the spheres and their circle of intersection, and r 1, r 2, r the distances of a point from their centres.

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  • If p denotes the density of the air or medium W' = sird 3 xp, (23) W' I p __ W I -1 3 k12 I k22 x2 ±i a 2= 101-1 3 '111 2= 2 tan g S = Q (l - a) x 2+ I (26) in which a/p may be replaced by 800 times the S.G.

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  • After his death, the Assyrians, who were still nominally the vassals of Babylonia, threw off neser L - g n a ll disguise, and Shalmaneser I.

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  • On mixing the eslactones and reducing (d + l)-mnanitol was obtained, identical with a-acritol.

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  • Many pretty little finches fly about the maize-fields and fruit-gardens, and a little green parakeet is met with as l;.igh as 12,000 ft.

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  • In other Entoprocta the buds on a horseshoe retain a high degree of individuality, a shaped l o p h o - thread-like stolon giving off the cylindrical phore; stalks, each of which dilates at its end i, Ectocyst; into the body of a zooid.

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  • The remarkable grace of this moun- Fe L tams curvean inverted catenarymakes it one of the most beautiful in the world, and has obtained for it a prominent place in Japanese decorative art.

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  • British engineers surveyed the routes for the first lines and superintended the work of construction, but within a few years the, l apanese were able to dispense with foreign aid altogether, both in building and operating their railways.

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  • Annales des mines belgiques appears quarterly, and L' Art moderne weekly at Brussels.

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  • We know that in 498 he was staying at Edessa l; in or about 507, according to Theophanes, he was summoned by the emperor to Constantinople; and he finally presided at a synod at Sidon which was the means of procuring the replacement of Flavian by Severus.

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  • He had an oracle at Orchomenus, but during a plague it became L silent and remained so in Plutarch's time (De Defectu Oraculorum, 44).

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  • The small eyes are some- T y p h l o p s bra- times covered by transparent shields.

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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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  • 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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  • For if C l and C2 are the capacities and Q i and Q2 are the charges after contact, then Qi/CI and Q2/C2 are the potential differences of the coatings and must be equal.

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  • The heat absorbed in this change is called the latent heat of change of state, and may be represented by the symbol L'.

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  • 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,..

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  • The same equations apply to the case of fusion of a solid, if L is the latest heat of fusion, and v', s', v", s" the specific volumes and specific heats of the solid and liquid respectively.

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  • If the substance at the temperature 0 undergoes a change of state, absorbing latent heat, L, we have merely to add the term Lie to the above expression.

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  • The direct integration of this equation requires that L and v" - v' should be known as functions of p and 0, and cannot generally be performed.

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  • Although the duke strove after peace at almost any price, he was nearly always involved in war and l o st many possessions, including Geneva and Vaud.

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  • In negotiations between Anglican and Russian churchmen the confession of Dositheus l usually comes to the front.

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  • An instance is given, in L' Art de verifier les dates, of a date in which the year is reckoned from the 18th of March; but it is probable that this refers to the astronomical year, and that the 18th of March was taken for the day of the vernal equinox.

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  • The reason for this is readily seen; if a mass M of any gas occupies a volume V at a temperature T (on the absolute scale) and a pressure P, then its absolute density under these conditions is O = M/V; if now the temperature and pressure be changed to l and P,, the volume V l under these conditions is VPT/PIT1, and the absolute density is MP,T/VPT I.

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  • The volume u may be determined by repeating the experiment when only air is in the cup. In this case v =o, and the equation becomes (u --al l) (h - k') =uh, whence u = al' (h - k l) /k'.

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  • Calling the weight of the empty vessel w, when filled with the liquid W, and when filled with the standard substance W l, it is obvious that W - w, and W1 - w, are the weights of equal volumes of the liquid and standard, and hence the relative density is (W - w)/(Wi - w).

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  • If the bead of density dl be at the distance l l above the crystal, and that of d 2 at l 2 below, it is obvious that if the density of the column varies uniformly, then the density of the test crystal is (d1l2-+d211)/(ll+l2).

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  • His prince, abating those points which are purely Italian or strongly tinctured with the author's personal peculiarities, prefigured the monarchs of the 16th and 17th centuries, the monarchs whose motto was L'e'tat c' est moil His doctrine of a national militia foreshadowed the system which has given strength in arms to France and Germany.

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  • Important innovations in the constitution of 1897 are the office of lieutenantgovernor, and the veto power of the governor which may extend to parts and clauses of appropriation bills, but a bill may be passed over his veto by a three-fifths vote of each house of the legislature, and a bill becomes a law if not returned to the legislature withil l ten days after its reception by the governor, unless the session of the legislature shall have expired in the meantime.

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  • L' Entree en Espagne, preserved in a 14th-century Italian compilation, relates the beginning of the Spanish War, the siege of Pampeluna, and the legendary combat of Roland with Ferragus.

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  • The circles for position angle and declination are read by micrometer-microscopes illuminated by the lamp L; the scales are illuminated by the lamp 1.

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  • After a short stay in France he returned to Italy and identified himself with the Liberal movement; he became an active journalist, and founded a newspaper called L' Opinione in 1847.

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  • Their centres s l, s2, are held respectively by the pieces A, B, which together form a sliding pair.

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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.

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  • Clearly the integral is the sum of the values of mu g for all the molecules of the first kind in unit volume, thus p=v mu l +v'm'u 2 +...

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  • Ellis, l ater expanded, and in the process somewhat weakened, into his P liritan Age and Rule in the Colony of the Massachusetts Bay, 1629-168 5 (Boston, 1888; 3rd ed., 1891).

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  • If we draw a line at right angles to TCV, meeting TCV produced in M and parallels through A and B in K and L, the area of the triangle ATB is KL.

