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vanish

vanish

vanish Sentence Examples

  • Didn't he vanish somewhere?

    225
    98
  • And then all threads of hope will finally vanish from the fabric of my life.

    159
    83
  • Attacked in detail, they vanish one after another into as many teasing spectra of uncertainty.

    79
    53
  • It was plain that at the first revolutionary blast from without, or the first insurrectionary outburst from within, the " Bach System would vanish like a mirage.

    61
    28
  • Thus Russell's contradiction vanishes, and an examination of the other contradictions shows that they vanish also.

    44
    26
  • Shortly below Kut-el-Amara all traces of ancient canalization on the east side vanish, and it would appear as though much of that region, now largely under water at flood time, constituted an inland sea.

    42
    35
  • Shortly below Kut-el-Amara all traces of ancient canalization on the east side vanish, and it would appear as though much of that region, now largely under water at flood time, constituted an inland sea.

    42
    35
  • I feel that I cannot vanish, since nothing vanishes in this world, but that I shall always exist and always have existed.

    29
    25
  • The elongation is generally found to reach a maximum under a magnetizing force of 50 to 120 units, and to vanish under a force of 200 to 400, retraction occurring when still higher forces are applied.

    26
    13
  • It follows that when the fluid has come to rest, the tangential stress in any plane in its interior must vanish, and the stress must be entirely normal to the plane.

    22
    15
  • Such a symbolic product, if its does not vanish identically, denotes an invariant or a covariant, according as factors az, bz, cz,...

    22
    18
  • aj Hence the system of values also causes to vanish in this case; dx and by symmetry aj and Fz also vanish.

    16
    11
  • Every unit of the rth species which does not vanish is the product of r different units of the first species; two such units are independent unless they are permutations of the same set of primary units e i, in which case they are equal or opposite according to the usual rule employed in determinants.

    16
    13
  • Most of the many names of gods are mere names that appear and vanish again in particular districts and temples.

    15
    13
  • But lo! the lovely maiden only smiles more sweetly, and breathes upon the icy battlements of her enemies, and in a moment they vanish, and the glad Earth gives her a royal welcome.

    15
    15
  • But all my hopes vanish when I come to explain the principles that unite our successive perceptions in our thought or consciousness.

    14
    14
  • " The day," says Ernest Renan, " in which the belief in an after-life shall vanish from the earth will witness a terrific moral and spiritual decadence.

    13
    14
  • " The day," says Ernest Renan, " in which the belief in an after-life shall vanish from the earth will witness a terrific moral and spiritual decadence.

    13
    14
  • In order that the force may vanish we must also have ~, 5~=o, i.e.

    12
    11
  • The supporters of the solar theory look upon Memnon as the son of the dawn, who, though he might vanish from sight for a time, could not be destroyed; hence the immortality bestowed upon him by Zeus.

    12
    13
  • For his speculations on sets had already familiarized him with the idea that multiplication might in certain cases not be commutative; so that, as the last term in the above product is made up of the two separate terms ijyz' and jizy', the term would vanish of itself when the factorlines are coplanar provided ij = - ji, for it would then assume the form ij(yz' - zy').

    11
    11
  • Integrating by parts in (II), we get J e = ikr d7 pc-11 / d (e r - ay= rJ Z d y - r / 1 dY, in which the integrated terms at the limits vanish, Z being finite only within the region T.

    10
    10
  • Below this region flow the streams of the Great Basin, none of which reach the sea, but either terminate in lakes having no outlet or else vanish in sloughs or " sinks."

    9
    10
  • If al, a2, ...a, n be the roots of f=o, (1, R2, -Ai the roots of 0=o, the condition that some root of 0 =o may qq cause f to vanish is clearly R s, 5 =f (01)f (N2) � �;f (Nn) = 0; so that Rf,q5 is the resultant of f and and expressed as a function of the roots, it is of degree m in each root 13, and of degree n in each root a, and also a symmetric function alike of the roots a and of the roots 1 3; hence, expressed in terms of the coefficients, it is homogeneous and of degree n in the coefficients of f, and homogeneous and of degree m in the coefficients of 4..

    9
    10
  • Woman is the impersonation of man's sensuous and fallen nature; on the final return to the divine unity, distinction of sex will vanish, and the spiritual body will be regained.

    9
    10
  • Thus Cyrenaicism did not entirely vanish with its absorption in Epicureanism.

    8
    8
  • Hence if A does not vanish x 1 = x 2 =...

    8
    9
  • Thus the Allobroges now disappear and the colonia of Vienna takes their place: the Volcae vanish and we find Nemausus (Nimes).

    7
    6
  • Again, when extraneous forces P act on the joints, the equation is Z(P.&P)+S.Os=-o, where op is the displacement of any joint in the direction of the corresponding force P. If ~(P. Op) =o, the stresses are merely indeterminate as before; but if ~ (P. op) does not vanish, the equation cannot be satisfied by any finite value of S, since Os =0.

