A ?- *(1 5 C 16C 2+ C 3) C1 +$(C i - C2) -lO(C 2 - C3) (v) m a multiple of 12.
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.
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.
A similar character must be assigned to the remaining verses of chap. xiv., with the exception of the colophon in v.
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)').
A treatise on the diseases of women, contained in the Hippocratic collection, and of remarkable practical v alue, is attributed to this school.
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.
About 1780 Riga Velestiniul, a Hellenized Vlach from Macedonia who is also known by the purely Greek name of Rigas Phereos, had founded in Bucharest a patriotic and revolutionary association known as the Society of Friends (e'Taepia 7c;'v 4LXcvv) which gradually attained great in- The fiuence.
According to Cedrenus, a Greek writer of the firth century (2uvoIits `Ivropu,)v, i.
According to Florio (i 6 i 1) V is "sometimes a vowel, and sometimes a consonant."
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 Rabbi Johanan it derived its name from the allusion in v.
Accounts are By article v.
Accounts of his professional services are in Charnock's Biographia Navalis, v.
Actual Energy of a Shifting Body.The energy which must be exerted on a body of the weight w, to accelerate it from a state of rest up to a given velocity of translation v, and the equal amount of work which that body is capable of performing by overcoming resistance while being retarded from the same velocity of translation v to a state of rest, is wvfI2g.
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.
Again, in 1870, the ceremonial use of incense was condemned by Sir Robert Phillimore in the suit of Sumner v.
Again, the velocities parallel and perpendicular to OP change in the time & from it, v to uvb0, v+ubG, ultimately.
Also the velocity v at the end of the arc is given by (87) ve = u e sec 0 cos n.
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.
Although, outside the information we get from Christian chroniclers, this age is for the people of the north one of complete obscurity, it is evident that the Viking Age corresponds with some universal disturbance or unrest among the Scandinavian nations, strictly analogous to the unrest among more southern Teutonic nations which many centuries before had heralded the break-up of the Roman empire, an epoch known as that of the Folk-wanderings (V olkerwanderungen).
Among his most important decisions were Texas 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.
Among the denominational institutions are the Theological Seminary (Presbyterian) at Princeton; the Drew Theological Seminary (Methodist Episcopal) at Madison; Seton Hall College (Roman Catholic), at South Orange; St Peter's College (Roman Catholic) at Jersey City; St Benedict's College (Roman Catholic) at Newark; the German Theological School of Newark 1 The state's title to its riparian lands was established, after a long controversy, in 1870 in the case of Stevens v.
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.
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.
And we now see that the square of V is the negative of Laplace's operator; while V itself, when applied to any numerical quantity conceived as having a definite value at each point of space, gives the direction and the rate of most rapid change of that quantity.
Another constituent of Portland cement which influences 1 V ..
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.
Arentschild won a notable success over the improvised Prussian and Coburg division of General v.
Arguing in the Lessons that a mathematical point must have quantity, though this were not reckoned, he had explained the Greek word UTCy v, used for a point, to mean a visible mark made with a hot iron;; whereupon he was charged by Wallis with gross ignorance for confounding artypii and o - y,ua.
Aristotle recommended the paean v v -.
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.
As attorney-general he argued the famous cases, the United States v.
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.
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.
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).
At this point selection ceases; the remaining molten metal freezes as a whole, and in freezing splits up into a conglomerate eutectic of (1) austenite of about 2.2% of carbon, and therefore saturated with that element, and (2) cementite; and with this eutectic is mixed the " primary " austenite which froze out as the temperature sank from v to v'.
Both monarchs delegated the conduct of affairs to their ministers, who constructed new railways, reformed the educational system, and gradually improved the economic ro 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.
But if v is the surface density, E=47rv, and a=Q/S.
But in 1780 we find his prospects suddenly improved, by his appearance in the case of Ackroyd v.
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.
But its velocity relative to the cup, as it passes backwards, is - (V 2 - V 1), and since the forward velocity of the cup is Vi, the absolute velocity of the water is - (V2 - Vi) +VI or2V i - V2.
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.
But recent cases in the United States have raised the question whether the allowance should be made where the fire occurs in port, and is extinguished, not by the master, but by a public authority acting in the interests of the public. The Supreme Court of the United States decided against the allowance in 1894 in a case of Ralli v.
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
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.).
But this was not followed in Montgomery v.
But through his motion v in the second, he receives only the waves in distance U + w - v.
