# How to use *Vanishes* in a sentence

This stream flows north-westward from the last lake and

**vanishes**underground within 3 m.We find Prester John in one more phase before he

**vanishes**from Asiatic history, real or mythical.If all the water be frozen, we have the vapour pressure curve of ice OB; while, if the pressure be raised, so that all the vapour

**vanishes**, we get the curve OC of equilibrium between the pressure and the freezing point of water.Again, the form is such that if it be taken away the nature infallibly

**vanishes**...This will be recognized as the resultant of the two linear forms. If the two linear forms be identical, the umbral sets a l, a2; b l, b 2 are alternative, are ultimately put equal to one another and (ab)

**vanishes**.AdvertisementThe quartic has four equal roots, that is to say, is a perfect fourth power, when the Hessian

**vanishes**identically; and conversely.When C

**vanishes**j has the form j = pxg x, and (f,j) 3 = (ap) 2 (aq)ax = o.The discriminant is the resultant of ax and ax and of degree 8 in the coefficients; since it is a rational and integral function of the fundamental invariants it is expressible as a linear function of A 2 and B; it is independent of C, and is therefore unaltered when C

**vanishes**; we may therefore take f in the canonical form 6R 4 f = BS5+5BS4p-4A2p5.We can see that (abc)a x b x c x is not a covariant, because it

**vanishes**identically, the interchange of a and b changing its sign instead of leaving it unchanged; but (abc) 2 is an invariant.When R =0, and neither of the expressions AC - B 2, 2AB -3C

**vanishes**, the covariant a x is a linear factor of f; but, when R =AC - B 2 = 2AB -3C =0, a x also**vanishes**, and then f is the product of the form jx and of the Hessian of jx.AdvertisementWhen a z and the invariants B and C all vanish, either A or j must vanish; in the former case j is a perfect cube, its Hessian vanishing, and further f contains j as a factor; in the latter case, if p x, ax be the linear factors of i, f can be expressed as (pa) 5 f =cip2+c2ay; if both A and j vanish i also

**vanishes**identically, and so also does f.For strong magnetizing forces (which in these experiments did not exceed II= 48.9) the permeability remains almost constant at its initial value (about 400), until the temperature is within nearly i oo of the critical point; then the permeability diminishes more and more rapidly until the critical point is reached and the magnetization

**vanishes**.It

**vanishes**when u =mlr, m being any whole number other than zero.In like manner we may find the illumination in any other direction, and it is obvious that it

**vanishes**when sin 0 is any multiple of A/a.If we take a direction such that the light (of given wave-length) from a single aperture

**vanishes**, the evanescence continues even when the whole series of apertures is brought into contemplation.AdvertisementAt a moment when the eye, or object-glass of a telescope, occupies a dark position, the star

**vanishes**.The cilia are lost, the eye-spots disappear, the digestive sac

**vanishes**and the larva becomes a sac or "sporocyst" full of germ-cells.If there is no external world, the distinction between substance and accidents

**vanishes**, and these become the sole essence of material objects, so that there is no room for any change whilst they remain as before.But now that the date is put back to about 112 the difficulty

**vanishes**, since Polycarp was not much over forty when he received the letter.The term Pv/V added up for a complete wave

**vanishes**, for P/V is constant and Zv=o, since on the whole the compression equals the extension.AdvertisementFrom these hills southward the ridge gradually becomes less abrupt until in Walsh county it

**vanishes**into prairie.A few of the large streams may, when in flood, spr.ead out in a temporary shallow sheet qn a dead level of clay, or playa, in a basin centre, but the sheet of water

**vanishes**in the warm season and the stream shrinks far up its course, the absolutely barren clay floor of the playa, impassable when wet, becomes firm enough for crossing when dry.The dualism, therefore, between "practice" and "theory" also

**vanishes**; a "theory" unrelated to practice (however indirectly) is simply an illusion.Anher appears in the XIth dynasty; and Khentamenti, the god of the western Hades, rises to importance in the middle kingdom and then

**vanishes**in the XVIIIth.But the numerical factor appears to be yz'+zy', while it is the quantity yz' - zy' which really

**vanishes**.AdvertisementIf, in particular, the point K coincides with A, so that the resultant

**vanishes**, the given system of forces is said to be FIG.When the latter invariant, but not the former,

**vanishes**, the displacement is equivalent to a pure rotation.When the latter invariant, but not the former,

**vanishes**, the system reduces to a single force.It appears from (24) that through any assigned point 0 three rectangular axes can be drawn such that the product of inertia with respect to each pair of co-ordinate planes

**vanishes**; these are called the principal axes of inertia at 0.A point on a central orbit where the radial velocity (drfdt)

**vanishes**is called an apse, and the corresponding radius is called an apse-line.If at any instant the direction of one of the crank-arms coincides with the line of connection, the common perpendicular of the line sf connection and the axis of that crank-arm

**vanishes**, and the 3irectional relation of the motions becomes indeterminate.The latter tendency is called a centrifugal couple, and

**vanishes**for rotation about a principal axis.The story of James de la Cloche is indeed itself another historical mystery; he abruptly

**vanishes**as such at Rome at the end of 1668, and thus provides a disappearance of convenient date; but the question concerning him is complicated by the fact that a James Henry de Bovere Roano Stuardo, who married at Naples early in 1669 and undoubtedly died in the following August, claiming to be a son of Charles II., makes just afterwards an equally abrupt appearance; in many respects the two men seem to be the same, but Monsignor Barnes, following Lord Acton, here regards James Stuardo as an impostor who traded on a knowledge of James de la Cloche's secret.Henceforward Greek culture practically

