Didn't he vanish somewhere?
And then all threads of hope will finally vanish from the fabric of my life.
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.
Thus Russell's contradiction vanishes, and an examination of the other contradictions shows that they vanish also.
Attacked in detail, they vanish one after another into as many teasing spectra of uncertainty.
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.
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.
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.
Aj Hence the system of values also causes to vanish in this case; dx and by symmetry aj and Fz also vanish.
I feel that I cannot vanish, since nothing vanishes in this world, but that I shall always exist and always have existed.
Such a symbolic product, if its does not vanish identically, denotes an invariant or a covariant, according as factors az, bz, cz,...
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.
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.
Thus the Allobroges now disappear and the colonia of Vienna takes their place: the Volcae vanish and we find Nemausus (Nimes).
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.
Since y must vanish at the upper end (x 1), the admissible values of a are determined by o2=gz2/41, Jo(z)=o.
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.
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) ï¿½ ï¿½;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..
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.
=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.
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.
The other coefficients in (8) vanish in virtue of the symmetry.
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.
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.
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).
Most of the many names of gods are mere names that appear and vanish again in particular districts and temples.
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.
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.
But all my hopes vanish when I come to explain the principles that unite our successive perceptions in our thought or consciousness.
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.
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').
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.
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.
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.
In order that the force may vanish we must also have ~, 5~=o, i.e.
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.
.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+...
In the case of a multiple root the minors of ~(o2) all vanish, and the basis for the determination of the quantities ar disappears.
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.
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.
" 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.
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."
Hence if A does not vanish x 1 = x 2 =...
=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.
Thus Cyrenaicism did not entirely vanish with its absorption in Epicureanism.
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.
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.
If A or B vanish we have an equiangular spiral, and the velocity at infinity is zero.
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 = $?
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.
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.
The first and fourth of these indicate that (a 2) w is a homogeneous function of X i, X2, and of /u1, ï¿½ 2 separately, and the second and third arise from the fact that (X / 1) is caused to vanish by both Da ï¿½ and Dï¿½A.
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.
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.
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.
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.
On the other hand they appear and vanish 15, exercise miraculous powers", and fly 17.
It may be observed that the correction would vanish if we could write dh=wodp/do=wL/(v-w).
Since the terms which are bilinear in respect to ~, y,, and E, ~, ~ vanish, in virtue of the relations (l).
For in this case the n equations are not independent since identically Alï¿½ft+ A2ï¿½ f2+...+Anï¿½fn = 0, and assuming that the minors do not all vanish the satisfaction of ni of the equations implies the satisfaction of the nth.
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.
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.
Were the feudal tie broken, the crown must soon vanish, and the constitution of medieval society undergo a radical change.