But where the reason for putting in is to avoid some danger, such as a storm or 1 Per Bowen, L.J., in Svensden v.
But, if no argument can be based on the discrepancy between the two names, we may at least assume that the namelessness of the priest in v.
By a suitable choice of the generalized co-ordinates it is possible to reduce T and V simultaneously to sums of squares.
By combining the evidence of Plutarch (in his comparison of Nicias and Crassus), Thuc. v.
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.
By equation (72) we have E = w(v,2 vi2)/ag which, being divided by V=1/2(v,+vi), gives E/V=w(vfvi)/g; and consequently V2 in = gE/Vw (73)
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 .
By the morning of the 29th Manteuffel and Goeben lay north, v.
By undue pressure he secured a decision of the judges, in the test case of Godden v.
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.
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.
Charles did not secure his v.
Chemie, 1868, p. 34), or by heating the sulphonate with sodium formate (V.
Chief the rng these cosmic deities was the sun-god Re, whose supremacy V ned predestined under the cloudless sky of Egypt.
Clausius, which may be written RO i p - v = RO (v - b) (A - B0 n) /p(v+a)'0,ti;.
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.
De Officiis (Ilepi TW V '040cxicov), a sketch, written in an unattractive style, of court and higher ecclesiastical dignities and of the ceremonies proper to different occasions.
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)].
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.
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.
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.
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.
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").
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,..
Dividing 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.
Doyle also wrote chapters i., ii., v.
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.
Eight years later the Supreme Court of the United States decided in the case of Fletcher v.
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.
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.
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.
Employing this type of equation, all the thermodynamical properties of the substance may conveniently be expressed in terms of the diminution of volume c due to the formation of compound or coaggregated molecules, (v - b) =RO/p - co(Oo/O) n =V - c. .
Equating the muzzle-energy and the work in foot-tons (2) E= w V 2 _XM.E.P.
Eriu was itself almost certainly a contraction from a still more primitive form Iberiu or Iveriu; for when the name of the island was written in ancient Greek it appeared as Iovcpvia (Ivernia), and in Latin as Iberio, Hiberio or Hibernia, the first syllable of the word Eriu being thus represented in the classical languages by two distinct vowel sounds separated by b or v.
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 '?"
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.
Falckenstein was now called to Bohemia, and v.
Fenno (8 Wallace, 533), 1869, in defence of that part of the banking legislation of the Civil War which imposed a tax of io% on state bank-notes, and Hepburn v.
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.
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).
First of these was the friction involved in the case, before the Supreme Court of the United States, of Chisolm v.
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.
For a stated value of the boiler pressure and the cut-off the mean pressure p is a function of the piston speed 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.
For other examples see Notes and Queries, 1st series, v.
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.
For the German and Austrian nobility, see v.
For the preparation of pure cerium compounds see Auer v.
For the rise in the boiling-point, we have by Clapeyron's equation, dp/do = L/ov, nearly, neglecting the volume of the liquid as compared with that of the vapour v.
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.
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).
Four years later (1823) Webster argued the case of Gibbons 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.
Given the ballistic coefficient C, the initial velocity V, and a range of R yds.
Greenidge, p. 102 ff.; Szanto's article "Ephoroi" in Pauly-Wissowa, Realencyclopcidie, v.
Hampe gives 8.945 (V) for perfectly pure and compact copper.
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).
He began his work at Anathoth, but v.
He was fond of adven- wiliiam, I'V.
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 I = M/v = ml/v = m/a, v being the volume and a the sectional area.
Hence if a train is travelling up the gradient at a speed of V ft.
Hence if the force is zero the potential V must be constant.
Hence if the system be started from rest in a configuration for which V is less than in the equilibrium configuration considered, this quantity must sUll further decrease (since T cannot be negative), and it is evident that either the system will finally come to rest in some other equilibrium configuration, or V will in the long run diminish indefinitely.
Hence if V is the volume of a mass M of liquid bounded by a surface whose area is S, the integral M = f f f pdx dydz, (I) where the integration is to be extended throughout the volume V, may be divided into two parts by considering separately the thin shell or skin extending from the outer surface to a depth within which the density and other properties of the liquid vary with the depth, and the interior portion of the liquid within which its properties are constant.
Hence if we write T= f E (x - xo) p d v,.
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.
Hence the potential V at the centre of the inner sphere is given by V =Q/R1 - Q/R2+Q/R3.