**vanishes**and gives place to Aramaic; it is significant that in future the kings of Mesene stamped their coinage with Aramaic legends.But the most characteristic passage of the epopee is the mysterious disappearance of Shah Kaikhosrau, who suddenly, when at the height of earthly fame and splendour, renounces the world in utter disgust, and, carried away by his fervent longing for an abode of everlasting tranquillity,

**vanishes**for ever from the midst of his companions.The surface-tension diminishes as the temperature rises, and when the temperature reaches that of the critical point at which the distinction between the liquid and its vapour ceases, it has been observed by Andrews that the capillary action also

**vanishes**.The two systems that have just been described were those that most prominently attracted the attention of the ancient world, so far as it was directed to ethics, from their Later almost simultaneous origin to the end of the 2nd Greek century A.D., when Stoicism almost

**vanishes**from our philo- view.One of these, called the "Bourne," bursts forth a short way above the town at irregular intervals of one to ten years or more; and after running a torrent for two or three months, as quickly

**vanishes**.A coin

**vanishes**and then audibly reappears in a folded handkerchief held by a spectator.When Sarah gets to the fountain she

**vanishes**leaving only a small whirlwind in the Shadows.We have 62=W12+W22+032=P2 (N) 2 Y 2+P2 (A I - 3) 2 If AN, AD be both finite, we learn from (7) that there is no direction perpendicular to the primary (polarized) ray in which the secondary light

**vanishes**.If the jth column be identical with the i ll ' the determinant A

**vanishes**identically; hence if j be not equal to i, k, or r, a 11 a 21 a31 0 =I alk a2k a3k A11.Such a determinant when of uneven degree

**vanishes**, for if we multiply each row by - I we multiply the determinant by (- I) n = -1, and the effect of this is otherwise merely to transpose the determinant so that it reads by rows as it formerly did by columns, an operation which we know leaves the determinant unaltered.If Q be on the circle described upon OA as diameter, so that u = a cos 4,, then Q' lies also upon the same circle; and in this case it follows from the symmetry that the unsymmetrical aberration (depending upon a)

**vanishes**.Again, considering the systems which start from the P normal ranges, we see that there is a probability p/(P+p) which

**vanishes**in the limit, that a system selected at random from these will be in an abnormal state after a sufficient time.If, however, hinges or joints are introduced at the points of contrary flexure, they become necessarily points where the bending moment is zero and ambiguity as to the stresses

**vanishes**.The contradiction here is palpable; and at the same time the antithesis of " just " and " good " ultimately

**vanishes**.I feel that I cannot vanish, since nothing

**vanishes**in this world, but that I shall always exist and always have existed.It

**vanishes**in the light of day, but shines in the darkness.The flatness problem

**vanishes**because the huge expansion blows the universe up so much that it smooths out irregularities.For many women, sex equality is a thin veneer which

**vanishes**as soon as they take on caring responsibilities.Within a few feet of the old trunk of the tree he

**vanishes**.That affects whether type C becomes uncommon, or

**vanishes**altogether.Then he

**vanishes**in a puff of smoke....The spectator again chooses a card and it, too

**vanishes**in an instant !As regards the polarization of the dispersed light as dependent on the angle at which it is emitted, we find that although, when terms of the second order are included, the scattered light no longer

**vanishes**in the same direction as before, the peculiarity is not lost but merely transferred to another direction.Thus Russell's contradiction

**vanishes**, and an examination of the other contradictions shows that they vanish also.Hence in all there are mn such systems. If, therefore, we have a third equation, and we substitute each system of values in it successively and form the product of the mn expressions thus formed, we obtain a function which

**vanishes**if any one system of values, common to the first two equations, also satisfies the third.For a single quantic of the first order (ab) is the symbol of a function of the coefficients which

**vanishes**identically; thus (ab) =a1b2-a2bl= aw l -a1ao=0 and, indeed, from a remark made above we see that (ab) remains unchanged by interchange of a and b; but (ab), = -(ba), and these two facts necessitate (ab) = o.The first transvectant, (f,f') 1 = (ab) a x b x,

**vanishes**identically.This method of solution fails when the discriminant R

**vanishes**, for then the Hessian has equal roots, as also the cubic f.If, moreover, 0

**vanishes**identically f is a perfect cube.In the limiting case in which the medium is regarded as absolutely incompressible S

**vanishes**; but, in order that equations (2) may preserve their generality, we must suppose a at the same time to become infinite, and replace a 2 3 by a new function of the co-ordinates.When hardened in spirit, however, the greater part of this experimental amyloid in the fowl

**vanishes**, and the reactions are not forthcoming.Charles, duke of Lower Lorraine, who was thrown into prison by Hugh Capet in 991, left two sons, the last male descendants of the Carolingians, Otto, who was also duke of Lower Lorraine and died without issue, and Louis, who after the year loon

**vanishes**from history.For though Aristotle's divergence from Plato is very conspicuous when we consider either his general conception of the subject of ethics, or the details of his system of virtues, still his agreement with his master is almost complete as regards the main outline of his theory of human good; the difference between the two practically

**vanishes**when we view them in relation to the later controversy between Stoics and Epicureans.A chosen card

**vanishes**from the deck, only to appear stuck to a window !Depression that arrives as days (and daylight time) shorten in autumn and winter yet

**vanishes**in the spring and summer when longer days of sunlight resume.When one half of the Dual Cube is matched with two cubes of the same color, it

**vanishes**, leaving behind a solid cube of the other color.Every time a set of balls

**vanishes**, the meter at the top of the screen fills up.Virgo men are known for their good looks and winning smiles, but just when you think you have one of them snared, poof, he

**vanishes**.The most commonly reported encounter with Resurrection Mary is that people offer her a ride, and then the woman

**vanishes**while inside the car or when they pass the cemetery.Usually, it's a woman that acts strange while in the car, but upon reaching the destination she

**vanishes**.