Z sentence example

z
  • To unlock Indiana Jones and the Fate of Atlantis, hold the Z button, then press A, the UP direction twice, then B, the DOWN direction twice, LEFT, RIGHT, LEFT direction, then B at the main menu.
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  • In that case, always try to have at least one rise or dip available for those pieces and don't worry because once you place a 'Z' piece another rise or dip becomes available to use if you need.
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  • While it's probably not advisable to pick a career based solely on where it falls in the alphabet, it can be helpful to see a full list of careers from A to Z when you're considering the available options.
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  • Natural diamond color varies and the highest quality white diamonds should appear colorless or clear.The GIA color grading scale rates diamond color from D (no color) thru Z (rich colors / fancy colored diamonds).
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  • 757, after driving out Beornred, who had succeeded a few months earlier on the murder of A z Ethelbald.
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  • All civil cases involving less than z oo roubles value were within their competence, and more important cases by consent of the parties.
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  • With a more direct course, and in a widening, fertile valley it continues past Downton, Fordingbridge and Ringwood, skirting the New Forest on the west, to Christchurch, where it receives the Stour from the west, and 2 z m.
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  • 'hlatherv i W A WoodVillef w Scale, 1:2,200,000 English Miles 20 30 40 Longitude Nest gi of Greenwich z fishery on the reefs in the Sound, much developed since 1880.
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  • It owes its importance to the iron mines in the mountain Malmberget 4 z m.
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  • If triple bonds, q in number, occur also, and the energy of such a bond be Z, the equation for H becomes H = nE-+-mn -1-p(2X - Y) +q(3X - Z).
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  • The voiced sound to this is generally written z as in azure, but sometimes s as in pleasure.
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  • A relation (R) is serial when (I) it implies diversity, so that, if x has the relation R to y, x is diverse from y; (2) it is transitive, so that if x has the relation R to y, and y to z, then x has the relation R to z; (3) it has the property of connexity, so that if x and y are things to which any things bear the relation R, or which bear the relation R to any things, then either x is identical with y, or x has the relation R to y, or y has the relation R to x.
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  • Krumau is principally celebrated because its ancient castle was long the stronghold of the Rosenberg family, known also as pani z ruze, the lords of the rose.
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  • The coagulum is next flattened out by a wooden or iron roller to get rid of the cavities containing watery liquid, and the sheets are then hung up for fourteen days to dry, when they weigh about 2 lb, the sheets being usually z to a in.
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  • In the theory of surfaces we transform from one set of three rectangular axes to another by the substitutions 'X=' by+ cz, Y = a'x + b'y + c'z, Z =a"x+b"y-l-c"z, where X 2+Y2+Z2 = x2+ y2+z2.
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  • Further we find x=aX+a'Y+a"Z, y=bX z= cX+c'Y+ c"Z, and the problem is to express the nine coefficients in terms of three independent quantities.
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  • � Oxl d 2x 77n If we have new variables z such that zs=4s(yl, Y2,...yn), we have also z s =1 Y 8(x1, x2,���xn), and we may consider the three determinants which i s 7xk, the partial differential coefficient of z i, with regard to k .
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  • = 0, we find that, eliminating x, the resultant is a homogeneous function of y and z of degree mn; equating this to zero and solving for the ratio of y to z we obtain mn solutions; if values of y and z, given by any solution, be substituted in each of the two equations, they will possess a common factor which gives a value of x which, corn bined with the chosen values of y and z, yields a system of values which satisfies both equations.
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  • If three equations, each of the second degree, in three variables be given, we have merely to eliminate the six products x, 2, z 2, yz, zx, xy from the six equations u = v = w = o = oy = = 0; if we apply the same process :to thesedz equations each of degree three, we obtain similarly a determinant of order 21, but thereafter the process fails.
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  • X (1 +PD1+12D2+...+�8D8+...) fm, and now expanding and equating coefficients of like powers of /t D 1 f - Z(Difi)f2f3.
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  • = a l z = e a2z =e.3.=...
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  • The number of partitions of a biweight pq into exactly i biparts is given (after Euler) by the coefficient of a, z xPy Q in the expansion of the generating function 1 - ax.
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  • Moreover, instead of having one pair of variables x i, x2 we may have several pairs yl, y2; z i, z2;...