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.
Hence the work done in raising the mass will be represented by mg v 2 /2g, that is, Zmv 2 ergs.
Hence the work done on the air is (P-+zw)v, and the work done per cubic centimetre is (P+Zw)v/V.
Hence we have (V 1 - V 2) d=47rQ/S or C= Q/(V i - V 2) = S/47rd (13).
Hence when, say, V decreases the couple VM decreases, and hence the north end of the balanced magnet rises, and vice versa.
Here the agricultural character of her ritual is well marked; the first oxen used in ploughing were, according to an Argive myth, dedicated to her as E v cSia; and the sprouting ears of corn were called "the flowers of Hera."
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.
His next great case was that of M'Culloch v.
His story is told in one of the oldest songs of the Edda, the V OlundarkiOda and, with considerable variations, in the prose P13rekssaga (Thidrek's sage), while the Anglo-Saxon Beowulf and Deor's Lament contain allusions to it.
His success in Russia procured for him, on the death of Baron v.
His voluminous writings are classified in the Jewish Encyclopedia, v.
How otherwise are we to explain such Hebraisms (or Syriacisms) as Evui pEEC rb g Xacov E ct ro (§ 9), ov elir€v.
I, which reads 6 'yap ayysXos TT7s ELpilv77s M577'yei Tr 7 v aurOU.
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 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.
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.
If it, v be the component velocities at P along and perpendicular to OP (in the direction of 0 increasipg), FIG.
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.
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.
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 T denote the kinetic energy, we may say then that the sum T + V is in any interval of time increased by an amount equal to the work done by the extraneous forces.
If the body be supposed to roll - (say to the right) until the curves touch at J, and if JJ=bs, the angle through which the u,pper figure rotates is Is/p +Is/p, and the horizontal displace- V ment, of G is equal to the product of this expression into h.
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.
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 the linear velocity of the cups in feet a second is V 1, and the linear velocity of the jet is V2, then the velocity of the jet relative to the cup is V2 - V1 feet a second, and if the whole energy of the water is to be given up to the cups, the water must leave the cup with zero absolute 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.
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.
If 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.
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 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.
If then the balls are both charged to a potential V they will repel each other, and the threads will stand out at an angle 20, which can be observed on a protractor.
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.
If then two experiments are made, first with the upper plate connected to earth, and secondly, connected to the object being tested, we get an expression for the potential V of this conductor in the form V=A(d' - d), where d and d' are the distances of the fixed and movable plates from one another in the two cases, and A is some constant.
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.
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+..
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 V =V' there is no change in osmotic pressure with hydrostatic pressure, and osmotic pressure depends on concentration and temperature only.
If V be the value of v corresponding to CA, viz.
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.
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.
If v is very large compared with the mean value of the potentials of the two quadrants, as it usually is, then the above expression indicates that the couple varies as the difference of the potentials between the quadrants.
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.
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.
If W is the weight required to depress the attracted disk into the same sighted position when the plates are unelectrified and g is the acceleration of gravity, then the difference of potentials of the conductors tested is expressed by the formula V - V'=(d - d') /87 W where S denotes the area of the attracted disk.
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 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.
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.
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 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 .
If we suppose a normal v less than E to be drawn from the surface S into the liquid, we may divide the shell into elementary shells whose thickness is dv, in each of which the density and other properties of the liquid will be constant.
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.
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.
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.
In 1857 it was decided, in Regina v.
In 1863 the privy council declared, in Long v.
In 1868 Sir Robert Phillimore (Dean of the Arches) pronounced the ceremonial use of incense to be illegal in the suit of Martin v.
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.
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.
In Aristotle, again, the principle which sets all nature under the rule of thought, and directs it towards a rational end, is vows, or the divine spirit itself; while Aoyos is a term with many senses, used as more or less identical with a number of phrases, ou €v€Ka, ivEpyaaa, ivr€X aa, ovwia, e hos, popcIA, &c.
In civil proceedings at common law, it may also be laid down that the public cannot be excluded from the court; in Malan v.
In equation (4) there is a fixed relation between w, V and D given by the expression.
In front of the body the relative velocity of the fluid and the body varies from V where the fluid is at rest, to zero at the cutwater on the front surface of the body.
In German, however, V is used with the same value as F, while W takes the value that V has in English.
In Northern French and in Italian it has become the labio-dental v, and from French English has adopted this value for it.