    6
    4
  • =n3, 'If' the forms a:, b:, cy 7 ...be identical the symbols are alternative, and provided that the form does not vanish it denotes an invariant of the single form ay.

    6
    7
  • .q,, that they shall vanish in the configuration in question: The potential energy is then given with sufficient approximation by an expression of the form 2V=ciiqi1+clzqii+...

    5
    5
  • The other coefficients in (8) vanish in virtue of the symmetry.

    4
    3
  • If, instead of supposing the motion at dS to be that of the primary wave, and to be zero elsewhere, we suppose the force operative over the element dS of the lamina to be that corresponding to the primary wave, and to vanish elsewhere, we obtain a secondary wave following quite a different law.

    4
    3
  • If, instead of supposing the motion at dS to be that of the primary wave, and to be zero elsewhere, we suppose the force operative over the element dS of the lamina to be that corresponding to the primary wave, and to vanish elsewhere, we obtain a secondary wave following quite a different law.

    4
    3
  • The fundamental assumption is that each group of strips of the trapezette may be replaced by a figure for which differences of u, above those of a certain order, vanish (§ 54).

    4
    4
  • The greater part of the German clergy again proved their loyalty to Frederick, who hurried to Germany only to see the oDposition vanish before him.

    4
    4
  • Again it is necessary and sufficient for equilibrium that the sum of the projections of the forces on each of two perpendicular directions should vanish, and (moreover) that the sum of the moments about some one point should be zero.

    4
    4
  • Since y must vanish at the upper end (x 1), the admissible values of a are determined by o2=gz2/41, Jo(z)=o.

    4
    4
  • In all cases to which it is necessary to have regard the integrated terms vanish at both limits, and we may write f o (z)dz = 3f2' z 3 4(z)dz, f o z(z)dz = 'a' z4 cb(z)d z; (36) so that Ko = 3 f o z3 ?(z) dz, To = $?

    4
    4
  • =y la xl -i-y2a x2 must also vanish for the root a, and thence ax, and a must also vanish for the same root; which proves that a is a double root of f, and f therefore a perfect square.

    4
    5
  • In words: the sum of the projections of the forces on each of the co-ordinate axes must vanish; and, the sum of the moments of the forces about each of these axes must vanish.

    4
    5
  • =y la xl -i-y2a x2 must also vanish for the root a, and thence ax, and a must also vanish for the same root; which proves that a is a double root of f, and f therefore a perfect square.

    4
    5
  • Were the feudal tie broken, the crown must soon vanish, and the constitution of medieval society undergo a radical change.

    4
    6
  • For in this case the n equations are not independent since identically Al�ft+ A2� f2+...+An�fn = 0, and assuming that the minors do not all vanish the satisfaction of ni of the equations implies the satisfaction of the nth.

    4
    7
  • If r, or z, be infinite, Jo(z), J 1 (z) vanish, and the whole illumination is expressed by 71-R 2, in accordance with the general principle.

    4
    7
  • If r, or z, be infinite, Jo(z), J 1 (z) vanish, and the whole illumination is expressed by 71-R 2, in accordance with the general principle.

    4
    7
  • When 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.

    3
    2
  • Regnault's formula for the total heat is here again seen to be inadmissible, as it would make the latent heat of steam vanish at about 870° C. instead of at 365° C. It should be observed, however, that the assumptions made in deducing the above formulae apply only for moderate pressures, and that the formulae cannot be employed up to the critical point owing to the uncertainty of the variation of the specific heats and the cooling effect Q at high pressures beyond the experimental range.

    3
    3
  • It is always an invariant or covariant appertaining to a number of different linear forms, and as before it may vanish if two such linear forms be identical.

    3
    4
  • If the forms be identical the sets of symbols are ultimately equated, and the form, provided it does not vanish, is a covariant of the form ate.

    3
    4
  • The two forms ax, bx, or of, 0, may be identical; we then have the kth transvectant of a form over itself which may, or may not, vanish identically; and, in the latter case, is a covariant of the single form.

    3
    4
  • The first and fourth of these indicate that (a 2) w is a homogeneous function of X i, X2, and of /u1, � 2 separately, and the second and third arise from the fact that (X / 1) is caused to vanish by both Da � and D�A.

    3
    4
  • During the Macedonian period Greek influences had been steadily gaining ground in Phoenicia; relations with the Greek world grew closer; the native language fell into disuse, and from the beginning of the Roman occupation Greek appears regularly in inscriptions and on coins, though on the latter Phoenician legends do not .entirely vanish till the 2nd century A.D.; while the extent to which Hellenic ideas penetrated the native traditions and mythologies is seen in the writings of Philo of Byblus.

    3
    4
  • If A or B vanish we have an equiangular spiral, and the velocity at infinity is zero.

    3
    4
  • Instead of making d4 vanish, a certain value can be assigned to it which will produce, by the addition of the two lenses, any desired chromatic deviation, e.g.

    3
    4
  • On the other hand they appear and vanish 15, exercise miraculous powers", and fly 17.