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  • We frequently meet with cogredient and contragedient quantities, and we have in general the following definitions:-(i) " If two equally numerous sets of quantities x, y, z,...
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  • + ���, Z = v16+v2%/+v3" +���, wherein it should be noticed that new quantities are expressed in terms of the old, as regards the latter set, and not vice versa."
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  • If u, a quantic in x, y, z, ..., be expressed in terms of new variables X, Y, Z ...; and if, n,, ..., be quantities contragredient to x, y, z, ...; there are found to exist functions of, n, ?, ..., and of the coefficients in u, which need, at most, be multiplied by powers of the modulus to be made equal to the same functions of E, H, Z, ...
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  • -2 _ ab 2an-2bn-2Crz z x () x x x, Each term on the right-hand side may be shown by permutation of a, b, c to be the symbolical representation of the same covariant; they are equivalent symbolic products, and we may accordingly write 2(ac) (bc)ai -1 bi -1 cx 2 =(ab)2a:-2b:-2c:, a relation which shows that the form on the left is the product of the two covariants n (ab) ay 2 by 2 and cZ.
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  • First observe that with f x =a: = b z = ���,f1 = a l a z ', f 2 = a 2 az-', f x =f,x i +f 2 x i, we find (ab) - (a f) bx - (b f) ax.
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  • In fact, if f and 4, have these forms, it is easy to verify that (f, 4,)i= (A j z) (rs)r x s x .
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  • 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.
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  • It is shown in the article on Combinatorial Analysis that (w; 0,n) is the coefficient of a e z w in the ascending expansion of the fraction 1-a.
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  • We may, by a well-known theorem, write the result as a coefficient of z w in the expansion of 1 - z n+1.
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  • - zn +9 1 -z2.1 -z3....1-z8; and since this expression is unaltered by the interchange of n and B we prove Hermite's Law of Reciprocity, which states that the asyzygetic forms of degree 0 for the /t ie are equinumerous with those of degree n for the The degree of the covariant in the variables is e=nO-2w; consequently we are only concerned with positive terms in the developments and (w, 0, n) - (w - r; 0, n) will be negative unless nO It is convenient to enumerate the seminvariants of degree 0 and order e=n0-2w by a generating function; so, in the first written generating function for seminvariants, write z2 for z and az n for a;.
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  • As we have to do only with that part of the expansion which involves positive powers of z, we must try to isolate that portion, say A n (z).
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  • Again, for the cubic, we can find A3(z) - -a6z6 1 -az 3.1 -a 2 z 2.1 -a 3 z 3.1 -a4 where the ground forms are indicated by the denominator factors, viz.: these are the cubic itself of degree order I, 3; the Hessian of degree order 2, 2; the cubi-covariant G of degree order 3, 3, and the quartic invariant of degree order 4, o.
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  • For these two cases the perpetuants are enumerated by z 2 23 -z2' and l -z2.1-z3 respectively.
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  • These latter forms are enumer ated by I - z 24 I -z 4; hence the generator of quartic perpetuants must be z4 z4 z7 1-z 2.1 -z 3.1z 4 1-z 2.1-s 4 1-22.1-z3.1-z4' and the general form of perpetuants is (4 K+ 1 3A+1 2�).
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  • 1 Bz4' That Is, By The Coefficient Of Z W In Zp '.
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  • Taking The First Generating Function, And Writing Az P, Bz4, 2 For A, B And Z Respectively, We Obtain The Coefficient Of Aobe'Zpo 0' 2W That Is Of A E B E 'Z �, In 1 Z 2 1 Azp. 1 Azp 2....1 A2 P 2.1 Az P .
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  • Thus, For Two Linear Forms, P =Q = I, We Find 1 Z 2 1 Az.
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  • For w = i the form is A i ai+Bib i, which we may write aob l -albo = ao(I) b -(I)abo; the remaining perpetuants, enumerated by z I - 2' have been set forth above.
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  • For the case 8=1, 0' =2, the condition is a i r 1 72 = A032=0; and the simplest perpetuant, derived directly from the product A 1 B 21 is (I)a(2)b-(21)b; the remainder of those enumerated by z3 I z.
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  • 1 - z 2.1 -z 3.1 - z4' The series may be continued, but the calculations soon become very laborious.
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  • They consist of a square citadel (Bairam Ali Khan kalah), s z m.
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  • 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.
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  • (b) If n = a z, then x =tog a n.