In order to integrate this expression we need to know L and v as functions of the temperature and pressure.
In other dialects of Italy b is found representing an original voiced guttural (gw), which, however, is regularly replaced by v in Latin.
In particular, if there are no extraneous forces T + V is constant.
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.
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.
In Roman times the modern V drill (52) is usual.
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.
In symbols, if v be the velocity and p the perpendicular from 0 to the tangent to the path, pv=h, (1)
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.
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.
In the motion consequent on any slight disturbance the total energy T+V is constant, and since T is essentially positive it follows that V can never exceed its equilibrium value by more than a slight amount, depending on the energy of the disturbance, This implies, on the present hypothesis, that there is an upper limit to the deviation of each co-ordinate from its equilibrium value; moreover, this limit diminishes indefinitely with the energy of the original disturbance.
In the nests of Bombi are found various beetle larvae that live as inquilines or parasites, and also maggots of drone-flies (V olucella), which act as scavengers; the Volucella-fly is usually a" mimic ' vades.
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.
In the Phoenician alphabet Zain was the seventh letter, occupying the same position and having the same form approximately (i) as the early Greek Z, while in pronunciation it was a voiced s-sound; Samech () followed the 'symbol for n of and was the ordinary s-sound, though, as we have seen, e it is in different Greek states at the earliest period as well as E; after the symbol for p came Zade (v), which was a strong palatal s, though in name it corresponds to the Greek Nra; while lastly Shin (W) follows the symbol for r, and was an sh-sound.
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.
In the present particular case putting m 10 = 1 2, mot= v and m P4 =o otherwise M10t+M01n+...+Mpot P n 4 +...
In the south the Cevennes separate the cold and barren tablelands v.
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).
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.
In this, however, the government did not meet them, and in 1882 the Clericals, under Prince Alfred v.
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.
Integrating by parts, we find v i.
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.
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.
It consists of a heavy cast-iron platform (a) mounted on four steel balls (b) which run in V guides of hardened steel.
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).
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.
It is called V u-mi, Imperial rice, because it was first cultivated in my gardens.
It is first mentioned in the year 220 by Polybius v.
It is hardly doubtful that the verses are derived from a different source to that of their immediate context, possibly the same as 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).
It is improbable that these conflicting features in v.
It is now established, almost with certainty, that he returned to the neighbourhood of Paris; and it is supposed that his residence was known to the French ministers, who, however, firmly v.
It is obvious that the ratio V (x,y,z) (22)
It is part of a quotation from Amos v.
It is plausible to regard v.
It is the Abana of 2 Kings v.
It may be looked upon as an equation to determine p when V is given or vice versa.
It may even be admitted that the swift-flowing movement, and the simplicity of thought and style, which we admire in the Iliad are an inheritance from the earlier " lays " - the 104a &v&p&v such as Achilles and Patroclus sang to the lyre in their tent.
It survived longest when followed by o or v, as at the beginning of the name of the town of Corinth.
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.
It varies in colour, but a black mark on the head like an inverted V remains nearly always visible.
It was also decided in Druce v.
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).
Lambert is also regarded as the author of the Historia Hersfeldensis, the extant fragments of which are published in Band 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.
Let a mixture of gases contain per unit volume v molecules of the first kind, v' of the second kind, and so on.
Let a represent the area of the section of a piston made by a plane perpendicular to its direction of motion, and v its velocity, which is to be considered as positive when outward, and negative when inward.
Let P, Q be the positions of a u-i.aa moving point at times t, t + &, V Q
Let R be the receiver at a given instant, R' its position a second later, its velocity being v.
Let this potential be denoted by V, and let v be the potential of the guard plate and the aluminium flap. This last potential is maintained constant by guard plate and flap being part of the interior coating of a charged Leyden jar.
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.
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.
Let V 1 and V2 be the potentials of the plates, and let a charge Q be given to one of them.
Let v be the common velocity of the two pitch-circles, ri, C2, their radii; then the above equation becomes /1 I
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.
Let V denote the volume of the inEssay Instrument.
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.
Mention of him is suppressed in v.
Mention of Taillefer is made by Guido, bishop of Amiens, in his Carmen de bello Hastingensi, v.