    3
    5
  • As the temperature 0" is lowered, the area of the cycle increases, but since W can never exceed H', there must be a zero limit of temperature at which the pressure would vanish and the area of the cycle become equal to the whole heat absorbed at the higher temperature.

    2
    2
  • Met with a firm resistance, it would, he believed, vanish away, with no worse result than the possible plunder of a few houses by the city mobs.

    2
    2
  • The value of G will in general vary with the position of 0, and will vanish when 0 lies on the line of action of the single resultant.

    2
    2
  • In the case of a multiple root the minors of ~(o2) all vanish, and the basis for the determination of the quantities ar disappears.

    2
    2
  • The .sextic covariant t is seen to be factorizable into three quadratic factors 4 = x 1 x 2, =x 2 1 - 1 - 2 2, 4) - x, which are such that the three mutual second transvectants vanish identically; they are for this reason termed conjugate quadratic factors.

    2
    3
  • for 0=2, (a l a i +v 2 a 2) w; either v l or cr 2 will vanish if a1a2=A2=o; but every term, in the development, is of the form (222...)Ar and therefore vanishes; so that none are left to undergo reduction.

    2
    3
  • Thus every quaternion may be written in the form q = Sq+Vq, where either Sq or Vq may separately vanish; so that ordinary algebraic quantities (or scalars, as we shall call them) and pure vectors may each be regarded as special cases of quaternions.

    2
    3
  • We will suppose that A> B> C. From the form of the polhode curves referred to in 19 it appears that the angular velocity q about the axis of mean moment must vanish periodically.

    2
    3
  • Thus every quaternion may be written in the form q = Sq+Vq, where either Sq or Vq may separately vanish; so that ordinary algebraic quantities (or scalars, as we shall call them) and pure vectors may each be regarded as special cases of quaternions.

    2
    3
  • 1, may be determined by direct integration of (12), or from the observation that by their constitution G and H vanish when u= oo, coupled with the fact that C and S then assume the value 2.

    2
    4
  • As an example of the general equations, take the simplest case of a uniform field of gravity, with Oz directed vertically downward; employing the gravitation unit of force, 1 dp i dp t dp dp/dz = p = pzn (4) z n+I pz 1 /n p-p n-H ?t), (5) supposing p and p to vanish together.

    2
    4
  • It may be observed that the correction would vanish if we could write dh=wodp/do=wL/(v-w).

    2
    4
  • since the terms which are bilinear in respect to ~, y,, and E, ~, ~ vanish, in virtue of the relations (l).

    2
    4
  • In general his object is to reduce the final equation to a simple one by making such an assumption for the side of the square or cube to which the expression in x is to be equal as will make the necessary number of coefficients vanish.

    0
    0
  • This can be seen at once because the factor in question being once repeated in both differentials, the resultant of the latter must vanish.

    0
    0
  • P141 P242 ��� -1 hp, - hpg = is converted into where dlo = d a P,q-1 - dapg vanish.

    0
    0
  • 32 ax l ay 2 ax2ay1' which, operating upon any polar, causes it to vanish.

    0
    0
  • n of k; if k = o we have the product of the two forms, and for all values of k>n the transvectants vanish.

    0
    0
  • It is obvious that, when k is uneven, the kth transvectant of a form over itself does vanish.

    0
    0
  • We may usually suppose that a large number of the outer rings are incomplete, so that the integrated term at the upper limit may properly be taken to vanish.

    0
    0
  • If we suppose that everything is symmetrical on the two sides of the primary plane y=o, the coefficients B, (3, S vanish.

    0
    0
  • In spite of any inequality between p and p', the definition will be good to this order of approximation, provided a and y vanish.

    0
    0
  • Thus, if we supply heat to the mixture of ice, water and steam ice will melt and eventually vanish.

    0
    0
  • Thus, in this special case, the term in ij ought to vanish.

    0
    0
  • Further, by suitably choosing the positions of the deflectors and the coefficient of torsion of the fibre, it is possible to make the temperature coefficient vanish.

    0
    0
  • If F, Q, R, be any three forces acting along BC, CA, AB, respectively, the line of action of the resultant is determined by the consideration that the sum of the moments about any point on it must vanish.

    0
    0
  • In particular cases, of course, the translation, or the rotation, may vanish.

    0
    0
  • Since R2=X2+Y2+Z2, G2=L1+M2+N2, it is necessary and sufficient for equilibrium that the six quantities X, Y, Z, L, M, N, should all vanish.

    0
    0
  • (m-2)th degrees must vanish.

    0
    0
  • They can be traced down to the 7th century, and then they seem to vanish.

    0
    0
  • On ladies' seals the owner is often gracefully depicted standing and holding flower or bird, or with shields of arms. After the 14th century, the figures of ladies, other than queens, vanish from seals.

    0
    0
  • " They had seen," he says, " the car of Simon Magus blown away by the mouth of Peter and vanish at the name of Christ.

    0
    0
  • This may be achieved in seven thousand years, when man will vanish from the world.