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  • Taking co-ordinates in the plane of the screen with the centre of the wave as origin, let us represent M by, n, and P (where dS is situated) by x, y, z.
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  • Trans., 1834) in his original investigation of the diffraction of a circular object-glass, and readily obtained from (6), is z z 3 25 27 J1(z) = 2 2 2.4 + 2 2.4 2.6 2 2.4 2.6 2.8 + When z is great, we may employ the semi-convergent series Ji(s) = A/ (7, .- z)sin (z-17r) 1+3 8 1 ' 6 (z) 2 3.5.7.9.1.3.5 5 () 3 1 3.5.7.1 1 3 cos(z - ?r) 8 ' z (z) 3.5.7.9.11.1.3.5.7 1 5 + 8.16.24.32.40 (z
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  • Now by definition J (z) _ C cos (z cos e) do = 1 - 22-%2?
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  • 12 -7r2R4 x2 f 2 The roots of Jo(z) after the first may be found from We may compare this with the corresponding result for a rectangular aperture of width a, tlf = X/a; and it appears that in consequence of the preponderance of the central parts, the compensation in the case of the circle does not set in at so small an obliquity as when the circle is replaced by a rectangular aperture, whose side is equal to the diameter of the circle.
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  • When z has one of the values thus determined, (z)=Jo(z).
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  • The accompanying table is given by Lommel, in which the first column gives the roots of J2(z) =o, and the second and third columns the corresponding values of the functions specified.
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  • We have 12 = 71-212.4 4J12(z) X 2 f 2 z2 z = 21rRr/X f (20).
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  • 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.
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  • In any case the proportion of the whole illumination to be found outside the circle of radius r is given by J02(z)+J12(z).
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  • For the dark rings Ji(z) =o; so that the fraction of illumination outside any dark ring is simply Jo 2 (z).
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  • When z is great, the descending series (io) gives i 2J 1 (z) = 2 sin (z1 7r) 22; (2) z so that the places of maxima and minima occur at equal intervals.
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  • It may be instructive to contrast this with the case of an infinitely narrow annular aperture, where the brightness is proportional to Jo 2 (z).
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  • When z is great, J°(z) = ()cos (z '-hir).
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  • The mean brightness varies as .51; and the integral f J02(z)zdz is not convergent.
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  • Now by (17), (18) z 1 J1(z) =Jo(z)- (z); where P increases.
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  • The extreme value possible for a is a right angle, so that for the microscopic limit we have Z X o/µ (2).
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  • The formation of bands thus requires that the retarding plate be held upon the side already specified, so that zs be positive; and that the thickness of the plate (to which z is proportional) do not exceed a certain limit, which we may call 2T 0.
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  • Comparing the expressions for C, S in terms of M, N, and in terms of G, H, we find that G = z (cos u+sin u)-M, H = z (cos u-sin u) +N.
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  • (19), 1 abA) ' ' we may write 12= (cos 27rv 2 .dv) 2 + (f sin zirv 2 .dv) 2 (20), or, according to our previous notation, 12 = (2 - C 2 +(z - Sv)2= G2 +H2 Now in the integrals represented by G and H every element diminishes as V increases from zero.
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  • The co-ordinates of J, J' being (- z, - z), I 2 is 2; and the phase is, period in arrear of that of the element at 0.
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  • Let x, y, z be the co-ordinates of any particle of the medium in its natural state, and, 7 7, the displacements of the same particle at the end of time t, measured in the directions of the three axes respectively.
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  • According to this notation, the three equations of motion are dt2 = b2v2E + (a2 - b2) d.s dt =b2v2rj+(a2 - b2) dy d2 CIF - b2p2+(a2_b2)dz It is to be observed that denotes the dilatation of volume of the element situated at (x, y, z).
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  • If we suppose that the force impressed upon the element of mass D dx dy dz is DZ dx dy dz, being everywhere parallel to the axis of Z, the only change required in our equations (I), (2) is the addition of the term Z to the second member of the third equation (2).