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  • Similarly, for a corresponding figure K'L'BA outside the parabola, the area is lK'L'(K'A+4M'C +L'B).

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  • It follows from §§ 48 and 51 that, if V is a solid figure extending from a plane K to a parallel plane L, and if the area of every cross-section parallel to these planes is a quadratic function of the distance of the section from a fixed plane parallel to them, Simpson's formula may be applied to find the volume of the solid.

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  • A -n- (64C1 - 20C2+C4) ' R C 1+9 (C 1 - C2) ?1(C l - C4).

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  • If the data of the briquette are, as in § 86, the volumes of the minor briquettes, but the condition as to close contact is not satisfied, we have y "`x P u dx dy = K + L + R - X111010-0,0 f xo yo i'?

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  • Either or both of the expressions K and L will have to be calculated by means of the formula of § 84; if this is applied to both expressions, we have a formula which may be written in a more general form f f 4 u4(x, y) dx dy = u dx dy.

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  • In the latter case the two sections are taken at distances t 2H/ A l 3 = = 2887H from the middle section, where H is the total internal length; and their arithmetic mean is taken to be the mean section of the cask.

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  • Let a be the radius of a circle, and 0 (circular measure) the unknown angle subtended by an arc. Then, if we divide 0 into m equal parts, and L 1 denotes the sum of the corresponding chords, so that L i =2ma sin (0/2m), the true length of the arc is L1 +a9 3 - 5 + ..., where cp. =B/2m.

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  • The method of § 71 then shows that, by taking a (4L 0 - L 2) as the value of the arc, we get rid of terms in 0 2.

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  • His chief works were First Lines of the Practice of Physic (1774); Institutions of Medicine (1770); and Synopsis Nosologicae Medicae (1785), which contained his classification of diseases into four great classes - (t) Pyrexiae, or febrile diseases, as typhus fever; (2) Neuroses, or nervous diseases, as epilepsy; (3) Cachexiae, or diseases resulting from bad habit of body, as scurvy; L and (4) Locales, or local diseases, as cancer.

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  • The blanks are placed in the slide J and the lowest one is carried forward to the die in two successive movements of the " layer-on " K, a rod working backwards and forwards on a horizontal plate and actuating the finger L, fig.

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  • This movement proceeds until the stirrup L below the left-hand hanger is raised far enough to touch the rod M, which is equal in weight to twice the remedy.

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  • The season for catching l amperns closes in the Thames about the middle of March.

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  • Live-stock and dairy products are important factors in the T C t o L %i, aa.

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  • Thus let the particle which was at L be at to the right or forwards, at a given instant.

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  • At L there is also displacement towards B and again compression.

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  • At L the displacement backward decreases, or the motion is forward FIG.

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  • Let AC be the H L FIG.

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  • We may represent the displacement due to one of the trains by y l =a sin 2 i (24) where x is measured as in equation (16) from an ascending node as A in fig.

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  • In this case AH = 4X 1 =1, the length of the tube, and the frequency n1= U/X 1 = U/4 l.

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  • If these lengths are h and l 2, then l2-11=ZX and 2(l2 - ll) - ll is the correction for the open end.

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  • In the next mode H and L represent the ends and HL =2.2 =1 and n 2 = U/X 2 =2U/2l.

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  • The flame there is much H K' L affected by the nodal pressure changes, while the other two vibrate only slightly.

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  • If L is the distance between successive dust-heaps, i.e.

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  • If L 1 is the internodal distance and U 1 the velocity in a gas, L and U being the corresponding values for air, we have U 1 /U =L1/L.

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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.

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  • Taking the squares of the amplitude to represent the intensity or loudness of the sound which would be heard by an ear at the point, this is 4a 2 cos t ir(ni - n2)t =2a 2 {1 -cos 27r(n l - n2)t}, a value which ranges between o and 4a 2 with frequency .n1 - n2.

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  • In the park is the fine Colombo Museum, founded by Sir William Gregory l; and near the neighbouring Campbell Park are the handsome buildings of a number of institutions, such as Wesley College, and the General, Victoria Memorial Eye and other hospitals.

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  • If r, r i be the radii of two spheres, d the distance between the centres, and 0 the angle at which they intersect, then d2=r2+ r12 2rr l cos ¢ hence 2rr 1 cos =d2r2 - r22.

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  • Then w 3 = (w l +w 2)1 2 /(Cds-1 2) = (w i -Fw 2)lr/ (Cs -lr), where C is a constant for any type of girder.

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  • The reactions at the abutments are R 1 = Wm/1 and R2 = W (l - m)/l.

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  • In that case the loads on either side of C are proportional to m and l - m.

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  • I c Is I f l ?

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  • Let P be the cost of one pier; G the cost of the main girders for one span, erected; n the number of spans; 1 the length of one span, and L the length of the bridge between abutments.

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  • Remembering that in this case the centre bending moment Ewl will be equal to wL 2 /8, we see that the horizontal tension H at the vertex for a span L (the points of support being at equal heights) is given by the expression 1..

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  • Divide the span L into any convenient number n of equal parts of length 1, so that nl = L; compute the radii of curvature R 1, R2, R3 for the several sections.

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  • Let measurements along the beam be represented according to any convenient scale, so that calling L 1 and 1 1 the lengths to be drawn on paper, we have L = aL i; now let r1, r 2, r 3 be a series of radii such that r 1 = R i /ab, r 2 = R 2 /ab, &c., where b is any convenient constant chosen of such magnitude as will allow arcs with the radii, r 1, &c., to be drawn with the means at the draughtsman's disposal.

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  • Rankine gives the approximate rule Working deflection =5= l a /t o,000h, where l is the span and h the depth of the beam, the stresses being those usual in bridgework, due to the total dead and live load.