More weighty contributions are the anonymous theological discussion The Kernel and the Husk (1886), Philomythus (1891), his book on Cardinal Newman as an Anglican (1892), and his article "The Gospels" in the ninth edition of the Encyclopaedia Britannica, embodying a critical view which caused considerable stir in the English theological world; he also wrote St Thomas of Canterbury, his Death and Miracles (1898), Johannine V ocabulary (1905), Johannine Grammar (1906).
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).
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,..
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.
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.
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.
Now, by increasing v, leaving W and V unchanged, we may increase the range of the instrument indefinitely.
Obviously OV is parallel to the tangent to the path atP, and its magnitude is ds/dt, where s is the arc. If we project OV on the co-ordinate axes (rectangular or oblique) in the usual manner, the projections u, v, w are called the component velocities parallel to the axes.
Of Christianity he can have been able to learn very little, even in Medina; as may be seen from the absurd travesty of the institution of the Eucharist in v.
Of the Bohemian writings of Huss, who contributed greatly to the development of his native language, the most important is his V yklad viry, desatera Boziho prikazani, a patere (exposition of the creed, the ten commandments and the Lord's Prayer) written in 1412.
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."
Of the XIth Dynasty is the EARLY PREHISTORIC 7000-8000 B.C. V
Of these references the most important are, perhaps, Strabo v.
On a crag above the town stands the v.
On the day of Koniggratz the Prussians moved into position to attack the Bavarians, and on the 4th of July v.
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.
One of his most famous cases was that of The State of Pennsylvania v.
One of the names given in 1 Esdras v.
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.
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.
Other firsthand narratives of importance are the American officers' reports (Reports of Military Observers, General Staff, U.S.A.); Major v.
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.
P. Norris (Journal of Philology) wished to transpose chapters v.
Passing to Amsterdam he was introduced to John Locke and to Philip v.
Perceiving that air is necessary to life, that the universe is surrounded by air, he was con v inced that out of air all things have resulted.
Perry (Steam Engine, p. 580), assuming a characteristic equation similar to Zeuner's (which makes v a linear function of the temperature at constant pressure, and S independent of the pressure), calculates S as a function of the temperature to satisfy Regnault's formula (10) for the total heat.
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.
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.
Porcius Cato sets forth the doctrine of the Stoics which is shown by Cicero to agree with that of Antiochus of Ascalon; in v.
R appears in the Greek form without a tail, and V and Y are both found for the same sound.
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.
See also Selden, Titles of Honor, p. 678, and the Archceological Journal, v.
See Gratz, History of the Jews, v.
See Mustoxidi, Delle cose Corciresi (Corfu, 1848); Lunzi, IIEpi Tjs - 'ETrramp-a 'Ever&v (Athens, 1856); Ansted, The I.
See Rustow, Militarische Biographien, 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.
Similarly initial v became gw, as in gwin, from Latin vinum, remaining between vowels, though now written w, as in ciwed from civitas.
Sinai or Horeb (according to the Deuteronomic tradition), in the ears of the whole people on the "day of the assembly," and rehearsed in v.
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 .
Since e is a line of insensible magnitude compared with the dimensions of the mass of liquid and the principal radii of curvature of its surface, the volume of the shell whose surface is S and thickness will be and that of the interior space will be V - SE.
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.
Since the distribution of electricity may be considered to be constant over the surface S of the attracted disk, the mechanical force f on it is given by the expression,' f S(V - v)2 8 ird2 where d is the distance between the two plates.
Since the electrical repulsion of the balls is equal to C 2V2 4 12 sin 2 0 dynes, where C = r is the capacity of either ball, and this force is balanced by the restoring force due to their weight, Wg dynes, where g is the acceleration of gravity, it is easy to show that we have _ 21sin 0 r " tan V 8 r as an expression for their common potential V, provided that the balls are small and their distance sufficiently great not sensibly to disturb the uniformity of electric charge upon them.
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.
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.
Since the volume is constant, we have the condition mv'--l-(I-m)v"=constant.
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).
Since there are n waves in distance U + w - u the number he actually receives is n(U + w - v)/(U + w - u).
Singularity excites our wonder in Thaumastocheles zaleucus, v.
So far, however, energy and Successes v i g i lance made them successful.
Strabo follows up the topographical data with a few brief historical statements - "OaKot €t ov Kai raur'v Kai 111v e0-js no,u?rniav.
Substituting these symbols in the expression for the area, the relation becomes H=o(p' - p„)(v„_v')/(o' - o").
Substituting this value in the expression for v, the volume of the body inserted in the cup becomes known.
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.