    0
    0
  • The dead would rise, trouble and sickness vanish, and youth and beauty come to all alike.

    0
    0
  • " But it is requisite, that the Prisme and Lens be placed steddy, and that the paper, on which the colours are cast be moved to and fro; for, by such motion, you will not only find, at what distance the whiteness is most perfect but also see, how the colours gradually convene, and vanish into whiteness, and afterwards having crossed one another in that place where they compound Whiteness, are again dissipated and severed, and in an inverted order retain the same colours, which they had before they entered the composition.

    0
    0
  • Hence the invention of Galahad, son to Lancelot by the Grail king's daughter; predestined by his lineage to achieve the quest, foredoomed, the quest achieved, to vanish, a sacrifice to his father's fame, which, enhanced by connexion with the Grailwinner, could not risk eclipse by his presence.

    0
    0
  • a, b, c a' b' c', a"b" c", b", that is, every term which does not vanish contains as a factor the abc-determinant last written down; the sum of all other factors a0'y" is the a/37-determinant of the formula; and the final result then is, that the determinant on the left-hand side is equal to the product on the right-hand side of the formula.

    0
    0
  • In the Croatian Karst the seven streams of the Lika unite and plunge into a rocky chasm near Gospic, and the few small brooks of this region usually vanish underground in a similar manner.

    0
    0
  • He had to humble himself before Austria and the whole of Europe; and it was high time for Fleury, now fallen into second childhood, to vanish from the scene (January 1743).

    0
    0
  • They may, however, be distinguished by the fact that on previous transmission through a quarter-wave plate this property is retained in the case of common light, while with the two other types the relative intensity of the streams depends upon the orientation of the rhomb, and with circularly polarized light one stream may be made to vanish.

    0
    0
  • Elliptically polarized, partially elliptically polarized and partially plane polarized light give with Iceland spar two streams of, in general, unequal intensity, neither of which can be made to vanish.

    0
    0
  • These attain their maximum visibility when the plane of analysation is at 45° to these planes, and vanish when the plane of polarization is parallel to either of the principal planes.

    0
    0
  • It announced, he tells us, that in the north, in Finland, there should be born a prince who should lay waste Germany and vanish in 1632.

    0
    0
  • While only days ago I wouldn't have believed they would so summarily vanish, events recently would have frightened them, especially Martha with baby Claire to care for, to the core.

    0
    0
  • And then all threads of hope will finally vanish from the fabric of my life.

    0
    0
  • We have all seen over the years aid pouring into Africa, only to vanish into thin air.

    0
    0
  • A warrior might perform valiant deeds, but his fame would soon vanish if he had no bard to record them for posterity.

    0
    0
  • Catching hermit crabs, watching bright red sticky beadlet anemones catch a passing shrimp, watching the slippery butterfish vanish beneath a rock.

    0
    0
  • There are evils which have sported with the weakness and subdued the strength of all human contrivances to vanish them.

    0
    0
  • cosmic in scope the many selves vanish and the One Self alone remains.

    0
    0
  • Thy fairest hopes undone bring desolation, or else, fulfilled, shall vanish in a day.

    0
    0
  • For thus, man may extend thy progeny, Vntill man doe but vanish, and not die.

    0
    0
  • gaggle of geese vanish.

    0
    0
  • inadvisable to apply linseed oil, stain or vanish to unpainted oak doors.

    0
    0
  • It is generally inadvisable to apply linseed oil, stain or vanish to unpainted oak doors.

    0
    0
  • Three naked nymphs vanish as I'm jerked back to wakefulness.

    0
    0
  • overlord states and finally they will vanish.

    0
    0
  • Third Vanish - Perhaps make the paintbrush change a bit more smooth.

    0
    0
  • What a great pity to see a project with such remarkable talent vanish.

    0
    0
  • Dirty Marks carpet Usually respond to carpet shampoo e.g. 1001 or Vanish.

    0
    0
  • shim material for an instant vanish.

    0
    0
  • splattered on the ground, the warm weather tends to vanish.

    0
    0
  • uncanny ability to vanish whenever you want.

    0
    0
  • valiant deeds, but his fame would soon vanish if he had no bard to record them for posterity.

    0
    0
  • vanish a coin from a spectators hand without touching it!

    0
    0
  • vanish forever.

    0
    0
  • When, with renewed vigor, he resumed beating it, the snakes began to vanish.

    0
    0
  • The symmetry also requires that the intensity of the scattered light should vanish for the ray which would be propagated along the axis; for there is nothing to distinguish one direction transverse to the ray from another.

    0
    0
  • Now experiment tells us plainly that there is such a direction, and therefore we are driven to the conclusion that either AN or AD must vanish.

    0
    0
  • Attacked in detail, they vanish one after another into as many teasing spectra of uncertainty.

    0
    0
  • Thus the Allobroges now disappear and the colonia of Vienna takes their place: the Volcae vanish and we find Nemausus (Nimes).