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  • At first appeared a single number of the Moniteur patriote, followed on the 12th of September by the first number of the Publiciste parisien, which on the 16th of September took the title of L' Ami du peuple and which he edited, with some interruptions, until the 21st of September 1792.

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  • The Lion, as the symbol of fire, L represented the culmination of the solar heat.

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  • The Greeks, who had been squandering the money provided by the loans in every sort of senseless extravagance, affected to despise the Egyptian invaders, but they n h l`n were soon undeceived.

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  • Thus the path of the ray when the aether is at rest is the curve which makes fds/V least; but when it is in motion it is the curve which makes fds/(V+lug-m y -I-nw) least, where (l,m,n) is the direction vector of Ss.

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  • The product on the left-hand side may be taken to k terms only, thus if k =4, we have I I+x 2 .I+x 4 .I, I l?

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  • John's brother, Robert de Stratford, was also one of Edward II L's principal ministers.

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

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  • Moreover, in the unbridled exercise of speculation, the number of divine beings was increased indefinitely; and these fantastic accessions to l Olympus in the system of Iamblichus show that Greek philosophy 'is returning to mythology, and that nature-religion is still a power in the world.

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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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  • 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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  • 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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  • The main question with which we have now to deal is that of whether the dominant figure of the Saviour (l w-rlip) in Gnosticism is of specifically Christian derivation, or whether this can also be explained apart from the assumption of Christian influence.

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  • The equations finally arrived at are DX2(A2_ 2) (x2_ A2m)2+g2A2 ' DgA3 (A A l m) 2 +g 2 A2 ' where is the wave-length in free ether of light whose refractive index is n, and A m the wave-length of light of the same period as the electron, is a coefficient of absorption, and D and g are constants.

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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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  • The southern side is occupied by the "refectory" (K), from the west end of which by a vestibule the kitchen (L) is reached.

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  • The guest-house (L) was close by.

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  • At the eastern verge of the vast group of buildings we find the novices' lodgings (L), with a third cloister near the novices' quarters and the original guest-house (M).

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  • At L was the staircase to the dormitory.

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  • The general test of irrationality which he established is that, if a l a, a, be an interminate continued fraction, a l, a2,

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  • Not more than five or six of the 126 poems appear to have been composed by poets who I l iad been born in Islam.

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  • The ethics of these principles were worked out in Discours sur le bonheur, La Volupte, and L' Art de jouir, in which the end of life is found in the pleasures of the senses, and virtue is reduced to self-love.

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  • The readings of X which can be deduced from considering the agreements in B, C, D will be of higher antiquity and of greater external aut l ority than any of the readings in B, C, D taken singly.

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  • Let L Denote The Number Of The Dominical Letter Of Any Given Year Of The Era.

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  • Then, Since Every Year Which Is Not A Leap Year Ends With The Same Day As That With Which It Began, The Dominical Letter Of The Following Year Must Be L 1, Retrograding One Letter Every Common Year.

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  • In The Year Preceding The First Of The Era, The Dominical Letter Was C; For That Year, Therefore, We Have L =3; Consequently For Any Succeeding Year X, L =7M 3 X, The Years Being All Supposed To Consist Of 365 Days.

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  • The Value Of L Is Always Given By The Formula For The Dominical Letter, And P And 1 Are Easily Deduced From The Epact, As Will Appear From The Following Considerations.

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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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  • It Will Be Remarked, That As L 1 Cannot Either Be O Or Negative, We Must Add 7 To Las Often As May Be Necessary, In Order That L 1 May Be A Positive Whole Number.

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  • For The Golden Number We Have N = (401 $ 1) R; Therefore L = Before Easter.

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  • The constitution of the oxyazo compounds has attracted much attention, some chemists holding that they are true azophenols of the type R N 2 R l OH, while others look upon them as having a quinonoid structure, i.e.

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  • This collection was begun by Raphael Mengs, who secured casts of the most valuable antiques in Italy, l 'some of which no longer exist.

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  • We may say therefore that if the difference between the frequencies n 1 and n, of the two waves is such that in the combined image of the slit the intensity at the minimum between -the two maxima falls to 0.81, the lines are just resolved and n l /(n l n 2) may then be called the resolving power.

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  • If 1 2 and t l are thicknesses traversed by the extreme rays, t = t 2 - t,, and if, as is usually the case, the prism is filled right up to its refraction cap, = o, and t becomes equal to the greatest thickness of the medium which is made use of.

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  • After this time it becomes manifest that, as we should expect, documents were the recognized authorities for the Gospel history; but there is still some uncertainty as to the documents upon which reliance was placed, and the precise estimation in which l For the only two that can be held to be such in the first half of the 2nd century, and the doubts whether they refer to our present Gospels, see Mark, Gospel Of, and Matthew, Gospel Of.

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  • In order to eliminate any error due to the zero of the scale D not being exactly below the mirror magnet, the support L is then removed to the west side of the instrument, and the settings are repeated.

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  • The earliest African tradition, on the other hand, preserved by Tertullian l (De pudicitia, c. 20), but certainly not invented by him, ascribed the epistle to Barnabas.

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  • L, Nut to expand chamber filling bowl.

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  • Then let us heat both ice and solution through the infinitesimal temperature range dT to the freezing point T of the solvent, melt the ice by the application of an amount of heat L, which measures its latent heat of fusion, and allow the solvent so formed to enter the solution reversibly through a semi-permeable wall into an engine cylinder, doing an amount of work Pdv.

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  • In order to integrate this expression we need to know L and v as functions of the temperature and pressure.

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  • The latent heat L at any temperature is given by L=Lo - f 0 64 0 (s - s')dT, where Lo is value at To and s--s' is the difference in the specific heats of water and ice.