Suppose it is required to measure the difference of potentials V and V' of two conductors.
Symbols exactly like k, X, and (a), X, are found in the Carian alphabet, and transliterated by Professor Sayce 1 as v (and ii), h and kh respectively.
Tafel, Ber., 1886, 19, p. 1924), by distilling the amido-acids with lime, by heating phenols with zinc chloride ammonia (V.
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.
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.
The allantrapezium; Ito V, first to fifth digit.
The area DABbd under the return path (v diminishing) represents work done on the substance, or against the back-pressure, and is negative.
The badge and ribbon is illustrated on Plate V, fig.
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).
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.
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.
The bearings for receiving these trunnions are V-shaped; the V on one side is fixed, while the other is cut through and can be narrowed or made wider, thus lifting or lowering the trunnion by means of two capstan-headed screws.
The berosh, or beroth, of the Hebrew Scriptures, translated "fir" in the authorized version, in I Kings v.
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.
The body of the Brachiopod v usually occupies about the posterior half of the space within the shell.
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 .
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.
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 church of Babylon mentioned in r Peter 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.
The components of angular momentum about Ox, Qy, 01 will be denoted as usual by X, u, v.
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.
The consonants, b, d, f, k, I, m, n, p, r, v, z, are as in English; g = Eng.
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)].
The Court of Appeal has decided that it has power to sit in private; in Mellor v.
The density of the liquid is MN/V, where N is the number of solvent molecules, and V the total volume of the liquid.
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.
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.
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.
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.
The energy stored up in the jar in joules is expressed by the value of CV 2, where C is the capacity measured in farads and V the potential difference of the coatings in volts.
The equation of the latter, referred to its principal axes, being as in II (41), the co-ordinates of the point J where it is met by the instantaneous axis are proportional to p, q, r, and the direction-cosines of the normal at J are therefore proportional to Ap, Bq, Cr, or X, u, v.
The equation to these lines in terms of v and 0 is obtained by integrating dE=sd0+(Odp/de - p)dv = o .
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.
The external work done is p(v-b), where p is the constant pressure, v the volume of the vapour at 0, and b the volume of the liquid at Bo.
The fact that the Phoenician Vau was retained in the Greek alphabets, and the vowel v added, shows that when the alphabet was introduced the sound denoted by was still in full vigour.
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.
The first equation leads, as before, to t=C{T (V)-T(v)}, (29) x=C{S(V)-S(v)}.
The first published account of the simple camera obscura was discovered by Libri in a translation of the Architecture of v.
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 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.
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).
The Hebrew phrase is "men of grace," as in v.
The highest pressures recorded for cane-sugar are nearly three times as great as those given by van't Hoff's formula for the gas-pressure, but agree very well with the vapour-pressure theory, as modified by Callendar, provided that we substitute for V in Arrhenius's formula the actual specific volume of the solvent in the solution, and if we also assume that each molecule of sugar in solution combines with 5 molecules of water, as required by the observations on the depression of the freezing-point and the rise of the boiling-point.
The history of V as the Latin numeral for 5 is uncertain.
The individualism with which he starts, howsoever afterwards mitigated by his doctrine of To Ti v eivac or eiSos constituting the individual in a system of intelligible relations, confined him in an inadmissible way to the subject-attribute formula.
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 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.
The jar can be charged so that a certain potential difference V, reckoned in volts, exists between the two coatings.
The kitchen with its offices (V) lies behind the refectory, accessible from the outer court without entering the cloister.
The Kuma, which alone pursues an independent course through the steppes, farther north than the v.
The later "c-w-µ€v was at first a solecism, an attempt to conjugate a " verb in µ.c " like the " verbs in w."
The latter was perhaps regarded as a "smith," cp. v.
The locus of the point V is called the hodograp/z (q.v.); and it appears that the velocity of the point V along the hodograph represents in magnitude and in directon tbt acceleration in the original orbit.
The magnet is in equilibrium under the influence of the couple VM due to the vertical component V, and the couple due to the fact that the centre of gravity is slightly on one side of the knife-edge.
The magnitude of the radial acceleration is given by the expression vi/BC, v being the velocity of the point B about the point C. This velocity can always be found from the velocity diagram of the chain of which the link forms a part.
The main ridge runs north and south along the line of the greatest diameter, and from the heights descend many torrents, the v% hole island being well watered.
The mass of the whole shell will therefore be S f E pdv, and that of the interior part of the liquid (V - SE)po.