    0
    0
  • Below this region flow the streams of the Great Basin, none of which reach the sea, but either terminate in lakes having no outlet or else vanish in sloughs or " sinks."

    0
    0
  • In general his object is to reduce the final equation to a simple one by making such an assumption for the side of the square or cube to which the expression in x is to be equal as will make the necessary number of coefficients vanish.

    0
    0
  • The supporters of the solar theory look upon Memnon as the son of the dawn, who, though he might vanish from sight for a time, could not be destroyed; hence the immortality bestowed upon him by Zeus.

    0
    0
  • Thus Russell's contradiction vanishes, and an examination of the other contradictions shows that they vanish also.

    0
    0
  • If any symmetrical determinant vanish and be bordered as shown below all a12 a13 Al a12 a22 a23 A2 a13 a23 a33 A3 Al A2 A3 � it is a perfect square when considered as a function of A 11 A2, A3.

    0
    0
  • Denote by A the determinant (a11a22���ann)� Multiplying the equations by the minors A l, .., A2,,,,���Ani., respectively, and adding, we obtain x 1 (ai, Aig+a2p.A2lc+���+an�An�) =x�A=o, since from results already given the remaining coefficients of x 11' x 2, ...x � 'i x�+I,...x, vanish identically.

    0
    0
  • Hence if A does not vanish x 1 = x 2 =...

    0
    0
  • For in this case the n equations are not independent since identically Al�ft+ A2� f2+...+An�fn = 0, and assuming that the minors do not all vanish the satisfaction of ni of the equations implies the satisfaction of the nth.

    0
    0
  • If al, a2, ...a, n be the roots of f=o, (1, R2, -Ai the roots of 0=o, the condition that some root of 0 =o may qq cause f to vanish is clearly R s, 5 =f (01)f (N2) � �;f (Nn) = 0; so that Rf,q5 is the resultant of f and and expressed as a function of the roots, it is of degree m in each root 13, and of degree n in each root a, and also a symmetric function alike of the roots a and of the roots 1 3; hence, expressed in terms of the coefficients, it is homogeneous and of degree n in the coefficients of f, and homogeneous and of degree m in the coefficients of 4..

    0
    0
  • aj Hence the system of values also causes to vanish in this case; dx and by symmetry aj and Fz also vanish.

    0
    0
  • This can be seen at once because the factor in question being once repeated in both differentials, the resultant of the latter must vanish.

    0
    0
  • P141 P242 ��� -1 hp, - hpg = is converted into where dlo = d a P,q-1 - dapg vanish.

    0
    0
  • d p4sp4 +Dp4(pg)+1; d P4 causes every other signle part function to vanish, and must cause any monomial function to vanish which does not comprise, one of the partitions of the biweight pq amongst its parts.

    0
    0
  • =n3, 'If' the forms a:, b:, cy 7 ...be identical the symbols are alternative, and provided that the form does not vanish it denotes an invariant of the single form ay.

    0
    0
  • It is always an invariant or covariant appertaining to a number of different linear forms, and as before it may vanish if two such linear forms be identical.

    0
    0
  • If the forms be identical the sets of symbols are ultimately equated, and the form, provided it does not vanish, is a covariant of the form ate.

    0
    0
  • 32 ax l ay 2 ax2ay1' which, operating upon any polar, causes it to vanish.

    0
    0
  • n of k; if k = o we have the product of the two forms, and for all values of k>n the transvectants vanish.

    0
    0
  • The two forms ax, bx, or of, 0, may be identical; we then have the kth transvectant of a form over itself which may, or may not, vanish identically; and, in the latter case, is a covariant of the single form.

    0
    0
  • It is obvious that, when k is uneven, the kth transvectant of a form over itself does vanish.

    0
    0
  • The first and fourth of these indicate that (a 2) w is a homogeneous function of X i, X2, and of /u1, � 2 separately, and the second and third arise from the fact that (X / 1) is caused to vanish by both Da � and D�A.

    0
    0
  • The Aronhold process, given by the operation a as between any two of the forms, causes such an invariant to vanish.

    0
    0
  • The .sextic covariant t is seen to be factorizable into three quadratic factors 4 = x 1 x 2, =x 2 1 - 1 - 2 2, 4) - x, which are such that the three mutual second transvectants vanish identically; they are for this reason termed conjugate quadratic factors.

    0
    0
  • Such a symbolic product, if its does not vanish identically, denotes an invariant or a covariant, according as factors az, bz, cz,...

    0
    0
  • When 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.

    0
    0
  • for 0=2, (a l a i +v 2 a 2) w; either v l or cr 2 will vanish if a1a2=A2=o; but every term, in the development, is of the form (222...)Ar and therefore vanishes; so that none are left to undergo reduction.

    0
    0
  • The elongation is generally found to reach a maximum under a magnetizing force of 50 to 120 units, and to vanish under a force of 200 to 400, retraction occurring when still higher forces are applied.

    0
    0
  • It was plain that at the first revolutionary blast from without, or the first insurrectionary outburst from within, the " Bach System would vanish like a mirage.

