# V Sentence Examples

Hence the work done in raising the mass will be represented by mg

**v**2 /2g, that is, Zmv 2 ergs.If a body whose mass is m grammes be moving with a velocity of

**v**centimetres per second relative to the earth, the available kinetic energy possessed by the system is Zmv 2 ergs if m be small relative to the earth.If the speed is given in miles per hour, S say,

**V**=1.466 S (6) The revolutions of the axle per second, n, are connected with the radians turned through per second by the relation n =w/27r = w/6.38 (7) § 2.In the time of Ptolemy their territory is limited to the district between the Ciabrus (Tzibritza) and Utus (Vid), in the modern Bulgaria, their chief town being Oescus (OtvKos Tpc aXX6

**v**).They consist of two rows of balls rolling in two pairs of

**V**races or grooves.This

**V**has been variously interpreted.As attorney-general he argued the famous cases, the United States

**v**.For the German and Austrian nobility, see

**v**.Finding that the walls of autocracy could not be overturned by blasts of revolutionary trumpets in the periodical press and in clandestinely printed seditious proclamations, the young enthusiasts determined to seek the support of the masses, or, as they termed it, " to go in among the people " (idti

**v**narod).Where a branch diverges from a main line, one rail of the one must cross one rail of the other, and a

**V**-crossing is formed (**V**).AdvertisementIf the total resistance against which the train is maintained in motion with an instantaneous velocity of

**V**feet per second is R, the rate at which energy is expended in moving the train is represented by the product RV, and this must be the rate at which energy is supplied to the train after deducting all losses due to transmission from the source of power.In equation (4) there is a fixed relation between w,

**V**and D given by the expression.The relation between the b.h.p. and the torque on the driving-axle is 55 o B.H.P. =Tu., (9) It is usual with steam locomotives to regard the resistance R as including the frictional resistances between the cylinders and the driving-axle, so that the rate at which energy is expended in moving the train is expressed either by the product RV, or by the value of the indicated horse-power, the relation between them being 55 0 I.H.P. =RV (Io) or in terms of the torque 55 0 I.H.P.X€=RVe=TW (II) The individual factors of the product RV may have any value consistent with equation (to) and with certain practical conditions, so that for a given value of the I.H.P. R must decrease if

**V**increases.Hence Engine resistance, R e = 80 X20 = 1600 lb Vehicle resistance, R

**v**=200 X8.5 = 1700 „ Train resistance, R = 3300 „ The speed, 40 m.Hence if a train is travelling up the gradient at a speed of

**V**ft.AdvertisementDividing thr Hugh by

**V**and multiplying through by 550, 2240W 2240Wa R =Were+W vry t G (23) ' 'an expression giving the value of R the total tractive resistance.If the draw-bar pull is known to be R

**v**, then applying the same principles to the vehicle alone which above are applied to the whole train, total draw-bar pull = Wvry 2240Wv 2240Wva.**V**or slipping will take place.The expression for the indicated horse-power may be written I.H.P. =pay/550 (27) where

**v**is the average piston speed in feet per second.For a stated value of the boiler pressure and the cut-off the mean pressure p is a function of the piston speed

**v**.AdvertisementThe berosh, or beroth, of the Hebrew Scriptures, translated "fir" in the authorized version, in I Kings

**v**.For other examples see Notes and Queries, 1st series,

**v**.Yet another expedition in 839 would seem to 2 See for chronology, Babylonia And Assyria, §§

**v**.A peculiar feature is presented by the level upland basins which furnish abundant pasturage during the summer months; the more remarkable are the Omalo in the White Mountains (about 4000 ft.) drained by subterranean outlets (KaTa(30Opa), Nida (Eis T7)

**v**"IBav) in Psiloriti (between 5000 and 6000 ft.), and the Lassithi plain (about 3000 ft.), a more extensive area, on which are several villages.It

**v**e mires very little moisture, grows luxuriantly on the thin calcareous soil of Yucatan and is cultivated almost exclusively by the large landowners.AdvertisementThere are three pairs of spermathecae situated in segments III-

**V**, a testis in**V**and an ovary in VI.His next great case was that of M'Culloch

**v**.Four years later (1823) Webster argued the case of Gibbons

**v**.Accounts of his professional services are in Charnock's Biographia Navalis,

**v**.It can be traced back to the intestine i near the surface of the visceral hump, and it is found that the apex of the coil formed by the hump is occupied by the liver h and the stomach

**v**.The ciliated band of the left side of the velar area is indicated by a line extending from

**v**to**v**; the foot f is seen between the pharynx ph and the pedicle of invagination pi.Tiedemann's carefully-wrought Anatomic and N aturgeschichte der

**V**gel - which shows a remarkable advance upon the work which Cuvier did in 1805, and in some respects is superior to his later production of 1817.Ha lln

**v**-_ trey .His coins of 270 struck at Alexandria bear the legend

**v**(ir) c(onsularis) R(omanorum) im(perator) d(ux) R(omanorum) and display his head beside that of Aurelian, but the latter alone is styled Augustus.This letter corresponds to the second symbol in the Phoenician alphabet, and appears in the same position in all the European alphabets, except those derived, like the Russian, from medieval Greek, in which the pronunciation of this symbol had changed from b to

**v**.When this consonantal u (English w as seen in words borrowed very early from Latin like wall and wine) passed into the sound of English

**v**(labio-dental) is not certain, but Germanic words borrowed into Latin in the 5th century A.D.The rabbinical discussions of the book are mentioned in Shabbath, 30b; Megilla, 7a; Eduyoth,

**v**.On a crag above the town stands the

**v**.A diagnosis covering all the Ratitae (struthio, rhea, casuarius, dromaeus, apteryx and the allied fossils dinornis and aepyornis) would be as follows - (i) terrestrial birds without keel to the sternum, absolutely flightless; (ii) quadrate bone with a single proximal articulating knob; (iii) coracoid and scapula fused together and forming an open angle; (iv) normally without a pygostyle; (

**v**) with an incisura ischiadica; (vi) rhamphotheca compound; (vii) without apteria or bare spaces in the plumage; (viii) with a complete copulatory organ, moved by skeletal muscles.Of the tri-substitution derivatives, 1.2.3.-compounds are known as " adjacent " or " vicinal " (

**v**), the 1.2.4 as " asymmetrical " (as), the 1.3.5 as " symmetrical " (s), of the tetrasubstitution derivatives, 1.2.3.4-compounds are known as " adjacent," 1.2.3.5 as " asymmetrical," and 1.2.4.5 as " symmetrical."Di-derivatives x x x p