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  • (b2V2 + n2) (a2 - b 2) = - z It will now be convenient to introduce the quantities a l, a 2', 7731 which express the rotations of the elements of the medium round axes parallel to those of co-ordinates, in accordance with the equations Ty - 1 = dz ' 3= - dy 2 = dx - In terms of these we obtain from (7), by differentiation and subtraction, (b 2 v 2 + n 2) 7,3 = 0 (b 2 0 2 +n 2) .r i = dZ/dy (b 2 v 2 +n 2)', , 2 = - dZ/dx The first of equations (9) gives 3 = 0 (10) For al we have ?1= 47rb2, f dy e Y tkr dx dy dz
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  • Since the dimensions of T are supposed to be very small in com d parison with X, the factor dy (--) is sensibly constant; so that, if Z stand for the mean value of Z over the volume T, we may write TZ y d e T ?
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  • This displacement, which we may denote by; is in the plane containing z and r, and perpendicular to the latter.
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  • By all real estate deeds the sale of intoxicating liquors is for ever prohibited in the city; and an act of the state legislature in 1909 prohibited the sale of intoxicating liquor within r z m.
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  • After leaving the Central Provinces, the river widens out in the fertile district of Broach, with an average breadth of z m.
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  • It lies partly within Stillwater and partly within Half-Moon townships, in the bottom-lands at the mouth of the Anthony Kill, about 1 z m.
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  • 2 The date of L and Z is given as the end of the 15th century in the introduction to Wyse's edition.
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  • 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.
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  • From the gas-equation in general, in the atmosphere n d dp _ I dp 1 de _ d0 de i de (8) z p dz-edz-p-edz-k-edz' which is positive, and the density p diminishes with the ascent, provided the temperature-gradient de/dz does not exceed elk.
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  • With uniform temperature, taking h constant in the gas-equation, dp / dz= =p / k, p=poet/ k, (9) so that in ascending in the atmosphere of thermal equilibrium the pressure and density diminish at compound discount, and for pressures p 1 and 1, 2 at heights z 1 and z2 (z1-z2)11?
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  • The time rate of increase of momentum of the fluid inside S is )dxdydz; (5) and (5) is the sum of (I), (2), (3), (4), so that /if (dpu+dpu2+dpuv +dpuw_ +d p j d xdyd z = o, (b)` dt dx dy dz dx / leading to the differential equation of motion dpu dpu 2 dpuv dpuv _ X_ (7) dt + dx + dy + dz with two similar equations.
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  • As a rule these equations are established immediately by determining the component acceleration of the fluid particle which is passing through (x, y, z) at the instant t of time considered, and saying that the reversed acceleration or kinetic reaction, combined with the impressed force per unit of mass and pressure-gradient, will according to d'Alembert's principle form a system in equilibrium.
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  • Clebsch has shown, from purely analytical considerations (Crelle, lvi.); and then = Z d(?G, m), ?
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  • If homogeneous liquid is drawn off from a vessel so large that the motion at the free surface at a distance may be neglected, then Bernoulli's equation may be written H = PIP--z - F4 2 / 2g = P/ p +h, (8) where P denotes the atmospheric pressure and h the height of the free surface, a fundamental equation in hydraulics; a return has been made here to the gravitation unit of hydrostatics, and Oz is taken vertically upward.
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  • In particular, for a jet issuing into the atmosphere, where p=P, q 2 /2g = h - z, (9) or the velocity of the jet is due to the head k-z of the still free surface above the orifice; this is Torricelli's theorem (1643), the foundation of the science of hydrodynamics.
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  • For instance, in a uniplanar flow, radially inward towards 0, the flow across any circle of radius r being the same and denoted by 27rm, the velocity must be mfr, and 0=m log r,, y=m0, +4,i =m log re ie, w=m log z.
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  • 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?
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  • The expression for w in (i) § 29 may be increased by the addition of the term im log z =-m0 + im log r, (1) representing vortex motion circulating round the annulus of liquid.
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  • 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 '?"
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  • Employing the equation of continuity when the liquid is homogeneous, 2 (cly - d z)?
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  • 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.
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  • /c - a2, 1 z a = (c2 +a2)2 "2 +a21 J z z 2 ?
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  • This is a closed Sumner line for n =I, when the boundary consists of two parallel walls; and n= z gives an Elastica.
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  • For a cavity filled with liquid in the interior of the body, since the liquid inside moves bodily for a motion of translation only, 41 = - x, 42 = -, 43 = - z; (2) but a rotation will stir up the liquid in the cavity, so that the'x's depend on the shape of the surface.
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  • 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 =..
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  • , (4) where X, Y, Z, L, M, N denote components of external applied force on the body.