    0
    0
  • Every unit of the rth species which does not vanish is the product of r different units of the first species; two such units are independent unless they are permutations of the same set of primary units e i, in which case they are equal or opposite according to the usual rule employed in determinants.

    0
    0
  • We may usually suppose that a large number of the outer rings are incomplete, so that the integrated term at the upper limit may properly be taken to vanish.

    0
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  • If the one set of lines exactly bisect the intervals between the others, the grating interval is practically halved, and the previously existing spectra of odd order vanish.

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  • If we suppose that everything is symmetrical on the two sides of the primary plane y=o, the coefficients B, (3, S vanish.

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  • In spite of any inequality between p and p', the definition will be good to this order of approximation, provided a and y vanish.

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  • The other coefficients in (8) vanish in virtue of the symmetry.

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  • 1, may be determined by direct integration of (12), or from the observation that by their constitution G and H vanish when u= oo, coupled with the fact that C and S then assume the value 2.

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  • Integrating by parts in (II), we get J e = ikr d7 pc-11 / d (e r - ay= rJ Z d y - r / 1 dY, in which the integrated terms at the limits vanish, Z being finite only within the region T.

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  • It follows that when the fluid has come to rest, the tangential stress in any plane in its interior must vanish, and the stress must be entirely normal to the plane.

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  • As an example of the general equations, take the simplest case of a uniform field of gravity, with Oz directed vertically downward; employing the gravitation unit of force, 1 dp i dp t dp dp/dz = p = pzn (4) z n+I pz 1 /n p-p n-H ?t), (5) supposing p and p to vanish together.

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  • With the values above of u, v, w, u', v', w', the equations become of the form p x + 4 7rpAx -Fax -{-hy-}-gz =o, - p - dy+ 4?pBy + hx+ay+fz =o, P d p + TpCZ +f y + yz = o, and integrating p p 1+27rp(Ax2+By2+CZ2) +z ('ax e +ay e + yz2 2 f yz + 2gzx + 2 hx y) = const., (14) so that the surfaces of equal pressure are similar quadric surfaces, which, symmetry and dynamical considerations show, must be coaxial surfaces; and f, g, h vanish, as follows also by algebraical reduction; and 4c2 (c 2 - a2)?

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  • As the temperature 0" is lowered, the area of the cycle increases, but since W can never exceed H', there must be a zero limit of temperature at which the pressure would vanish and the area of the cycle become equal to the whole heat absorbed at the higher temperature.

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  • denote the values for x = xim ' of the successive differential coefficients of u with regard to x; the series continuing until the differential coefficients vanish.

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  • The fundamental assumption is that each group of strips of the trapezette may be replaced by a figure for which differences of u, above those of a certain order, vanish (§ 54).

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  • On the other hand they appear and vanish 15, exercise miraculous powers", and fly 17.

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  • Most of the many names of gods are mere names that appear and vanish again in particular districts and temples.

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  • Thus Cyrenaicism did not entirely vanish with its absorption in Epicureanism.

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  • Met with a firm resistance, it would, he believed, vanish away, with no worse result than the possible plunder of a few houses by the city mobs.

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  • Thus, if we supply heat to the mixture of ice, water and steam ice will melt and eventually vanish.

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  • During the Macedonian period Greek influences had been steadily gaining ground in Phoenicia; relations with the Greek world grew closer; the native language fell into disuse, and from the beginning of the Roman occupation Greek appears regularly in inscriptions and on coins, though on the latter Phoenician legends do not .entirely vanish till the 2nd century A.D.; while the extent to which Hellenic ideas penetrated the native traditions and mythologies is seen in the writings of Philo of Byblus.

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  • But all my hopes vanish when I come to explain the principles that unite our successive perceptions in our thought or consciousness.

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  • Were the feudal tie broken, the crown must soon vanish, and the constitution of medieval society undergo a radical change.

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  • The greater part of the German clergy again proved their loyalty to Frederick, who hurried to Germany only to see the oDposition vanish before him.

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  • Woman is the impersonation of man's sensuous and fallen nature; on the final return to the divine unity, distinction of sex will vanish, and the spiritual body will be regained.

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  • Thus, in this special case, the term in ij ought to vanish.

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  • For his speculations on sets had already familiarized him with the idea that multiplication might in certain cases not be commutative; so that, as the last term in the above product is made up of the two separate terms ijyz' and jizy', the term would vanish of itself when the factorlines are coplanar provided ij = - ji, for it would then assume the form ij(yz' - zy').

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  • Regnault's formula for the total heat is here again seen to be inadmissible, as it would make the latent heat of steam vanish at about 870° C. instead of at 365° C. It should be observed, however, that the assumptions made in deducing the above formulae apply only for moderate pressures, and that the formulae cannot be employed up to the critical point owing to the uncertainty of the variation of the specific heats and the cooling effect Q at high pressures beyond the experimental range.

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  • It may be observed that the correction would vanish if we could write dh=wodp/do=wL/(v-w).