**v**as $**v**as s Here we have assumed the substituent groups to be alike; when they are unlike, a greater number of isomers is possible.Ladenburg (Ber., 2, p. 140) devised his prism formula (IV), the six carbon atoms being placed at the six corners of a right equilateral triangular prism, with its plane projections (

**V**, VI).This method has been improved, especially by Justus

**v**.If we denote the critical volume, pressure and temperature by Vk, Pk and Tk, then it may be shown, either by considering the characteristic equation as a perfect cube in

**v**or by using the relations that dp/dv=o, d 2 p/dv 2 =o at the critical point, that Vk = 3b, Pk= a/27b2, T ic = 8a/27b.Eliminating a and b between these relations, we derive P k

**V**k /Tk= 8R, a relation which should hold between the critical constants of any substance.Van der Waal's equation (p-I- a/

**v**2) (**v**- b) = RT contains two constants a and b determined by each particular substance.In Phoenician itself and in the other Semitic alphabets the position of the middle legs of the W is altered so that the symbol takes such forms as or

**V**or w, ultimately ending sometimes in a form like K laid sideways, he.They consider themselves bound by the literal interpretation of James

**v**.It is first mentioned in the year 220 by Polybius

**v**.I, which reads 6 'yap ayysXos TT7s ELpilv77s M577'yei Tr 7

**v**aurOU.The latter was perhaps regarded as a "smith," cp.

**v**.But the idea of liberation continued to grow, and about 1780 the Society of Friends (`ETaepia Twv 4 c uK'

**v**) was founded at Bucharest by the fervent patriot and poet, Constantinos Rhigas (q.**v**.).Leonardo gave as solution the numbers 11 i 4 4, 16, 9 4 - 7 4 and 6197 T, - the squares of 3,, 41'

**v**and 2, 7; and the method of finding them is given in the Liber quadratorum.See Herodotus

**v**.They are called from the places in France where the most typical finds of palaeolithic remains have been made - Chellian from Chelles, a few miles east of Paris; Mousterian from the cave of Moustier on the river

**V**ezere, Dordogne; Solutrian from the cave at Solutre near Macon; and Madelenian from the rocky shelter of La Madeleine, Dordogne.The number of undissociated molecules is then I - a, so that if

**V**be the volume of the solution containing I gramme-molecule of the dissolved substance, we get q= and p= (I - a)/**V**, hence x(I - a)**V**=yd/V2, and constant = k.Thus in the case of cyanacetic acid, while the volume

**V**changed by doubling from 16 to 1024 litres, the values of k were 0.00 (37 6, 373, 374, 361, 362, 361, 368).The result of the investigation shows that the electrical work Ee is given by the_equation Ee =1 where

**v**is the volume of the solution used and p its osmotic pressure.This was decided in Liddell

**v**.His voluminous writings are classified in the Jewish Encyclopedia,

**v**.The body of the Brachiopod

**v**usually occupies about the posterior half of the space within the shell.On the opposite side of Betanzos Bay (the p yas Acµl i

**v**or Portus Magnus of the ancients) is the great port of Corunna or Coruna.Y ...a n

**v**, the summation being for all permutations of the n numbers, is called the determinant of the n 2 quantities.In the present particular case putting m 10 = 1 2, mot=

**v**and m P4 =o otherwise M10t+M01n+...+Mpot P n 4 +...Pope Leo had indeed, in a letter to the Franciscan ministergeneral (November 1898), and in an encyclical to the French clergy (September 1899), vigorously emphasized the traditionalist principles of his encyclical Providentissimus of 1893; he had even, much to his prompt regret, signed the unfortunate decree of the Roman Inquisition, January 1897, prohibiting all doubt as to the authenticity of the "Three Heavenly Witnesses" passage, John

**v**.See Livy

**v**.In the south the Cevennes separate the cold and barren tablelands

**v**.The moment, M, M or

**V**, of a uniformly and longitudinally magnetized bar-magnet is the product of its length into the strength of one of its poles; it is the moment of the couple acting on the magnet when placed in a field of unit intensity with its axis perpendicular to the direction of the field.Hence I = M/

**v**= ml/**v**= m/a,**v**being the volume and a the sectional area.If

**V**denote the potential, F the resultant force, X, Y, Z, its components parallel to the co-ordinate axes and n the line along which the force is directed, then - sn = F, b?= X, - Sy = Y, -s Surfaces for which the potential is constant are called equipotential surfaces.The potential due to a single pole of strength m at the distance r from the pole is

**V**= m/ r, (7) the equipotential surfaces being spheres of which the pole is the centre and the lines of force radii.The potential due to a thin magnet at a point whose distance from the two poles respectively is r and r' is

**V**=m(l/r=l/r') (8) When**V**is constant, this equation represents an equipotential surface.The potential at any point due to a magnetic shell is the product of its strength into the solid angle w subtended by its edge at the given point, or

**V**= Fu.Forces acting on a Small Body in the Magnetic Field.-If a small magnet of length ds and pole-strength m is brought into a magnetic field such that the values of the magnetic potential at the negative and positive poles respectively are

**V**1 and the work done upon the magnet, and therefore its potential energy, will be W =m(V2-Vi) =mdV, which may be written W =m d s- = M d**v**= - MHo = - vIHo, ds ds where M is the moment of the magnet,**v**the volume, I the magnetization, and Ho the magnetic force along ds.Therefore and m =

**v**I - 'm of d22 (47) constant cell B21 its object is to produce inside the tube a magnetic field equal and opposite to that due to the earth's magnetism.If

**V**is the volume of a ball, H the strength of the field at its centre, and re its apparent susceptibility, the force in the direction x is f= K'VH X dH/dx; and if K',, and are the apparent susceptibilities of the same ball in air and in liquid oxygen, K' Q -K'o is equal to the difference between the susceptibilities of the two media.We shall, therefore, ignoring the ocular somite, speak of the first, second, third, fourth, fifth and sixth legbearing somites of the prosoma, and indicate the appendages by the Roman numerals, I, II, III, IV,

**V**, VI, and whilst ignoring the praegenital somite we shall speak of the first, second, third, &c., somite of the mesosoma or opisthosoma (united mesosoma and metasoma) and indicate them by the Arabic numerals.Opisthosoma consisting of only ten somites, which have no tergal and sternal elements, the prae-genital somite contracted to form a " waist," as in the Pedipalpi; the last three narrowed to form a A B prae-1 2345 6789 io I I111I IV

**V**VI gen Opisttaosoma Prosoma FIG.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.How otherwise are we to explain such Hebraisms (or Syriacisms) as Evui pEEC rb g Xacov E ct ro (§ 9), ov elir€