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  • The probable error in neglecting any variation of specific heat is small, and we may calculate L from the values of Lo - (s - s') (To - T), where s - s' is about 0.5 calories.

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  • The variation of L with pressure is probably small.

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  • If the heat of solution be measured in a calorimeter, no work is done, so that, if we call this calorimetric heat of solution L, the two quantities are connected by the relation L = X+P(v - v).

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  • If L is zero or negligible, X = - P(v - v) and we have dP/dT = - P/T or dP/P = - dT/T, which on integration gives log P =log T+C, or P= kT, i.e.

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  • If l is the heat of dilution per unit change of volume in a calorimeter where all the energy goes to heat, the change in internal energy U is measured by ldv.

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  • In the case where l is negligible we have P/dP = T/dT, which on integration shows that the osmotic pressure, as in the special case of a dilute solution, is proportional to the absolute temperature.

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  • To the north of the church, beyond the sacristy (L), and the side chapels (M), we find the cell of the sub-prior (a), with its garden.

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  • The study of the physical characteristics of criminals is discussed at great length by Lombroso, L` Uomo delinguente (1897); Ferri, L'Omicidio (1895); von Baer, Der Verbrecher (1893); Laurent, Les Habitues des prisons (1890); and Havelock Ellis, The Criminal (1901).

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  • The "arcs of Lowitz" (L) are probably due to small oscillations of the vertical prisms.

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  • Both schemes appeared practically impossible; potassium cost about L 1 7 per lb, gave a very small yield and was dangerous to manipulate, while on the other hand, the only source of electric current then available was the primary battery, and zinc as a store of industrial energy was utterly out of the question.

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  • Under its influence twelve ministers at Kettering in October 1792 organized the Baptist Society for Propagating the Gospel among the Heathen, and subscribed L 13, 2s.

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  • The axis N 0 passes through the brass piece M, which stands on an insulating pillar of glass, and supports the plates A and C. At one extremity of this axis is the ball D, and the other is connected with a rod of glass, N P, upon which is fixed the handle L, and also the piece G H, which is separately insulated.

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  • If two Leyden jars L, L were hung upon the conductors which supported the combs, with their outer coatings put in connexion with one another by M, a series of strong spark discharges passed between the discharge balls.

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  • L, Edge of the mantle not removed in the front part of the specimen.

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  • Functional male and female organs have been shown to exist in Pyronema and Boudiera; in Lachnea stercorea both ascogonia and antheridia a are present, but the antheridium a1 is non-functional, the ascogonial _s- - (fema l e) nuclei fusing in pairs; /'y' this is also the case' in Humaria /;' h; granulate and Ascobolus furfurs -./ '"aceus, where the antheridium is _ / /, - entirely absent.

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  • Again, as the temperature in turn falls past Ar l this hardenite mother-metal splits up into cementite and ferrite grouped together as pearlite, with the resulting recalescence, and the mass, as shown in Alloys, Pl., fig.

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  • All these phenomena are parallel with those of 1 oo% carbon steel at this same critical point Ar l.

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  • Between H and S, Ar 3 and Ar 2 occur together, as do Ar 2 and Ar l between S and P' and Ar 3, Ar 2 and Ar t at S itself; so that these critical points in these special cases are called Ar 3 _ 2, Ar2_1 and Ar 3 _ 2 _ 1 respectively.

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  • The farther descent of the bucket being thus arrested, the special cable T is now slackened, so that the conical bottom of the bucket drops down, pressing down by its weight the the string of moulds, each thus containing a pig, moves slowly forward, the pigs solidify and cool, the more quickly because in transit they are sprayed with water or even submerged in L Winter Stock Pile .?t' S ..

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  • The tilting working chamber is connected with the stationary ports L and L' by means of the loose water-cooled joint W in Campbell's system, which is here shown.

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  • According to Hantzsch the isomeric diazo hydroxides are structurally identical, and the differences in behaviour are due to stereo-chemica l relations, the isomerism being comparable with that of the oximes.

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  • At Drah abu'l nagga, opposite to it, are tombs of its princes under the VIth Dynasty.

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  • The necropolis extends from Kurna in the north through Drah abu'l nagga, the Assasif, and Shekh abd el Kurna to Kurnet Murrai of Medinet Habu.

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  • Some petioles are long, slender and sensitive to contact, and function as tendrils by means of which the plant climbs; as in the l,' nasturtiums (Tropaeolum), clematis and c in others; and in compound leaves the midrib and some of the leaflets may similarly be transformed into tendrils, as in the pea and vetch.

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  • There are a well-known grammarschool, founded by Edward VI., with university scholarships; a college school, a literary ` L institute, and a school of art.

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  • His greatest work, L' Electrisation localisee (1855), passed through three editions during his lifetime, though by many his Physiologie des mouvements (1867) is considered his masterpiece.

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  • It has until lately been the practice to remove these to the museum at Naples; but the present tendency is to leave them (and even the movable objects found in the houses) in situ with all due precautions as to their preservation (as in the house of the Vettii, of the Silver Wedding, of the Golden Cupids, &c.), which adds immensely to the interest of the houses; indeed, with the l,eip of judicious restoration, their original condition is in large measure reproduced.'

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  • Valle Crucis Abbey (L lan Egwest) is a Cistercian ruin at the foot of Bronfawr hill, some 2 m.

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  • Turning to the left bank, there is the same high-level canal from the upper system irrigating the basins K, P and L, as well as the large basin E in such years as it cannot be irrigated from the main canal.

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  • Ferdinand L, who like all the German sovereigns after him was recognized as emperor without being crowned by the pope, made it a prime object of his short reign to defend and and enforce the religious peace of Augsburg for which he was largely responsible.

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  • His long Leopold L reign of 48 years was of great importance for Austria, as determining both the internal character and the external policy of the monarchy.