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  • Further, by suitably choosing the positions of the deflectors and the coefficient of torsion of the fibre, it is possible to make the temperature coefficient vanish.

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  • Again it is necessary and sufficient for equilibrium that the sum of the projections of the forces on each of two perpendicular directions should vanish, and (moreover) that the sum of the moments about some one point should be zero.

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  • If F, Q, R, be any three forces acting along BC, CA, AB, respectively, the line of action of the resultant is determined by the consideration that the sum of the moments about any point on it must vanish.

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  • The value of G will in general vary with the position of 0, and will vanish when 0 lies on the line of action of the single resultant.

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  • In particular cases, of course, the translation, or the rotation, may vanish.

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

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  • In words: the sum of the projections of the forces on each of the co-ordinate axes must vanish; and, the sum of the moments of the forces about each of these axes must vanish.

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  • Again, when extraneous forces P act on the joints, the equation is Z(P.&P)+S.Os=-o, where op is the displacement of any joint in the direction of the corresponding force P. If ~(P. Op) =o, the stresses are merely indeterminate as before; but if ~ (P. op) does not vanish, the equation cannot be satisfied by any finite value of S, since Os =0.

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  • since the terms which are bilinear in respect to ~, y,, and E, ~, ~ vanish, in virtue of the relations (l).

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  • If A or B vanish we have an equiangular spiral, and the velocity at infinity is zero.

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  • In order that the force may vanish we must also have ~, 5~=o, i.e.

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  • We will suppose that A> B> C. From the form of the polhode curves referred to in 19 it appears that the angular velocity q about the axis of mean moment must vanish periodically.

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  • .q,, that they shall vanish in the configuration in question: The potential energy is then given with sufficient approximation by an expression of the form 2V=ciiqi1+clzqii+...

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  • In the case of a multiple root the minors of ~(o2) all vanish, and the basis for the determination of the quantities ar disappears.

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  • Since y must vanish at the upper end (x 1), the admissible values of a are determined by o2=gz2/41, Jo(z)=o.

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  • (m-2)th degrees must vanish.

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  • Instead of making d4 vanish, a certain value can be assigned to it which will produce, by the addition of the two lenses, any desired chromatic deviation, e.g.

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  • They can be traced down to the 7th century, and then they seem to vanish.

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  • In all cases to which it is necessary to have regard the integrated terms vanish at both limits, and we may write f o (z)dz = 3f2' z 3 4(z)dz, f o z(z)dz = 'a' z4 cb(z)d z; (36) so that Ko = 3 f o z3 ?(z) dz, To = $?

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  • On ladies' seals the owner is often gracefully depicted standing and holding flower or bird, or with shields of arms. After the 14th century, the figures of ladies, other than queens, vanish from seals.

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  • " They had seen," he says, " the car of Simon Magus blown away by the mouth of Peter and vanish at the name of Christ.

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  • This may be achieved in seven thousand years, when man will vanish from the world.

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  • The dead would rise, trouble and sickness vanish, and youth and beauty come to all alike.

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  • " But it is requisite, that the Prisme and Lens be placed steddy, and that the paper, on which the colours are cast be moved to and fro; for, by such motion, you will not only find, at what distance the whiteness is most perfect but also see, how the colours gradually convene, and vanish into whiteness, and afterwards having crossed one another in that place where they compound Whiteness, are again dissipated and severed, and in an inverted order retain the same colours, which they had before they entered the composition.

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  • The forms seem to result from a general tendency to visualization as an aid to memory; the letter-forms may in the first instance be quite as frequent as the numberforms, but they vanish in early childhood, being of no practical value, while the number-forms continue as an aid to arithmetical work.

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  • Hence the invention of Galahad, son to Lancelot by the Grail king's daughter; predestined by his lineage to achieve the quest, foredoomed, the quest achieved, to vanish, a sacrifice to his father's fame, which, enhanced by connexion with the Grailwinner, could not risk eclipse by his presence.

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  • a, b, c a' b' c', a"b" c", b", that is, every term which does not vanish contains as a factor the abc-determinant last written down; the sum of all other factors a0'y" is the a/37-determinant of the formula; and the final result then is, that the determinant on the left-hand side is equal to the product on the right-hand side of the formula.

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  • In the Croatian Karst the seven streams of the Lika unite and plunge into a rocky chasm near Gospic, and the few small brooks of this region usually vanish underground in a similar manner.

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  • He had to humble himself before Austria and the whole of Europe; and it was high time for Fleury, now fallen into second childhood, to vanish from the scene (January 1743).

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  • They may, however, be distinguished by the fact that on previous transmission through a quarter-wave plate this property is retained in the case of common light, while with the two other types the relative intensity of the streams depends upon the orientation of the rhomb, and with circularly polarized light one stream may be made to vanish.

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  • Elliptically polarized, partially elliptically polarized and partially plane polarized light give with Iceland spar two streams of, in general, unequal intensity, neither of which can be made to vanish.