**v**.The

**v**, for f, is common in southern English pronunciation; vox, for fox, is found in the Ancren Riwle, c. 1230.The other physical features of the great day, the darkening of the lights of heaven, are a standing figure of the prophets from Amos

**v**.But his most distinguished effort at the bar was undoubtedly the speech for the House of Commons in the famous case of Stockdale

**v**.Plan of ' Main Entrance II Impluvium Bath IV Principal Hall '

**V**birth to the Christian kingdoms of the Peninsula, while the Monge de Cister, published in 1848, describes the time of King John I., when the middle class and the municipalities first asserted their power and elected a king in opposition to the nobility.If, for instance, we are told that 15= 4 of (x- 2), what is meant is that (I) there is a number u such that x=u+2, (2) there is a number

**v**such that u=4 times**v**, and (3) 15=3 times**v**.The values of x and y are different, unless

**V**(qq o) = o.Canton was laid out as a town in 1805, became the county-seat in 1808, was incorporated as a village in 1822 and in 1854

**V**S chartered as a city.A similar expression can be found for Q'P - Q"A; and thus, if Q' A =

**v**, Q' AO = where**v**=a cos (0", we get - - -AQ' = a sin w (sin 4 -sink") - - 8a sin 4 w(sin cktan 4 + sin 'tan cl)').In the present application 4' is not necessarily equal to; but if P correspond to a line upon the grating, the difference of retardations for consecutive positions of P, so far as expressed by the term of the first order, will be equal to mX (m integral), and therefore without influence, provided

**v**(sin 0-sin0') = nzX (11), where a denotes the constant interval between the planes containing the lines.If we put for shortness 7 for the quantity under the last circular function in (I), the expressions (i), (2) may be put under the forms u sin T,

**v**sin (T - a) respectively; and, if I be the intensity, I will be measured by the sum of the squares of the coefficients of sin T and cos T in the expression u sin T +**v**sin (T - a), so that I =u 2 +**v**2 +2uv cos a, which becomes on putting for u,**v**, and a their values, and putting f =Q .Integrating by parts, we find

**v**i.By separation of real and imaginary parts, C =M cos 27rv 2 +N sin 27rv2 1 S =M sin 27rv 2 - N cos 27rv2 where 35+357.9 N _ 7rv 3 7r 3

**v**7 + 1.3 1.3.5.7 1.3.5.7.9.11 These series are convergent for all values of**v**, but are practically useful only when**v**is small .Expressions suitable for discussion when

**v**is large were obtained 1 In experiment a line of light is sometimes substituted for a point in order to increase the illumination.If

**V**be the value of**v**corresponding to CA, viz.The position of Q corresponding to a given value of

**V**, that is, to a band of given order, is by (19) BQ= aa b AD=**V**?The origin of co-ordinates 0 corresponds to

**v**= 0; and the asymptotic points J, J', round which the curve revolves in an ever-closing spiral, correspond to**v**= =co .See Karl

**v**.So far, however, energy and Successes

**v**i g i lance made them successful.It is plausible to regard

**v**.By undue pressure he secured a decision of the judges, in the test case of Godden

**v**.Arentschild won a notable success over the improvised Prussian and Coburg division of General

**v**.The battle of Langensalza (June 27th) showed that the risks Moltke deliberately accepted when he transferred so many of the western troops to the Bohemian frontier were by no means imaginary, for

**v**.By the morning of the 29th Manteuffel and Goeben lay north,

**v**.Meanwhile the 8th Federal corps advanced also, but actuated probably by political motives it took the general direction of Cassel, and between the two German corps a wide gap opened, of which Vogel

**v**.On the day of Koniggratz the Prussians moved into position to attack the Bavarians, and on the 4th of July

**v**.Falckenstein was now called to Bohemia, and

**v**.A treatise on the diseases of women, contained in the Hippocratic collection, and of remarkable practical

**v**alue, is attributed to this school.Thus, for instance, in his account of the transition from savage to civilized life, he assumes at

**v**.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).In 1868 Sir Robert Phillimore (Dean of the Arches) pronounced the ceremonial use of incense to be illegal in the suit of Martin

**v**.Again, in 1870, the ceremonial use of incense was condemned by Sir Robert Phillimore in the suit of Sumner

**v**.The beaches which had been selected were, enumerating from right to left, " S " in Morto Bay, "

**V**" and " W " on either side of Cape Helles at the south-western end, and " X " and " Y " on the outer shore; "**V**" and " W " were regarded as of primary importance, as those two beaches offered suitable landing places from the point of view of subsequent operations.As it turned out, the actual disembarkations at " S," " X " and " Y " were carried out without any very great difficulty; but the troops detailed for " W " beach only gained a footing after incurring very heavy losses and by a display of indomitable resolution, while at "

**V**" the operation went very near to failing altogether.What was left of the force originally detailed for the landing at "

**V**" beach contrived during the early hours by stern fighting to occupy some high ground hard by, and also to join hands with the troops landed at " W " beach.Additional infantry was got ashore at " W " and " X " beaches, the first elements of the French division began disembarking at "

**V**" beach in the afternoon, and before evening touch had been gained with the battalion that had made good at " S " beach.Ottoman guns dominated the entire territory which the invaders had succeeded in the course of two months in conquering, as well as "

**V**" and " W " beaches which were the landing-places chiefly used by them.Embarkation operations were carried on almost entirely at "

**V**" and " W " beaches, at both of which there were provisional breakwaters in existence furnishing some shelter when there was an onshore breeze.The right half of the British were to withdraw by "

**V**" beach and the left half by " W " beach, except that the final detachments on the extreme left, representing the 13th Division, were to be got off at Gully beach.The symbol

**v**represents the inverse of the dispersive power, its value being (nD-i)/(C-F).Ignoring temperature effect, and taking the density as a function of the pressure, surfaces of equal pressure are also of equal density, and the fluid is stratified by surfaces orthogonal to the lines of force; n ap, dy, P d z, or X, Y, Z (4) are the partial differential coefficients of some function P, =fdplp, of x, y, z; so that X, Y, Z must be the partial differential coefficients of a potential -

**V**, such that the force in any direction is the downward gradient of**V**; and then dP dV (5) ax + Tr=0, or P+**V**=constant, in which P may be called the hydrostatic head and**V**the head of potential.Uniplanar Motion of a Liquid due to the Passage of a Cylinder through it.-A stream-function 4, must be determined to satisfy the conditions v24 =o, throughout the liquid; (I) I =constant, over any fixed boundary; (2) d,t/ds = normal velocity reversed over a solid boundary, (3) so that, if the solid is moving with velocity U in the direction Ox, d4y1ds=-Udy/ds, or 0 +Uy =constant over the moving cylinder; and 4,+Uy=41' is the stream function of the relative motion of the liquid past the cylinder, and similarly 4,-Vx for the component velocity