The matter was again raised in the case of Read and others v.
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.
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.
The most famous case that came before him was that of Chisolm v.
The motion of a rigid body in the most general case may be specified by means of the component velocities u, v, w of any point 0 of it which is taken as base, and the component angular velocities p, q, r.
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.
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.
The oldest testimony is that of Irenaeus 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 .
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.
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 particle comes to rest when V us Vf I Uo2\
The phrase used is AELTOvp'yEl y T 7 V XeLrovpyLav, " to liturgize the liturgy."
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.
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 position of the central ordinate is given by x = v 1 /po, and therefore is given approximately by pl/po.
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.
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 power absorption is then given by the expression (V 3 2 - V i 2 -V2 2)/2R.
The present effect of this unrepealed act, as stated in Boyd v.
The problem is identical with that of finding the common conjugate diameters of the ellipsoids T(x, y, I) =const., V(x, y, 1) =const.
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.
The punishment of the people is briefly recorded in v.
The quadratic expression for T is essentially positive, and the same holds with regard to V in virtue of the assumed stability.
The rabbinical discussions of the book are mentioned in Shabbath, 30b; Megilla, 7a; Eduyoth, v.
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.
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.
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.
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.
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 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.
The same redactor doubtless added v.
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 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.
The spirit with which he pleaded before the Star Chamber in a case of The Crown v.
The statement of the Epicurean doctrine is drawn from the work of Phaedrus HEpi O &,v, the criticism of this from Posidonius.
The succeeding duke was Albert's son, William V (called the Pious), who was educated by the Jesuits and was keenly attached to their tenets.
The success encouraged him to begin a new tragedy, Die V erschworung des Fiesco zu Genua, and he edited a lyric Anthologie auf das Jahr 1782, to which he was himself the chief contributor.
The symbol v represents the inverse of the dispersive power, its value being (nD-i)/(C-F).
The symbol x expresses the energy of unit of mass of the liquid at a depth v within the bounding surface.
The time of vibration is of course itself a function of the nature of the fluid and of the size of the drop. By the method of dimensions alone it may be seen that the time of infinitely small vibrations varies directly as the square root of the mass of the sphere and inversely as the square root of the capillary tension; and it may be proved that its expression is - V C?
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 United States Supreme Court decided the anti-Mormon legislation case of Davis v.
The v, for f, is common in southern English pronunciation; vox, for fox, is found in the Ancren Riwle, c. 1230.
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.
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..
The values of x and y are different, unless V (qq o) = o.
The volume of the sphere is V = 3 irr3, and the increment of volume is dV = 4lrr2dr Now if we suppose a quantity of air already at the pressure II+p, the work done in forcing it into the bubble is p dV.
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'.
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.
Then it is evident that v a.AB, (5)
Then the motion of P is perpendicular to the plane OPQ, and its velocity is v,.= y.
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).
Then, if the true moments are denoted by Pi, v 2, ..., their values are given by vi ?Pl P2 - 11.
There are extensive deposits of petroleum and natural gas, v hich have become of commercial importance.
There are three pairs of spermathecae situated in segments III-V, a testis in V and an ovary in VI.
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.
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).
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.
These additions, the secondary character of which is obvious both from the way in which they interrupt the context and also from their contents, are (1), v.
These can again be combined into a single resultant R acting in the direction (X, u, v), provided X=RX,YRu,ZRv.
These he styles verae (V).
These two classes, V and L, include 86% of the clausulae in the orations.
These V's are so arranged that the axis of the sight frame is always parallel to that of the gun.
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.
They consider themselves bound by the literal interpretation of James v.
They then made way for a ministry under Herr v.
This equation is found experimentally to be capable of representing the relation between p, v, and T over large ranges of values.
This framework is provided with guides on which the platform, whilst preserving its horizontality, is V the observer has to follow the eye-end in a comparatively small circle; another good point is the flattening of the cast-iron centrepiece of the tube so that the flange of the declination axis is attached as near to the axis of the telescope tube as is consistent with free passage of the cone of rays from the object-glass.
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.
This has been so since the famous law case of Williamson v.
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.
This leads to a determinantal equation in X whose 2n roots are either real and negative, or complex with negative real parts, on the present hypothesis that the functions T, V, F are all essentially positive.
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.
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.
This method has been improved, especially by Justus v.
This page gives an overview of all articles in the 1911 Brittanica which are alphabetized under V to Vas.