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  • Even in Greek, /itKEXoL is now sometimes used instead of nKE%L&rat.

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  • The swallow who heralded the summer was a German by birth, Adolph Wilhelm Schack von Staffeldt l (1769-1826), who came over to Copenhagen from Pomerania, and prepared the way for the new movement.

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  • The legend of Wayland probably had its home in the north, where he and his brother Egil l 2 were the types of the skilled workman, but there are abundant local traditions of the wonderful smith in Westphalia and in southern England.

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  • Hill@l's patience has become proverbial.

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  • L I subjected in a series of large cast-iron cylinders to the action of pyrites-burner gases and steam at a low red heat.

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  • The death of his father had left him an estate of 1900 acres, the income from which (about £400) gave him the position of an independent country gentleman; and while engaged in the law he had added to his farms after the ambitious Virginia fashion, until, when he married in his thirtieth year, there were s000 acres all paid for; and almost as much more l came to him in 1773 on the death of his father-in-law.

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  • The greatest length of the leopard is L about 7 ft.

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  • The figures given are the partial dispersions for ordinary crown and ordinary extra dense flint glasses, styled in Messrs Schott's catalogue of optical glasses as o 60 and 0.102 respectively, having refractive indices of 1 5179 and 1.6489 for the D ray respectively, and (µ D -I)/(l F -µc) =60 2 and 33.8 respectively to indicate their dispersive powers (inverted), = v.

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  • Let it be supposed that two positive lenses of equal curvature powers are made out of these two glasses, then in order to represent the combined dispersion of the two together the two 0µ's for each spectral region may be added together to form 0'µ as in the line below, and then, on again expressing the partial z'µ in terms of L'µ (C to F) we get the new figures in the bottom row beneath the asterisks.

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  • In practice the vertical circle is adjusted once for all, so that when the levels k and l are in the centre of their run, the verniers read true zenith distances.

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  • Suppose now, for the moment, that the readings of the levels k and l are identical in both observations, we have then, in the difference between the micrometer readings north and south, a measure of the difference of the two zenith distances expressed in terms of the micrometer screw; and, if the "` value of one revolution of the micrometer screw" is known in seconds of arc we have for the resulting latitude FIG.

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  • A is the calorimetric tube, B the air-jacket and L the gauge.

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  • Other frequent clausulae, which he terms licitae (L), are those in which a long syllable is resolved, as in verse, into two shorts, e.g.

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  • These two classes, V and L, include 86% of the clausulae in the orations.

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  • Jacques Cassini also proved that Arcturus had even since the time of Tycho Brahe shifted five minutes in latitude; for r l Bootis, which would have shared in the change, if it had been due to a motion of the ecliptic, had not moved appreciably.

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  • But even Sigwart's errors are outdone by Lotze, who not only reduces " Every NI is P " so " If S is M, S is P," but proceeds to reduce this hypothetical to the disjunctive, " If S is NI, S is P L or P 2 or 1 33, " and finds fault with the Aristotelian syllogism because it contents itself with inferring " S is P " without showing what P. Now there are occasions when we want to reason in this disjunctive manner, to consider whether S is I n or P 2 or P 3, and to conclude that " S is a particular P "; but ordinarily all we want to know is that " S is P "; e.g.

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  • For the depression of the freezing-point a relation of the same form applies, but do is negative, and L is the latent heat of fusion.

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  • This relation cannot be directly integrated, so as to obtain the equation for the saturation-pressure, unless L and v - w are known as functions of 0.

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  • The simplest assumptions to make are that the vapour behaves as a perfect gas (or that p(v-w) = Re), and that L is constant.

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  • It is obvious, however, that the assumption L =constant is not sufficiently accurate in many cases.

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  • Under these conditions both S and s may be regarded as approximately constant, so that L is a linear function of the temperature.

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  • Taking for ice and water the following numerical data, L = 674.7, 6 74.7, L 1 =595.2, L r = 79.5, R = o 11 03 cal./deg., po = 4.61 mm., s-S = 519 cal./deg., and assuming the specific heat of ice to be equal to that of steam at constant pressure (which is sufficiently approximate, since the term involving the difference of the specific heats is very small), we obtain the following numerical formulae, by substitution in (23), Ice..

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  • It is easy, however, to correct the formula for these deviations, and to make it thermodynamically consistent with the characteristic equation (13) by substituting the appropriate values of (v-w) and L =H -h from equations (13) and (is) in formula (21) before integrating.

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  • But this neglects the latent heat of solution, unless we may suppose it included by writing the internal latent heat L i in place of L in Callendar's formula.

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  • The latent heat L (formula 9) is found by subtracting from H (equation 15) the values of the heat of the liquid h given in the same article.

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  • On his retirement he turned to the astronomy of the Hebrews and Babylonians; his earlier results are given in his L' Astronomia nell' antico Testamento (1903), a work which has been translated into English and German, whilst later ones are to be found in various journals, the last being in Scientia (1908).

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  • At its north-west extremity rises the height of Arcona, with a l ighthouse.

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  • The symbol for 13 in Thera is nearer than any previously known to the Semitic letter (9) though, as not infrequently happens in the transference of a symbol from one people to another, its position is inverted - a fate which in this alphabet has befallen also A (Semitic L, Thera 1), and possibly o (Semitic N, Thera M).

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  • This page gives an overview of all articles in the 1911 Brittanica which are alphabetized under L to La.

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  • The strip B carries also a F L/ B strip of gld-leaf L, and the metal case is connected to earth.

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  • Since R2=X2+Y2+Z2, G2=L1+M2+N2, it is necessary and sufficient for equilibrium that the six quantities X, Y, Z, L, M, N, should all vanish.

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  • The first three terms express the work done by the components of a force (X, Y, Z) acting at 0, and the remaining three terms express the work of a couple (L, M, N).