**V**along Oy; and generally 1,1'= +Uy -Vx (4) is the relative stream-function, constant over a solid boundary moving with components U and**V**of velocity.If the liquid is stirred up by the rotation R of a cylindrical body, d4lds = normal velocity reversed dy = - Rx- Ry ds (5) ds 4' + 2 R (x2 + y2) = Y, (6) a constant over the boundary; and 4,' is the current-function of the relative motion past the cylinder, but now

**V**2 4,'+2R =o, (7) throughout the liquid.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?An ellipse interior to n = a will move in a direction opposite to the exterior current; and when n = o, U = oo, but

**V**= (m/c) sh a sin 13.Example 3.-Analysing in this way the rotation of a rectangle filled with liquid into the two components of shear, the stream function 1//1 is to be made to satisfy the conditions

**v**2 /1 =0, 111+IRx 2 = IRa 2, or /11 =o when x= = a, +b1+IRx 2 = I Ra2, y ' 1 = IR(a 2 -x 2), when y = b Expanded in a Fourier series, 2 232 2 cos(2n+ I)Z?rx/a a -x 7r3 a Lim (2n+I) 3 ' (1) so that '?"The components of velocity of the moving origin are denoted by U,

**V**, W, and the components of angular velocity of the frame of reference by P, Q, R; and then if u,**v**, w denote the components of fluid velocity in space, and u',**v**', w' the components relative to the axes at a point (x, y, z) fixed to the frame of reference, we have u =U +u' - yR +zQ,**v**=**V**+**v**-zP +xR, w=W +w -xQ +yP.As an application of moving axes, consider the motion of liquid filling the ellipsoidal case 2 y 2 z2 Ti + b1 +- 2 = I; (1) and first suppose the liquid be frozen, and the ellipsoid l3 (4) (I) (6) (9) (I o) (II) (12) (14) = 2 U ¢ 2, (15) rotating about the centre with components of angular velocity, 7 7, f'; then u= - y i +z'i,

**v**= w = -x7 7 +y (2) Now suppose the liquid to be melted, and additional components of angular velocity S21, 522, S23 communicated to the ellipsoidal case; the additional velocity communicated to the liquid will be due to a velocity-function 2224_ - S2 b c 6 a 5 x b2xy, as may be verified by considering one term at a time.Thus if T is expressed as a quadratic function of U,

**V**, W, P, Q, R, the components of momentum corresponding are dT dT dT (I) = dU + x2=dV, x3 =dW, dT dT dT Yi dp' dQ' y3=dR; but when it is expressed as a quadratic function of xi, 'x2, x3, yi, Y2, Y3, U = d,**V**= dx, ' w= ax dT Q_ dT dT dy 1 dy2 dy The second system of expression was chosen by Clebsch and adopted by Halphen in his Fonctions elliptiques; and thence the dynamical equations follow X = dt x2 dy +x3 d Y = ..., Z ..., (3) = dt1 -y2?y - '2dx3+x3 ' M =..For the body alone the resultant of the components of momentum W

**V**-cos andW**V**sin 0 is W**V**-sec. lb, acting along 00', and so is unaltered.The body is held fixed, and the reactio of the mechanism and the resultant of the impulsive pressure on th surface are a measure of the impulse, linear,, , and angula A, µ,

**v**, required to start the circulation.Lambert is also regarded as the author of the Historia Hersfeldensis, the extant fragments of which are published in Band

**v**.According to Florio (i 6 i 1)

**V**is "sometimes a vowel, and sometimes a consonant."**V**is therefore a voiced labio-dental spirant, the breath escaping through a very narrow slit between the lower lip and the upper teeth.In German, however,

**V**is used with the same value as F, while W takes the value that**V**has in English.Apart from some southern dialect forms which have found their way into the literary language, as vat (for fat or wine fat which still survives in the English Bible) and vixen the feminine of fox, all the words in English which begin with

**V**are of foreign, and most of Latin origin.In Northern French and in Italian it has become the labio-dental

**v**, and from French English has adopted this value for it.The history of

**V**as the Latin numeral for 5 is uncertain.**V**with a horizontal line above it was used for 5000.Tafel, Ber., 1886, 19, p. 1924), by distilling the amido-acids with lime, by heating phenols with zinc chloride ammonia (

**V**.The first published account of the simple camera obscura was discovered by Libri in a translation of the Architecture of

**v**.For more efficient condensation - and also for shortening the apparatus - the central tube may be flattened, bent into a succession of

**V**'s, or twisted into a spiral form, the object in each case being to increase the condensing surface.Doyle also wrote chapters i., ii.,

**v**.A, Fasciola hepatica, from the ventral surface (X 2); the alimentary and nervous systems only shown on the left side of the figure, the excretory only on the right; a, right main branch of the intestine; c, a diverticulum; g, lateral ganglion; n, lateral nerve; o, mouth; p, pharynx; s, ventral sucker; cs, cirrus sac; d, left anterior dorsal excretory vessel; m, main vessel;

**v**, left anterior ventral trunk; x, excretory pore.But the bundant steam given off by the volcano seems to have con- c ensed into copious rain, which, mixing with the light volcanic

**V**She wrote a little piece which Comte rated so pre-

**v**posterously as to talk about George Sand in the same sentence; it is in truth a flimsy performance, though it contains one or two gracious thoughts.In other dialects of Italy b is found representing an original voiced guttural (gw), which, however, is regularly replaced by

**v**in Latin.As the district was full of traders, Subura may very well be an imported word, but the form with C must either go back to a period before the disappearance of g before

**v**or must come from some other Italic dialect.The empress Victoria, who, after the death of her husband, was known as the empress Frederick, died on the 5th of August 1901 at the castle of Friedrichskron, Cronberg, near Homburg

**v**.It varies in colour, but a black mark on the head like an inverted

**V**remains nearly always visible.It is the Abana of 2 Kings

**v**.Returning to the case of the charged body with the space around it cut up into electric cells by the tubes of force and shells of potential, it is obvious that the number of these cells is represented by the product QV, where Q is the charge and

**V**the potential of the body in electrostatic units.An electrified conductor is a store of energy, and from the definition of potential it is clear that the work done in increasing the charge q of a conductor whose potential is

**v**by a small amount dq, is vdq, and since this added charge increases in turn the potential, it is easy to prove that the work done in charging a conductor with Q units to a potential**V**units is z QV units of work.Hence if the force is zero the potential

**V**must be constant.Thus if Q is the surface density, S the thickness of the shell at any point, and p the assumed volume density of the matter of the shell, we have