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  • (6) The least admissible value of p is that which makes the roots equal of this quadratic in µ, and then ICI s ec 0,, u= z - p (7) the roots would be imaginary for a value of p smaller than given by Cip 2 - 4(c 2 -c i)c2C 2 u 2 =o, (8) p2 = 4(c 2 -c l)cl C2.
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  • Land which contains less than about z /c, of lime usually needs the addition of this material.
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  • Forests cover nearly r z million acres, yielding valuable timber (teak, sandalwood, &c.), and affording grazing-ground for cattle.
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  • 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.
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  • Let us apply the above theorem to the case of a small parallelepipedon or rectangular prism having sides dx, dy, dz respectively, its centre having co-ordinates (x, y, z).
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  • Its angular points have then co-ordinates (x t Zdx, y t Zdy, z * zdz).
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  • Suppose that the dielectric has a constant K, then we must multiply both sides by K and the expression for the energy per unit of volume of the field is equivalent to z DE where D is the displacement or polarization in the dielectric.
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  • More characteristic, however, than the crystallized are the irregular forms,which, when large, are known as "nuggets" or " pepites," and when in pieces below - to z oz.
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  • The tank is of porcelain or glazed earthenware, the electrodes for impure solutions are z in.
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  • Every endeavour is made to gloss over, or modify, expressions which seemed derogatory to the ancestors of ' According to Zunz, Gottesdienstliche Vortrdge, 2nd ed., p. 80, its contents bear the following proportions to Genesis, z o o to Exodus, about 1 1 4 to Leviticus, s to Numbers, and 4 to Deuteronomy.
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  • Many fanciful legends about Abraham founded on Biblical accounts or spun out of the fancy are to be found in Josephus, and in post-Biblical and Mahommedan literature; for these, reference may be made to Beer, Leben Abrahams (1859); Gri nbaum, Neue Beitrdge z.
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  • The dose is 2 to 5 grains, that of aloin being z to 2 grains.
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  • The weight of the handles and their supports is balanced by the counterpoise z.
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  • The loss of weight by exposure to the atmosphere from drying may be from z to I of the total amount of water contained.
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  • Although at first it was no uncommon thing to find z% of phosphuretted hydrogen present in the acetylene, this has now been so reduced by the use of pure materials that the quantity is rarely above o�15%, and it is often not one-fifth of that amount.
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  • If 2mu 2 denote the mean value of 2mu 2 averaged over the s molecules of the first kind, equations (3) may be written in the form Z mu g = 2 mv 2 = 2 mw 2 = 2x,0 2 1 =.
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  • We obtain Cv = z (n +3) R /J m.
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  • (19) On the other hand, if the pressure of the gas is ke p t constant throughout the motion, T/v is constant and dQ = JC,,NmdT, whence C 5 = z (n +5) R /Jm.
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  • The archaeology of the western hemisphere should be divided as follows: (z) that of Indian activities; (2) the question of man's existence in a prior geological period.
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  • This page gives an overview of all articles in the 1911 Brittanica which are alphabetized under Z to Zym.
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  • Z(AK+BL)+3KL{CM-Z(AK+BL)} = sKL(AK+4CM+BL).
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  • If, on the other hand, we were to take them very close to KA and LB respectively, the area of K 0 M B Z the trapezette would be the greater.
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  • Of the latter we can determine twenty-six characters, while a twenty seventh probably corresponds to Arabic z (.).
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  • We have then only to consider the term z iav/V.
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  • The third 4= 5 X Z X z or ascent through an interval 4, which has no special name, and a descent through two octaves, and so on.
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  • Since no angular momentum goes out on the whole Z nwra 4 d0/dx -?- 2 pwra 4 Ud0/dt = o.
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  • Two spheres intersect in a plane, and the equation to a system of spheres which intersect in a common circle is x 2 + y 2 + z 2 +2Ax -fD = o, in which A varies from sphere to sphere, and D is constant for all the spheres, the plane yz being the plane of intersection, and the axis of x the line of centres.
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  • (5) Floating Bridges, the roadway being carried on z pontoons moored in the% stream.
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  • The shearing area of rivets in tension members was made r z times the useful section of plate in tension.
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  • Since 1859 it has formed the chief source of the water-supply of Glasgow, the aqueduct leaving the lake about z 2 m.
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  • 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.