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  • Hence th,l moment of the momentum (considered as a localized vector) about 0 will be constant.

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  • For given values of n and 0 we have two possible values of i,l provided n exceed a certain limit.

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  • If L, M, N be the moments of the extraneous forces about Ox, Oy, Os this must be equal to Xl--LOt.

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  • If we now apply them to the case of a rigid body moving about a fixed point 0, and make Ox, Oy, Oz coincide with the principal axes of inertia at 0, we have X, u, v=Ap, Bq, Cr, whence A (B C) qr = L,

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  • The length L of an endless belt connecting a pair of pulleys whose effective radii are r,, r,, with parallel axes whose distance apart is c, is given by the following formulae, in each of which the first term, containing the radical, expresses the length of the straight parts of the belt, and the remainder of the formula the length of the curved parts.

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  • Let S be the length of stroke of the reciprocating piece, L the length of the line of connection, and R the crank-arm of the continuously turning piece.

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  • On the connecting rod take a point L such that KLXKB =KO2.

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  • Immediately after the accession of Louis Philippe they started their famous newspaper, L' Avenir, hoping thereby to reconcile the Church with democracy, and make the pope the leader of the party of progress.

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  • Pius had fed on inspirations; Leo was a man of calm, deliberate judgment, little likely to po ' 'L pe eo XIII.

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  • This influence was common to all the continental states an,l indirectly was felt even in England.

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  • Hence the mass of an electron is y ff l iT uth of that of a hydrogen atom.

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  • Chamberlayne, Lacrimae nicossienses (Paris, 1894); and C. Enlart's volumes, L' Art gothique et la Renaissance en Chypre (Paris, 1899), deal with medieval architecture.

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  • His numerous works include the musical comedy, Pierre le Grand (1790), for Gretry's music, and the opera, Les Deux Journees (1800), music by Cherubini; also L' Abbe de l'epee (1800), and some other plays; and Causeries d'un vieillard (1807), Contes a ma fille (1809), and Les Adieux du vieux conteur (1835).

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  • Cuprous iodide, Cu 2 l 21 is obtained as a white powder, which suffers little alteration on exposure, by the direct union of its components or by mixing solutions of cuprous chloride in hydrochloric acid and potassium iodide; or, with liberation of iodine, by adding potassium iodide to a cupric salt.

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  • Let R = the revolutions per second of the flyer; r = the revolutions per second of the bobbin; d = the diameter of bobbin shaft plus the material; L = the length of sliver delivered per second; then (R - r) d.

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  • In the above expression R, it and L are constant, therefore as d increases the term (R - r) must decrease; this can happen only when r is increased, that is, when the bobbin revolves quicker.

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  • So precarious was the position Gustavus L, genius p p 1523-1560.

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  • If S (fig.5) be any optical system, rays proceeding from an axis point 0 under an angle u l will unite in the axis point O'1; and those under an angle 24 2 in the axis point 0'2.

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  • If the object point 0 be infinitely distant, u, and u 2 are to be replaced by h l and h 2, the perpendicular heights of incidence; the " sine condition " then becomes sin u',/h 1 = sin u' 2 /h 2 .

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  • Every simple continued fraction must converge to a definite limit; for its value lies between that of the first and second convergents and, since f ?n _ _1 I, L t.

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  • Let the fraction be a l a 2 al +...

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  • The functions p n and q n, regarded as functions of a l,..

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  • Le Calvaire (1887), a chapter of which on the defeat of 1870 aroused much discussion, was followed by L' Abbe Jules (1888), the story of a mad priest; by Sebastien Roch (1890), a bitter picture of the Jesuit school in which his own early years were spent; Le Jardin des supplices (1899), a Chinese story; Les Memoires d'une femme de chambre (1901); and Les Vingt-et-un jours d'un neurasthenique (1902).

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  • A pit called the "Maelstrom," in Croghan's Hall, is the spot most remote from the mouth of Gerta's Grotto Creighton's Dome Index Hovey's Cathedral 0' Martel Nelson's Domes p a e t a j-?l . ?Einbigler Dome Edna's Dome Galloway's Dome Chief City Violet.

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  • Pombal's dismissal, brought about by the influence of the queen-mother Mariana Victoria, Maria L, did not involve an immediate reversal of his policy.

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  • It is the seat of a l aimmakam or sub-governor, subordinate to the governor of 'Akka.

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  • If a i, a 2 represent the densities of the two infinite solids, their mutual attraction at distance z is per unit of area 21ra l a fZ '(z)dz, (30) or 27ra l 02 0(z), if we write f 4,(z)dz=0(z) (31) The work required to produce the separation in question is thus 2 7ru l a o 0 (z)dz; (32) and for the tension of a liquid of density a we have T = a f o 0 (z)dz.

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  • Let l be the breadth of the plates measured perpendicularly to the plane of the paper, then the length of the line which bounds the wet and the dry parts of the plates inside is 1 for each surface, and on this the tension T acts at an angle a to the vertical.

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  • We shall next consider the rise of a liquid between two plates of different materials for which the angles of contact are a l and a 2, the distance between the plates being a, a small quantity.

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  • Hence in all cases except that in which the angles a l and a 2 are supplementary to each other, the force is attractive when a is small enough, but when cos a i and cos a 2 are of different signs, as when the liquid is raised by one plate, and depressed by the other, the first term may be so small that the repulsion indicated by the second term comes into play.

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  • C D 0K2, a b c m Q c 6 L -...

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  • Ten years after the publication of the fourth book and nine after the supposed date of the author's death there appeared at Lyons sixteen chapters entitled l&'le sonnante par maistre Francois Rabelais, and two years later the entire fifth book was printed as such.