**v**=Abp. Then the quantity of electricity on any element of surface dS is A times the mass of the corresponding element of the shell; and if Q is the whole quantity of electricity on the ellipsoid, Q =A times the whole mass of the shell.Hence the density

**v**is given by 47rabc (x2/a4+y2/b4-I-z2/c4), and the potential at the centre of the ellipsoid, and therefore its potential as a whole is given by the expression, adS Q dS**V**f r 47rabc r' (x2/a4-I-y2/b4+z2/c4) Accordingly the capacity C of the ellipsoid is given by the equation 1 I J dS C 47rabc Y (x 2 +y 2 + z2)**V**(x2/a4+y2/b4+z2/c4) (5) It has been shown by Professor Chrystal that the above integral may also be presented in the form,' foo C 2 J o J { (a2 + X) (b +X) (c 2 + X) } (6).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.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.If then the outer cylinder be at zero potential the potential

**V**of the inner one is**V**=A log (R 2 /R 1), and its capacity C =1/2 log R2/R1.Let

**V**1 and V2 be the potentials of the plates, and let a charge Q be given to one of them.But if

**v**is the surface density, E=47rv, and a=Q/S.Hence we have (

**V**1 -**V**2) d=47rQ/S or C= Q/(**V**i -**V**2) = S/47rd (13).Hence the potential

**V**at the centre of the inner sphere is given by**V**=Q/R1 - Q/R2+Q/R3.Then when the inner cylinder is at potential

**V**1 and the outer one kept at of two potential**V**2 the lines of electric force between the cylinders Q (4).If a condenser of capacity C is charged to potential

**V**, and discharged n times per second through a galvanometer, this series of intermittent discharges is equivalent to a current nCV.Since then they are all charged with the same quantity of electricity, and the total over all potential difference

**V**is the sum of each of the individual potential differences V1, V2, V3, &c., we have Q=C I**V**I =C 2**V**2 =C 3**V**3 =&c., and**V**=V1-FV2+V3+&c. The resultant capacity is C = Q/**V**, and C= I/(I/C1 +I /C2+1/C3+&c) = I/Z(I /C) (15).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.Let

**V**be the potential at the centre of the prism, then the normal forces on the two faces of area dy.dx are respectively RI dx2 d xl and (dx 2 d x), dV d2 and similar expressions for the normal forces to the other pairs of faces dx.dy, dz.dx.Hence the total flux is - (+ d2V d 2

**V**d2V dye + dz2) dy dz, dx2 and by the previous theorem this must be equal to 4'rrp dxdydz.It may be looked upon as an equation to determine p when

**V**is given or vice versa.Since the potential of a conductor is defined to be the work required to move a unit of positive electricity from the surface of the earth or from an infinite distance from all electricity to the surface of the conductor, it follows that the work done in putting a small charge dq into a conductor at a potential

**v**is**v**dq.Take any horizontal line and divide it into small elements of length each representing dq, and draw vertical lines representing the potentials

**v**,**v**', &c., and after each dose.Then if U is the potential outside the surface due to this electric charge inside alone, and

**V**that due to the opposite charge it induces on the inside of the metal surface, we must have U+**V**=O or U = -**V**at all points outside the earthed metal surface.The area DABbd under the return path (

**v**diminishing) represents work done on the substance, or against the back-pressure, and is negative.The isothermals are approximately equilateral hyperbolas (pv= constant), with the axes of p and

**v**for asymptotes, for a gas or unsaturated vapour, but coincide with the isopiestics for a saturated vapour in presence of its liquid.Substituting these symbols in the expression for the area, the relation becomes H=o(p' - p„)(

**v**„_v')/(o' - o").In the notation of the calculus the relations become - dH/dp (0 const) = odv /do (p const) (4) dH/dv (0 const) =odp/do (

**v**const) The negative sign is prefixed to dH/dp because absorption of heat +dH corresponds to diminution of pressure - dp. The utility of these relations results from the circumstance that the pressure and expansion co efficients are familiar and easily measured, whereas the latent heat of expansion is difficult to determine.Finally, the substance is reconverted into the first state at the temperature 0", completing the cycle by the abstraction of a quantity of heat By the application of the first law, the difference of the quantities of heat absorbed and evolved in the cycle must be equal to the work represented by the area of the cycle, which is equal to (p' - p") (

**v**" -**v**') in the limit when the difference of pressure is small.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,..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.For a finite change it is necessary to represent the path by a series of small steps, which is the graphic equivalent of integration along the path represented by the given relation between

**v**and 0, or p and 0.The change of energy at constant volume is simply sdo, the change at constant temperature is (odp/de - p)dv, which may be written dE/de (

**v**const) =s, dE/dv (0 const) =odp/do - p .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.We thus obtain the relation ds/dv(o const) =od 2 p/d0 2 (

**v**const),.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 .The equation to these lines in terms of

**v**and 0 is obtained by integrating dE=sd0+(Odp/de - p)dv = o .The isothermal elasticity -

**v**(dp/dv) is equal to the pressure p. The adiabatic elasticity is equal to y p, where -y is the ratio S/s of the specific heats.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).In thiscase the ratio of the specific heats is constant as well as the difference, and the adiabatic equation takes the simple form, pv

**v**= constant, which is at once obtained by integrating the equation for the adiabatic elasticity, -**v**(dp/dv) =yp.This gives by equation (9) the condition Odp/d0 =p, which is satisfied by any substance possessing the characteristic equation p/0=f(

**v**), where f(**v**) is any arbitrary function of**v**.If we consider any short length of the stream bounded by two imaginary cross-sections A and B on either side of the plug, unit mass of the fluid in passing A has work, p'

**v**', done on it by the fluid behind and carries its energy, E'+ U', with it into the space AB, where U' is the kinetic energy of flow.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.If there is no external loss or gain of heat through the walls of the pipe, and if the flow is steady, so that energy is not accumulating in the space AB, we must evidently have the condition E'+U'+p'

**v**' =E'+ U"+p"**v**" at any two cross-sections of the stream.We have therefore, by equation, (11), Sd0 = (Odv/d0 -

**v**) d p,.Neglecting small terms of the second order, the equation may then be written in the form

**v**- b=RO/p - co(Oo/O)=**V**- c,..The value of the angular coefficient d(pv)/dp is evidently (b - c), which expresses the defect of the actual volume

**v**from the ideal volume Re/p. Differentiating equation (17) at constant pressure to find dv/do, and observing that dcldO= - nc/O, we find by substitution in (is) the following simple expression for the cooling effect do/dp in terms of c and b, Sdo/dp= (n+I)c - b..Other favourite types' of equation for approximate work are (I) p=RO/