This process involves the performance of 6 7 8 9 an amount of osmotic work P(v - v).
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.
This V has been variously interpreted.
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.
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.
This view is confirmed by (a) a comparison of v.
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.
This was decided in Liddell v.
This will become zero if V 1 is 2V 2, that is, if the linear velocity of the cupcentres is one-half that of the jet of water impinging upon them.
Thus Homer has 11 .c€v, we go, - - let us go.
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.
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 =..
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).
Thus in the story of the good layman Citta, it is an aspiration expressed on the deathbed; 2 in the dialogue on the subject, it is a thought dwelt on during life, 3 in the numerous stories in the Peta and Vimana V atthus it is usually some isolated act, in the discussions in the Dhamma Sangani it is some mental disposition, which is the Karma (doing or action) in the one life determining the position of the individual in the next.
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.
Thus the pressure is given by the equation (p+a/v 2) (v - b) =RNT, which is known as Van der Waals's equation.
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.
Thus, for instance, in his account of the transition from savage to civilized life, he assumes at v.
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.
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.
To find the total heat H of a vapour, we have H =E+p(v - b), where the intrinsic energy E is measured from the selected zero 9 0 of total heat.
To find the work done when m is brought to the point P in the neighbourhood of a solid body, the density of which is a function of the depth v below the surface, we have only to write instead of a pdz, and to integrate ?
To integrate this equation for a solid of given form is probably difficult, but it is easy to see that at some distance on either side of the body, where the liquid is sensibly at rest, the crest of the wave will approximate to an asymptote inclined to the path of the body at an angle whose sine is w/V, where w is the velocity of the wave and V is that of the body.
Trained at the Ecole des Chartes and the Ecole des Hautes Etudes, he made his first appearance in the world of scholarship as the author of an excellent book called Etudes sur l'industrie et la classe industrielle a Paris au XIII e et au XI V e siècle (1877).
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.
Turkish attacks Turkish corps V Serbian troops - ¦ /?
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.
V bridge, but it has also other ' `??
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.
V is therefore a voiced labio-dental spirant, the breath escaping through a very narrow slit between the lower lip and the upper teeth.
V or slipping will take place.
V with a horizontal line above it was used for 5000.
V?'o?took?s,l eSk ham o h `u Br1 n NewC l 4 ',fteg, r,a, t Sha?
Van der Waal's equation (p-I- a/v 2) (v - b) = RT contains two constants a and b determined by each particular substance.
Van't Hoff showed that the osmotic pressure P due to a number of dissolved molecules n in a volume V was the same as would be exerted by the same number of gas-molecules at the same temperature in the same volume, or that PV = ROn.
Various other works have been attributed to Moses, such as the Petirath Moshe, the 1 31 4 13Xos Aoywv, uucrrcK&v Mwuetws, The Exodus of Moses (in Slavonic), &c. See Charles, Assumption of Moses, pp. xiv.
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).
We have therefore, by equation, (11), Sd0 = (Odv/d0 - v) d p,.
We have, therefore, to consider the conditions under which n2172 (V a +5) T(p - U)g cannot be made negative.
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.
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.
We thus find V in terms of the constant and the difference of the two screw readings.
We thus obtain the relation ds/dv(o const) =od 2 p/d0 2 (v const),.
We Will Assume That When, As In Most Cases, Viscosity Maybe Neglected, The Mass (M) Of A Drop Depends Only Upon The Density (V), The Capillary Tension (T), The Acceleration Of Gravity (G), And The Linear Dimension Of The Tube (A).
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.
When a small body is partly immersed in a liquid originally at rest, and moves horizontally with constant velocity V, waves are propagated through the liquid with various velocities according to their respective wave-lengths.
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?
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.
When, in any problem, the values of u, v, w, p, q, r have been determined as functions of t, it still remains to connect the moving axes with some fixed frame of reference.
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).
White (7 Wallace, 700), 1869, in which he asserted that the Constitution provided for an "indestructible union composed of indestructible states," Veazie Bank v.
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.
Y ...a n v, the summation being for all permutations of the n numbers, is called the determinant of the n 2 quantities.
Y and Z were added in the last century of the republic for use in transliterating Greek words containing v and 1.1 The dialect which was most closely akin to Latin was Faliscan.
Yet another expedition in 839 would seem to 2 See for chronology, Babylonia And Assyria, §§ v.