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  • Similar forms are also found in early Aramaic, but another form 1 or L, which is found in the Phoenician of Cyprus in the 9th or 10th century B.C. has had more effect upon the later development of the Semitic forms. The length of the two back strokes and the manner in which they join the upright are the only variations in Greek.

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  • Each taeniola bears a strongly developed longitudinal muscle-band, stated by Claus and Chun to be developed from the endoderm, like the retractor muscles of the anthopolyp, but by other investigators it is affirmed that each retractor muscle of the scyphistoma arises from the lining of a funnel-shaped ectodermal ingrowth (" Septaltrichter ") growing down from the peristome inside each taeniola, in a manner similar to the infundibular cavities of Lucernaria, which in their turn are homologous with the sub f genital cavities of Scypho l A .` medusae.

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  • Vigorous and aggressive as a critic, his articles on literature and art in Villemessant's paper L' Evenement created a good deal of interest.

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  • The kite-like surfaces and angles made by the wing with the horizon (a, b) during the down strokes are indicated at c d e f g, j k l m, - those made during the up strokes being indicated at g h i.

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  • On the contrary, he will perceive that the under surface of the wing (during the down stroke) invariably looks forwards and forms a true kite with the horizon, the angles made by the kite varying at every part of the down stroke, as shown more particularly at c d e f g, i j k l m of fig.

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  • V?'o?took?s,l eSk ham o h `u Br1 n NewC l 4 ',fteg, r,a, t Sha?

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  • Under the Isolation Hospitals Acts 1893 and 1901, a county council may provide for the establishment of isolation hospitals for the reception of patients suffering from infectious diseases on Hospi t a l s the application of any local authority within the county, or on the report of the medical officer of the county that hospital accommodation is necessary and has not been provided, or it may take over hospitals already provided by a local authority.

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  • A similar Electric licence or order may be granted to a private person or l i ghting.

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  • At this time a mission church was built on the heights overlooking the bay by Captain Allen Gardner, R.N., who named the hill Berea in gratitude for support received from the settlers, whom he found " L 'more noble than those of " Zululand - Dingaan having refused to allow the captain to start a mission among his people.

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  • The use of EtSos in the sense of " poem " is somewhat doubtful, and so some have referred ELb 5XXca to El50s in its usual sense of " form " or L ` type."

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  • In 1865, Menelek, now a dejazmach l of Tigre, took advantage of Theodore's difficulties with the British government and escaped to Workitu, queen of the Wollo Galla country.

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  • On the advice of a member of Gung'l's band who had taken up his residence in Edinburgh, Mackenzie was sent for his musical education to Sondershausen, where he entered the conservatorium under Ulrich and Stein, remaining there from 1857 to 1861, when he entered the ducal orchestra as a violinist.

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  • Like the family of O'Neill, that of O'Donnell was descended from Niall of the Nine Hostages, king of Ireland at the beginning of the 5th century; the O'Neills, or Cinel l Owen, tracing their pedigree to Owen (Eoghan), and the O'Donnells, or Cinel Connell, to Conall Gulban, both sons of Niall.

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  • In the northern districts the rivers run along the valleys, receive the drainage from the country on !l either side, absorb broad tributaries and rush forward with an ever-increasing volume.

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  • If lo represents the intensity of the light which enters the surface, I l the intensity after passing through i centimetre, I 2 the intensity after passing through 2 centimetres, and so on; then we should expect that whatever fraction of Io is absorbed in the first centimetre, the same fraction of I, will be absorbed in the second.

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  • Mais apres l' Attila Hola!"

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  • Further fighting followed on this proclamation, which was by no means successful, and although peace was declared in the country in December 1882, the colonial authorities were very glad in 1884 to be relieved of the administration of a country which had already cost them L 3, 000,000.

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  • He was leader of the expedition wherein Porto Bello, one of the l, bestfortified ports in the West Indies, was surprised and plundered.

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  • The central and essential ceremonies of the hajj or greater pilgrimage are those of the day of Arafa, the 9th of the "pilgrimage month" (Dhu'l Hijja), the last of the Arab year; and every Moslem who is his own master, and can command the necessary means, is bound to join in these once in his life, or to have them fulfilled by a substitute 1 The latter perhaps was no part of the ancient omra; see SnouckHurgronje, Het Mekkaansche Feest (1880) p. 115 sqq.

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  • He therefore leaves Mecca in pilgrim garb on the 8th of Dhu'l Hijja, called the day of tarwiya (an obscure and pre-Islamic name), and, strictly speaking, should spend the night at Mina.

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  • VerticaZ.scal p l3Mires lonoituo n/al sale Dizonelerot,eio,l 1*M tom Surface of Ground Older and less parruu I strata._ FIG.

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  • If, therefore, the centre of that became so far removed to the right as to make j coincident with b, the diagram of stresses would become the triangle j'l'c', and the vertical pressure at the inner face would be nil.

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  • The end knife-edges are adjusted and tightly jammed into exact position by means of wedge pieces and set screws, and the beam is furnished with delicate adjusting weights at its top. The position of the beam with respect to the horizontal is shown by a horizontal pointer (not shown) projecting from one end of it, which plays past a scale, each division of which corresponds to the i l oth or i hth of a grain according to the size and delicacy of the machine.

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  • Using the symbols of the diagram, it can be shown that the effect of placing the weight W at E instead of F is to cause the end of the beam to descend, as if under the action of an additional weight, w, at F such that w Wa(ml - l +tan 0)/h.

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  • If now a small weight, as a penny, be passed through the slot, H, it falls into the small box, I, and causes the lever, J, to turn; the lever, J, which turns in friction wheels at K, and is counterbalanced at 0, carries a toothed segment, L, which actuates a small pinion on the same axle as F, and is free to turn on that axle by a sleeve.