**v**±f(**v**), which makes p a linear function of 0 at constant volume, as in van der Waal's equation; (2)**v**=RO/p+f(p), which makes**v**a linear function of 0 at constant pressure.In the case of imperfect gases, all the available experimental evidence shows that the specific volume tends towards its ideal value,

**V**=Re/p, in the limit, when the pressure is indefinitely reduced and the molecules are widely separated so as to eliminate the effects of their mutual actions.Denoting by So, so, these constant limiting values at p=o, we may obtain the values at any pressure by integrating the expressions (27) and (28) from co to

**v**and from o to p respectively.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.If J', J" represent the values of the function for unit mass of the substance of specific volumes

**v**' and**v**" in the two states at temperature 0 and pressure and if a mass m is in the state**v**', and 1-m in the.Since the volume is constant, we have the condition mv'--l-(I-m)

**v**"=constant.Assuming the function G to be expressed in terms of p and 0, this condition represents the relation between p and 0 corresponding to equilibrium between the two states, which is the solution of the relation (

**v**" -**v**')dp/dO=L/D, (5).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.This

**V**Olkerwanderung, as it is called by German historians, again transformed the face of Europe, resulting in the establishment of independent kingdoms and a great mixture of races and institutions.The allantrapezium; Ito

**V**, first to fifth digit.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.Let u represent the volume of air in the cup before the body was inserted,

**v**the volume of the body, a the area of the horizontal FIG.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'.Substituting this value in the expression for

**v**, the volume of the body inserted in the cup becomes known.The screw, turned by the wheels at g', acts in a toothed arc, whence, as shown in the figure, equal and opposite motion is communicated to the slides by the jointed rods

**v**,**v**.The tube

**V**, on the contrary, is attached to the cradle, and merely forms a support for the finder Q, the handles at f and p, and the moving ring P. The latter gives quick motion in position angle; the handles at p clamp and give slow motion in position angle, those at f clamp and give slow motion in right ascension and declination.The oldest testimony is that of Irenaeus

**v**.The validity of such an hypothesis was attacked as early as the 4th century by Dionysius of Alexandria in the fragment of his treatise irEpi 7ray yeAuA;

**v**, in Eusebius, H.E.See Gratz, History of the Jews,

**v**.Let a mixture of gases contain per unit volume

**v**molecules of the first kind,**v**' of the second kind, and so on.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.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.The aggregate amount of these pressures is clearly the sum of the momenta, normal to the boundary, of all molecules which have left dS within a time dt, and this will be given by expression (pp), integrated with respect to u from o to and with respect to

**v**and w from - oo to +oo, and then summed for all kinds of molecules in the gas.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.Thus the pressure is given by the equation (p+a/

**v**2) (**v**- b) =RNT, which is known as Van der Waals's equation.This equation is found experimentally to be capable of representing the relation between p,

**v**, and T over large ranges of values.If we divide throughout by T, we obtain d 2 (n+3)RN T +RNd

**v**, showing that dQ/T is a perfect differential.If the volume of the gas is kept constant, we put dv=o in equation (18) and dQ = JC0NmdT, where C

**v**is the specific Specific heat of the gas at constant volume and J is the mechanical equivalent of heat.This was arranged for by a movable leaf carrying the sighting

**V**, worked by means of a mill-headed screw provided with a scale in degrees and fractions to the same radius as the elevation scale, and an arrowb head for reading.These

**V**'s are so arranged that the axis of the sight frame is always parallel to that of the gun.There were, besides, branches at Turin (i temple, 2 pasteurs and 750 members), in other parts of Italy, including Sicily (46 temples and as many pasteurs,

**v**?hile the number of members was 5613, of day scholars 2704, and of Sunday school scholars 3707).By considering the circle as the limit of a polygon, it follows that the formulae (iii) and (

**v**) of § 26 hold for a right circular cylinder and a right circular cone; i.e.Draw the tangents at A and B, meeting at T; draw TV parallel to the axis of the parabola, meeting the arc in C and the chord in

**V**; and M draw the tangent at C, meeting AT and BT in a and b.Formulae giving the area of a trapezette should in general also be expressed so as to state the value of the mean ordinate (§§ 12 (

**v**), 15, 19).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.If u is an algebraical function of x of degree not exceeding p, and if the area of a trapezette, for which the ordinate

**v**is of degree not exceeding p+q, may be expressed by a formula Aovo-1--yivi+..This means that, if the minor trapezette consists of k strips,

**v**will be of degree k or k - I in x, according as the data are the bounding ordinates or the mid-ordinates.A ?- *(1 5 C 16C 2+ C 3) C1 +$(C i - C2) -lO(C 2 - C3) (

**v**) m a multiple of 12.Then, if the true moments are denoted by Pi,

**v**2, ..., their values are given by vi ?Pl P2 - 11.The position of the central ordinate is given by x =

**v**1 /po, and therefore is given approximately by pl/po.The formulae may be used for extending the accuracy of tables, in cases where, if

**v**represents the quantity tabulated, hdv/dx or h 2 d 2**v**/dx 2 can be conveniently expressed in terms of**v**and x to a greater degree of accuracy than it could be found from the table.The process practically consists in using the table as it stands for improving the first or second differences of

**v**and then building up the table afresh.His success in Russia procured for him, on the death of Baron

**v**.Hence the work done on the air is (P-+zw)

**v**, and the work done per cubic centimetre is (P+Zw)**v**/**V**.Let R be the receiver at a given instant, R' its position a second later, its velocity being

**v**.But through his motion

**v**in the second, he receives only the waves in distance U + w -**v**.Since there are n waves in distance U + w - u the number he actually receives is n(U + w -

**v**)/(U + w - u).**V**i brat i ons thus excited are termed forced vibrations, and their amplitude is greater the more nearly the period of the applied force approaches that of the system when vibrating freely.But keeping r/X small we may as before form stationary waves, and it is evident that the series of fundamental and overtones will be just as with the air in pipes, and we shall have the same three types - fixed at one end, free at both ends, fixed at both ends - with fundamental frequencies respectively 41, p ' 21

**V**p, and I velocity in rod =velocity in air X distance between dust heaps.Other firsthand narratives of importance are the American officers' reports (Reports of Military Observers, General Staff, U.S.A.); Major

**v**.**V**bridge, but it has also other ' `??If w is the weight of a locomotive in tons, r the radius of curvature of the track,

**v**the velocity in feet per sec.; then the horizontal force exerted on the bridge is wv 2 /gr tons.The minimum school term allowed by law is six Before the law passed by the first Legislative Assembly of the state to carry out this provision could come into effect, it was partially annulled by the decision of the United States Supreme Court in the case of Leisy