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  • These attain their maximum visibility when the plane of analysation is at 45° to these planes, and vanish when the plane of polarization is parallel to either of the principal planes.

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  • It announced, he tells us, that in the north, in Finland, there should be born a prince who should lay waste Germany and vanish in 1632.

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  • Dirty Marks Carpet Usually respond to carpet shampoo e.g. 1001 or Vanish.

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  • Coin Penetrations Use it with your M5 and some shim material for an instant vanish.

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  • Trouble is, with October away an ' the last leaves splattered on the ground, the warm weather tends to vanish.

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  • You have the uncanny ability to vanish whenever you want.

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  • Huge pricks vanish before your very eyes as they plummet into gapes of uncharted depths !

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  • The Raven - Visually vanish a coin from a spectators hand without touching it !

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  • A few of the major changes on the cards include: Old style classes will vanish forever.

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  • When, with renewed vigor, he resumed beating it, the snakes began to vanish.

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  • Requires participation in various marketing ventures before sending you information regarding a little-known tactic for making credit card debt vanish.

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  • There is a reason why you both decided to divorce and usually these reasons do not just vanish after you sign the paperwork.

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  • National Geographic refers to deforestation is a modern-day plague and warns, "The world's rain forests could completely vanish in a hundred years at the current rate of deforestation."

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  • That's a lofty claim, since most products tend to vanish within an hour or so.

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  • Most colors in this family seem to vanish quite quickly, in my experience.

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  • I've come across so many beautiful eye shadows that vanish within an hour or two of application or just crease in the worst way.

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  • The washer and dryer is a Bermuda Triangle for guitar picks as well, and sometimes picks just seem to vanish into thin air!

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  • While snoring problems may be too complicated to just vanish overnight, there are some things you can do that can help with reducing noise from snoring.

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  • Abandoned amusement parks are a fact of life in this competitive industry, but why do parks vanish and what becomes of their familiar rides and attractions?

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  • It will not vanish, effectively letting you sell it over and over again without losing it.

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  • Your job is to fire colored marbles to create matches of three or more to make them vanish.

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  • Once a line is completed, they vanish and points are scored.

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  • When a line is completed, those pieces vanish and the bricks sitting above move down.

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  • If Sony doesn't tweak their strategy and open their arms to a wider audience of gamers, they'll vanish from the top three very quickly.

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  • If a cube touches two or more other cubes of the same color (either vertically or horizontally), the cubes vanish.

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  • By making the bottom row vanish, players can cause the upper cubes to fall down and line up in groups of three or more, which causes them to vanish as well.

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  • You'll gain points every time they make a group of three cubes vanish and for creating chains of cubes.

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  • If you stick the ball so that it lands on a group of two or more balls of the same color, all of those balls vanish from the board.

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  • Even better, if there are other colored balls attached to only the group of balls that just vanished, they will vanish as well.

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  • If you hit the spring with a ball, it will vanish and push the balls back upward.

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  • Because they vanish, and so few of them appear, you should time your use of the Springs so you don't waste the extra time they give.

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  • The shot ball will insert itself into the chain, and if it is inserted beside two or more balls of the same color, those balls vanish.

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  • In Zuma, if you make a group of balls vanish, the balls on either side of the chain link together.

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  • After 15 years of abstinence, the risks of health problems from smoking virtually vanish.

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  • Normally, the extreme tiredness of being pregnant will vanish around the three-month mark.

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  • Of all of these categories, the most minimal swim looks can be found in the Vanish, Vamp and Vixen collections.

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  • These images range from dark shadows that appear and vanish to mist-like images.

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  • However, they simply vanish into thin air.

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  • The rules state that when Bloody Mary's image appears in the mirror, you should only address the image or she will vanish.

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  • Turn to see if she is there and she will vanish.

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  • In the 1930s, a number of motorists driving down Archer Avenue passed by Resurrection Cemetery and claimed that a young woman jumped onto the running boards of their cars, only to vanish as abruptly as she had appeared.

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  • What repair cannot do is make the bad stuff vanish from your records, which is what report repair companies claim they can do permanently.

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  • Even the most stubborn of coffee films vanish after three soaking efforts.

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  • The memories of you spending fitful poker-nights in his smoky best friend's apartment will vanish in favor of high-dining at Spago and evenings spent in symphony box seats.

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  • Do not overwrite existing opinions; if you do, the article will be restored to an earlier version and your own contribution will vanish.

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  • Yet at night, the knight and the hawk vanish under spooky circumstances, and a lovely lady, played by Michelle Pfeiffer, appears.

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  • The Aronhold process, given by the operation a as between any two of the forms, causes such an invariant to vanish.

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  • denote the values for x = xim ' of the successive differential coefficients of u with regard to x; the series continuing until the differential coefficients vanish.

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    1
  • The forms seem to result from a general tendency to visualization as an aid to memory; the letter-forms may in the first instance be quite as frequent as the numberforms, but they vanish in early childhood, being of no practical value, while the number-forms continue as an aid to arithmetical work.

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    1
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