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  • The value of l may be easily shown to be (r i -Er 2)1r/2 (r i t r 2)a-+-c cos a, where the positive sign is to be taken for a crossed belt and the negative sign for an open belt.

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  • If now the value l/ar=OJ be marked off, and a horizontal line be drawn through the point 0, the line OM represents r l +r 2 .

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  • The load, supported by the lower hook, is raised by hauling on the free end and, neglecting any slight obliquity of the plies of rope, the free end moves six times as fast H L C FIG.

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  • His brochures are very numerous and on a great variety of subjects, medical, historical, political, philosophical, &c. He died on the l 2th of August 1865.

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  • The A l -' 4 acid is obtained as its anhydride by heating A 2.4 dihydrophthalic anhydride with acetic anhydride.

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  • The number is divisible (i) by io if it ends in o; (ii) by 5 if it ends in o or 5; (iii) by 2 if the last digit is even; (iv) by 4 if the number made up of the last two digits is divisible by 4; (v) by 8 if the number made up of the last three digits is divisible by 8; (vi) by 9 if the sum of the digits is divisible by 9; (vii) by 3 if the s l um of the digits is divisible by 3; I 3=31 2 9 =32 3 27=33 481 =34 (viii) by II if the difference between the sum of the 1st, 3rd, 5th,.

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  • For practical purposes logarithms are usually calculated to base i o, so that log l o 10 = I, log i n I oo = 2, &C.

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  • Expression in L and decimals of LI is usually recommended, but it depends on circumstances whether some other method may not be simpler.

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  • For example, 3.14 16= 3Xi g t o = 3x l g = 3X g fxz 9= 3(I + 1 1) (I - 2-50-6) Hence, to multiply by 3.1416, we can multiply by 34, and subtract 2 0 o (_ .0004) of the result; or, to divide by 3 .

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  • There are also certain special units, such as the hectare, which is equal to a square hectometre, and the micron, which is i o l ?

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  • A and B are the coils to be compared, P and Q are two other L -x FIG.

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  • I Libera l?'

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  • In northern France, Calais and the county of Guines, and also the isolated county of Ponthieu, the inheritance of the wife of Edward L, were ceded to the English crown.

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  • During eight years, however, Pitts ministry was not nerely a Tory ministry resting on the choice of the king, but a L,iberal ministry resting on national support and upon advanced Dolitical knowledge.

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  • Later generations have learned by repeated experience that the eloquence of Hyde Park orators is not the voice of England; there were some even then-among those not immediately responsible for keeping orderwho urged the government to ti-ust the people;l but with the object-lesson of France before them it is not altogether surprising that ministers refused to believe ih the harmlessness of societies, which not only kept up a fraternal correspondence with the National Convention and the Jacobi.

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  • In 1877 appeared the second series of La Legende des siecles; and in the same year the author of that colossal work, treating no less of superhuman than of human things, gave us the loveliest and most various book of song on the loveliest and simplest of subjects ever given to man, L' Art d'être grandpere.

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  • One of its marked features is the five parallel furos l which from the north-west at almost regular intervals the Amazon sends to the Purus; the most south-westerly one being about 150 m.

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  • Considering an equation in point-co-ordinates, we may have among the component curves right lines, and if in order to put these in evidence we take the equation to be L 1 Y1..

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  • This is done, without interfering with the blast, in order to keep the fuel at the proper level in L, according to the indications of the burning zone, as shown through the peep-holes B 1 to B4.

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  • A son of Muley Abu'l Hassan, king of Granada, he was proclaimed king in 1482 in place of his father, who was driven from the land.

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  • Annesley l saw the king in 1890, with the hope of making a treaty, but failed in his object.

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  • The second narrative is P l, which tells how Korah, himself a Levite, at the head of 250 Israelites rebelled against the religious authority of Moses.

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  • In 1 839 he wrote a treatise L' Utilite de la celebration du dimanche which contained the germs of his revolutionary ideas.

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  • Moreover, the functions b'c" - b"c', b"c - bc", bc' - b'c used in the process are themselves the determinants of the second order l b",c"I?

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  • In the language of algebra putting m l, m2, m 3, &c. for the masses of the bodies, r1.2 r1.3 r2.3, &c. for their mutual distances apart; vi, v 2, v 3, &c., for the velocities with which they are moving at any moment; these quantities will continually satisfy the equation orbit, appear as arbitrary constants, introduced by the process of integration.

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  • The general expression for the angle will then be L =nt+Lo.

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  • Here the coefficients of 1 and l' may separately take all integral values, though as a general rule the coefficients a, b, c, &c. diminish rapidly when these coefficients become large, so that only small values have to be considered.

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  • It follows that L the motions of the mean longitudes are nearly in the same proportion re versed.

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  • In western New Guinea, according to the Dutch missionaries, there is a vague notion of a universal spirit, practically represented Spirit by several malevolent powers, as Manoin, the mostn the woods; Narw, in the worship. c p louds, u above the trrees, l a sort of Erl-Konig h o carries off children; Faknik, in the rocks by the sea, who raises storms. As a protection against these the people construct - having first with much ceremony chosen a tree for the purpose - certain rude images called karwars, each representing a recently dead progenitor, whose spirit is then invoked to occupy the image and protect them against their enemies and give success to their undertakings.

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  • Not the slightest change in the direction of such a star when in this position has ever been detected, and it is certain that if any occurs it can be but a minute fraction of a second of arc. As an atmosphere equal to ours in density would produce a deviation of an important fraction of a degree, it may be said that the moon can have no atmosphere exceeding in density the b b l o o that of the earth.

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  • Burnet now travelled in Italy, Germany and Switzerland, finally settling in Holland' l at the Hague, where he won from the princess of Orange a confidence which proved enduring.

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