**v**.We shall make the natural supposition that motion of the aether, say with velocity (u,

**v**,w) at the point (x,y,z), is simply superposed on the velocity**V**of the optical undulations through that medium, the latter not being intrinsically altered.But in the transition from molecular theory to the electrodynamics of extended media, all magnetism has to be replaced by a distribution of current; the latter being now specified by volume as well as by flow so that (u,

**v**,w) ST is the current in the element of volume 6T.The polarization itself is determined from the electric force (P,Q,R) by the usual statical formula of linear type which becomes tor an isotropic medium (.f',g',h') = c2(P,Q,R), because any change of the dielectric constant K arising from the convection of the material through the aether must be independent of the sign of

**v**and therefore be of the second order.Now the electric force (P,Q,R) is the force acting on the electrons of the medium moving with velocity

**v**; consequently by Faraday's electrodynamic law (P,Q,R) = (P',Q' - vc, R'+vb) where (P',Q',R') is the force that would act on electrons at rest, and (a,b,c) is the magnetic induction.If

**v**varies with respect to locality, or if there is a velocity of convection (p,q,r) variable with respect to direction and position, and analytical expression of the relation (ii) assumes a more complex form; we thus derive the most general equations of electrodynamic propagation for matter treated as continuous, anyhow distributed and moving in any manner.Trains of waves nearly but not quite homogeneous as regards wave-length will as usual be propagated as wave-groups travelling with the slightly different velocity d(VX-1)/dX-', the value of K occurring in

**V**being a function of X determined by the law of optical dispersion of the medium.One of the names given in 1 Esdras

**v**.From the 12th century it was governed by advocati (

**V**iigte), but in 1236 it came into the possession of Gera, and in 1550 of the younger line of the house of Plauen.Collecting all the coefficients, into one, we put (I) R = nd 2 p = nd 2 f (

**v**), where and n is called the coefficient of reduction.We first determine the time t in seconds required for the velocity of a shot, d inches in diameter and weighing w lb, to fall from any initial velocity

**V**(f/s) to any final velocity**v**(f/s).Since p is determined experimentally and tabulated as a function of

**v**, the velocity is taken as the argument of the ballistic table; and taking Av =10, the average value of p in the interval is used to determine AT.Denoting the value of T at any velocity

**v**by T (**v**), then (8) T(**v**) = sum of all the preceding values of AT plus an arbitrary constant, expressed by the notation (9) T(**v**) =Z(Av)/gp+ a constant, or fdv/gp+ a constant, in which p is supposed known as a function of**v**.The constant may be any arbitrary number, as in using the table the difference only is required of two tabular values for an initial velocity

**V**and final velocity**v**; and thus (to) T(**V**) - T(**v**) = Ev Ov/gp or fvdv/gp; and for a shot whose ballistic coefficient is C (II) t=C[T(**V**) - T(**v**)].Denoting by S(

**v**) the sum of all the values of AS up to any assigned velocity**v**, (is) S(**v**) =E(OS)+ a constant, by which S(**v**) is calculated from AS, and then between two assigned velocities**V**and**v**,**V**AT, = vAv or rvvdv vgp gp' and if s feet is the advance of a shot whose ballistic coefficient is C, (17) s=C[S(**V**) - S(**v**)].The differences OD and DI are thus calculated, while the values of D(

**v**) and I (**v**) are obtained by summation with the arithmometer, and entered in their respective columns.In any region of velocity where it is possible to represent p with sufficient accuracy by an empirical formula composed of a single power of

**v**, say**v**m, the integration can be effected which replaces the summation in (to), (16), and (24); and from an analysis of the Krupp experiments Colonel Zabudski found the most appropriate index m in a region of velocity as given in the following table, and the corresponding value of gp, denoted by f (**v**)or**v**m lk or its equivalent Cr, where r is the retardation.The first equation leads, as before, to t=C{T (

**V**)-T(**v**)}, (29) x=C{S(**V**)-S(**v**)}.Given the ballistic coefficient C, the initial velocity

**V**, and a range of R yds.Now these integrations are quite intractable, even for a very simple mathematical assumption of the function f(

**v**), say the quadratic or cubic law, f(**v**) =**v**2 /k or v3/k.Also the velocity

**v**at the end of the arc is given by (87) ve = u e sec 0 cos n.In this table (93) sin 20=Ca, where a is a function tabulated for the two arguments,

**V**the initial velocity, and R/C the reduced range in yards.Interior Ballistics The investigation of the relations connecting the pressure, volume and temperature of the powder-gas inside the bore of the gun, of the work realized by the expansion of the powder, of the

**V**FIG.Equating the muzzle-energy and the work in foot-tons (2) E= w

**V**2 _XM.E.P.Eltekow, Ber., 1878, 11, p. 414); by the action of metals on the halogen compounds Cn.H 20 Br 2 i by boiling the aqueous solution of nitrites of the primary amines (

**V**.P. Norris (Journal of Philology) wished to transpose chapters

**v**.Sumpner in 1891, an electrostatic voltmeter is employed to measure the fall of potential

**V**1 down any inductive circuit in which it is desired to measure the power absorption, and also the volt-drop V2 down an inductionless resistance R in series with it, and also the volt-drop V3 down the two together.The power absorption is then given by the expression (

**V**3 2 -**V**i 2 -V2 2)/2R.Diogenes Laertius says, "If the gods use dialectic, they can use none other than that of Chrysippus"; A yap

**v**Xpuvciriros, oinc av i**v**Ewa, ("Without Chrysippus, there had been no Porch").In 1879, however, Lecoq de Boisbaudran showed that Mosander's "didymium," contained samarium; while the residual "didymium" after removal of samarium, was split by Auer

**v**.See Homer, Iliad,

**v**.Thus we regard Rotifers as an independent stem branching off at the outset of the rise from the Platode type to higher Invertebrata The Polyzoa (q

**v**), which in many ways recall Rotifers, appear to be equally independent.There he found British

**v**detachments, 2000 strong, composed of troops whom Clinton had sent down separately under Generals Benedict Arnold and William Phillips to establish a base in the Chesapeake, as a diversion in favour of the operations of Cornwallis in the Carolinas.The phrase used is AELTOvp'yEl y T 7

**V**XeLrovpyLav, " to liturgize the liturgy."Detached from these, and separated entirely from the monastic buildings, were various workshops, which convenience required to be banished to the outer precincts, a saw-mill and oil-mill (UU) turned by water, and a currier's shop (

**V**), where the sandals and leathern girdles of the monks were made and repaired.See Orosius

**v**.This vast area, shaped like a broad-limbed

**V**or U, with Hudson Bay in the centre, is made up chiefly of monotonous and barren Laurentian gneiss and granite; but scattered through it are important stretches of Keewatin and Huronian rocks intricately folded as synclines in the gneiss, as suggested earlier, the bases of ancient mountain ranges.Thus, to take an example, he will not print a critical text of Plautus with two letters (Y and Z) which were no part of the Latin alphabet in the age of that comedian; still less will he introduce into Latin texts distinctions, such as i,j and u,

**v**, which were not used till long after the middle ages.Moreover, it is clear that Aristotle addressed himself to readers as well as hearers, as in concluding his whole theory of syllogisms he says, " There would remain for all of you or for our hearers (763,7 co y uµWV rt T&?