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  • We may now, as is somewhat the more natural course in the terrestrial application, take axes (x,y,z) which move with the matter; but the current must be invariably defined by the flux across surfaces fixed in space, so that we may say that relation (i) refers to a circuit fixed in space, while (ii) refers to one moving with the matter.
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  • In Slovakia, Jo z a eprka and his school have devoted themselves to interpreting peasant life.
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  • Collections have appeared, however, by Waclaw Zaleski, who writes under the pseudonyms of Waclaw z Oleska, Wojcicki, Roger, Zegota Pauli, and especially Oskar Kolberg.
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  • He wrote a fine descriptive work, Obrazy z zycia i podrozy (" Pictures of Life and Travel"), and also a poem, Piesn o ziemi naszej (" Song of our Land").
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  • The tops should be covered with z in.
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  • Thus a partition of 6 is 42; writing this in the form z 11' and summing the columns instead of the lines, we obtain the conjugate partition 2211; evidently, starting from 2211, the conjugate partition is 42.
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  • Introducing another letter z, and considering the function I+xz.
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  • I+x 3 z...,= I +z(x+x2+..)...
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  • +Nxnzk+.., we see that in the term Nx n z k of the development the coefficient N is equal to the number of partitions of n into k parts, with the parts I, 2, 3, 4,, without repetitions.
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  • I -x 2 z.
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  • +X15; I -xz.I-x 2 z.
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  • Special mention should be made of Wellhausen on the Synoptic Gospels (1903-1905), and Harnack, Beitrage z.
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  • Kanons (2 vols., 1888-1892, third to follow), Forschungen z.
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  • The largest, Texcoco, has an area of about I 1 z sq.
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  • The second Gospel fragment discovered in 1907 " consists of z single vellum leaf, practically complete except at one of the lower corners and here most of the lacunae admit of a satisfactory solution."
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  • This was surely such a meeting as we read of in z Cor.
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  • From the time of Eusebius this city has been identified with Sychem or Shechem (modern Nablus), and the well is still in existence I z m.
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  • The place usually assigned to it is occupied by the vaulted substructure of the dormitory (Z).
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  • - N / (z cot IC) =o, with centre sin A, sin B, sin C; the escribed circle opposite the angle A is - N I (- x cot ZA)+ -1 (y tan 2B) + -V (z tan 2C) =o, with centre - sin A, sin B, sin C; and the selfconjugate circle is x 2 cot A+y 2 cot B+z 2 cot C =o, with centre tan A, tan B, tan C. Since in areal co-ordinates the line infinity is represented by the equation x+y+z=o it is seen that every circle is of the form a 2 yz+b 2 zx+c 2 xy+(lx+my+nz)(x+y+z) = o.
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  • Outwards from the bay the level rises slowly to an average of about z 500 ft., but seldom reaches 2000 ft.
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  • French Forms Are Freely Turned Into Pure Canadianisms, Like Cageux, Raftsman, Boucane, Brushwood Smoke, Portage, &C. New Characters, Which Appeal More Directly To The Local Audience, Sometimes Supplant Old Ones, Like The Quatre Vieux Sauvages Who Have Ousted The Time Honoured Quatre Z Officiers From The Canadian Version Of Malbrouk.
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  • Z% liver is probably represented ?? ?
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  • The first charter, said to be a forgery, purports to have been given by i z Ethelstan.
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  • In the same figure the free part of the inner lamella of the inner gill-plate resting on the foot is marked z, whilst the attached parjt - the most anterior - has been snipped with scissors so as to show the genital and nephridial apertures x and y.
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  • Z will be the archetype of all our existing MSS., and we may embody our results in a pedigree of manuscripts or stemma codicum as follows: A 13 C D If we have done our work properly, the texts that we arrive at for X and for Y will be freer from error than the texts of the separate members of the families B, C and D, and E, F, G respectively, and that of Z freer from error than that authenticated by any existing MS.
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  • 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.
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  • This is obvious enough in the Metaphysics: it has two openings (Books A and a); then comes a nearly consecutive theory of being (B, F, E, Z, H, 0), but interrupted by a philosophical lexicon A; afterwards follows a theory of unity (1); then a summary of previous books and of doctrines from the Physics (K); next a new beginning about being, and, what is wanted to complete the system, a theory of God in relation to the world (A); finally a criticism of mathematical metaphysics (M, N), in which the argument against Plato (A 9) is repeated almost word for word (M 4-5).