**v**ipcpoapEVwv) a duty of according to the defects of the investigation consideration, to its discoveries much gratitude " (Sophistical Elenchi, 34, 184 b 6).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).Let

**V**denote the volume of the inEssay Instrument.Also W = (

**V**+IA)w i; or w1=W/(**V**+/A), w p =W/(**V**+plA), and wn =W/(Vd-nIA), or the densities of the several liquids vary inversely as the respective volumes of the instrument immersed in them; and, since the divisions of the scale correspond to equal increments of volume immersed, it follows that the densities of the several liquids in which the instrument sinks to the successive divisions form a harmonic series.If

**V**= N/A then N expresses the ratio of the volume of the instrument up to the zero of the scale to that of one of the scale-divisions.If we suppose the lower part of the instrument replaced by a uniform bar of the same sectional area as the stem and of volume

**V**, the indications of the instrument will be in no respect altered, and the bottom of the bar will be at a distance of N scale-divisions below the zero of the scale.The greatest density of the liquid for which the instrument described above can be employed is W/

**V**, while the least density is W/(Vd-nlA), or W/(**V**-Fv), where**v**represents the volume of the stem between the extreme divisions of the scale.Now, by increasing

**v**, leaving W and**V**unchanged, we may increase the range of the instrument indefinitely.First of these was the friction involved in the case, before the Supreme Court of the United States, of Chisolm

**v**.Eight years later the Supreme Court of the United States decided in the case of Fletcher

**v**.Of these references the most important are, perhaps, Strabo

**v**.Among the Chinese the name of the silkworm is " si, " Korean " soi "; to the ancient Greeks it became known as Q?p, the nation whence it came was to them ?r?pE S and the fibre itself o ptKc

**v**, whence the Latin sericum, the French soie, the German Seide and the English silk.If N be the frequency of a homogeneous vibration sent out by a molecule at rest, the apparent frequency will be N (1

**v**/**V**), where**V**is the velocity of light and**v**is the velocity of the line of sight, taken as positive if the distance from the observer increases.If all molecules moved with the velocity of mean square, the line would be drawn out into a band having on the frequency scale a width 2Nv/

**V**, where**v**is now the velocity of mean square.The spirit with which he pleaded before the Star Chamber in a case of The Crown

**v**.It is important to understand that Mach had developed this economical view of thought in 1872, more than ten years before the appearance of his work on the history of mechanics as he tells us in the preface, where he adds that at a later date similar views were expressed by Kirchhoff in his

**V**orlesungen fiber mathematische Physik (1874).According to him, we begin with an experience of ideas, in which object and idea are originally identical (

**V**orstellungsobject); we divide this unitary experience into its subjective and objective factors; and especially in natural science we so far abstract the objects as to believe them at last to be independent things; but it is the office of psychology to warn us against this popular dualism, and to teach us that there is only a duality of psychical and physical, which are divisible, not separable, factors of one and the same content of our immediate experience; and experience is our whole knowledge.According to Genesis

**v**.In civil proceedings at common law, it may also be laid down that the public cannot be excluded from the court; in Malan

**v**.The Court of Appeal has decided that it has power to sit in private; in Mellor

**v**.It was also decided in Druce

**v**.Mention of Taillefer is made by Guido, bishop of Amiens, in his Carmen de bello Hastingensi,

**v**.This has been so since the famous law case of Williamson

**v**.The Chinese name for central Tibet is Wei-Ts'ang, which is a transcription of the Tibetan designation of the two, provinces

**V**and Tsang (spelt dbus-gtsang) that constitute central Tibet.The part of Tibet under the rule of Lhasa, by far the largest and wealthiest, includes the central province of

**V**, Tsang, Nari and a number of large outlying districts in southern and even in eastern Tibet.The density of the liquid is MN/

**V**, where N is the number of solvent molecules, and**V**the total volume of the liquid.Writing

**v**for I/a, the specific volume of the vapour at the pressure p, and**V**for I/p, the specific volume of the liquid at the pressure P, and restricting the result to small changes, we get vdp =VdP.Let us imagine unit mass of solution of volume

**V**confined in a cylinder ABC between a fixed vapour sieve B and a solid piston A A B C FIG.Callendar has shown that the variation of vapour pressure of a solution with pressure is given by the expression

**V**'dP = vdp, where**V**' is the change in volume of the solution when unit mass of solvent is mixed with it.If

**V**=**V**' there is no change in osmotic pressure with hydrostatic pressure, and osmotic pressure depends on concentration and temperature only.The chief difficulty lies in the determination of the quantity

**V**', the change in volume the solution under the pressure Po when unit mass of solvent is mixed with it.In some solutions such as those of sugar the change in volume on dilution is nearly equal to the volume of solvent added;

**V**' then becomes equal to**V**, the specific volume of the solvent.The difference in the lowering of vapour pressures dp - dp' may be put equal to VdP/

**v**, where P is the osmotic pressure, and**V**the specific volume of the solvent.In order to integrate this expression we need to know L and

**v**as functions of the temperature and pressure.In the equation dP/dT= X/T(

**v**2 -**v**1), P is the osmotic pressure, T the absolute temperature and X the heat of solution of unit mass of the solute when dissolving to form a volume v2 - v1 of saturated solution in an osmotic cylinder.This process involves the performance of 6 7 8 9 an amount of osmotic work P(

**v**-**v**).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**).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.Now the velocities u and

**v**of the opposite ions under unit potential gradient, and therefore U and**V**under unit force, are known from electrical data.The kitchen with its offices (

**V**) lies behind the refectory, accessible from the outer court without entering the cloister.Passing to Amsterdam he was introduced to John Locke and to Philip

**v**.Judges

**v**.According to Cedrenus, a Greek writer of the firth century (2uvoIits `Ivropu,)

**v**, i.See also Selden, Titles of Honor, p. 678, and the Archceological Journal,

**v**.The badge of the order is, with variations for the different classes, a white enamelled Danish cross with red and gold borders, bearing in the centre the letter W (

**V**) and on the fourarms the inscription Gud og Kongen (For God and King).