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  • Oi, 1045 b 27-32, referring back to Z 1, or at the earliest to P 2.
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  • On either alternative, however, " the first discourses " mentioned may have originally been a separate discourse; for Book F begins quite fresh with the definition of the science of being, long afterwards called " Metaphysics," and Book Z begins Aristotle's fundamental doctrine of substance.
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  • Then follows the treatment of oligarchy, democracy, commonwealth and tyranny, and of the various powers of government (0), and independent investigation of revolution, and of the means of preserving states (E), and a further treatment of democracy and oligarchy, and of the different offices of the state (Z), and finally a return to the discussion of the right form of constitution (II, 0).
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  • But 0 and Z are a group interrupted by E, and H and 0 are another group unconnected with the previous group and with E, and are also distinguished in style by avoiding hiatus.
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  • Further, the group (0, Z) and the group (II, 0) are both unfinished.
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  • Finally the group (0, Z), the book (E) and the group (II, 0), though unconnected with one another, are all connected though imperfectly with " the first discourses " (A,B,F).
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  • This complicated arrangement may be represented in the following diagram: A,B,P, Z E H, 0 The simplest explanation is that Aristotle began by writing separate discourses, four at least, on political subjects; that he continued to write them and perhaps tried to combine them; but that in the end he failed and left the Politics unfinished and in disorder.
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  • For though both works rest on the reality of individual substances, the Categories (chap. 5) admits that universal species and genera can be called substances, whereas the Metaphysics (Z 13) denies that a universal can be a substance at all.
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  • On the other hand, in the Metaphysics (Z 13), he distinctly denies that any universal can be a substance, on the ground that a substance is a subject, whereas a universal is a predicate and a belonging of a subject, from which it follows as he says that no universal is a substance, and no substance universal.
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  • Such is Aristotle's realism of individuals and universals, contained in his primary philosophy, as expressed in the Metaphysics, especially in Book Z, his authoritative pronouncement on being and substance.
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  • Let X, Y, And Z Be The Three Quotients Of The Divisions; The Number Sought Will Then Be Expressed By 28 X Io, By 19 Y 2, Or By 15 Z 4.
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  • In Tirol, a single hole is made near the root of the tree in the spring; this is stopped with a plug, and the turpentine is removed by a scoop in the autumn; but each tree yields only from a few ounces to z lb by this process.
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  • - The mole-rats (Spalacidae) bring us to the mouselike section, or Myoidea, in which there are no premolars and the molars may be occasionally reduced to z; these teeth being either rooted or rootless, with either cusps or enamel-folds, and the first generally larger than the second.
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  • If K has a value nearly equal to unity, the pressure shift is z k2 " +3 (K- 1 - 1); and it is significant that for different values of n, the shifts should be in geometric ratio, because as stated above, the ratio occurring in the amounts observed with different lines of the same element are as 1: 2: 4.
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  • The spherical granules (G) are probably gland-secretions; the dark bodies (Z) are probably xanthellae, i.e.
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  • Z 3) or is only potentially substance (Met.
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  • The consonants, 30 in number, which are deemed to possess an inherent sound a, are the following: ka, k'a, ga, nga, ea, ca, ja, nya, ta, t'a, da, na, pa, p'a, ba, ma, tsa, ts'a, dza, wa, z'a, za, 'ha, ya, ra, la, s'a, sa, ha, a; the so-called Sanskrit cerebrals are represented by the letters ta, t'a, da, na, s'a, turned the other way.
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  • An inhabitant of Lhasa, for example, finds the distinction between s and z', or between s and z, not in the consonant, but in the tone, pronouncing s' and s with a high note and z' and z with a low one.
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  • At Z is the prison.
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  • Whatever were the means employed to rid air of accompanying oxygen, a uniform value of the density was arrived at, and this value was z% greater than that appertaining to nitrogen extracted from compounds such as nitrous oxide, ammonia and ammonium nitrite.
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  • These attain at places a height of from z oo to 150 ft., and are continually shifting to the westward.
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  • Alpeinerscharte (Breitlahner to St Jodok am Brenner), foot path (Z) .
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  • 7,763 Tuxerjoch or Schmirnjoch (Mayrhofen to St Jodok am Brenner), foot path (Z).
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  • Outdoor crops require to be sown, the smaller seeds from z to i in., and the larger ones from 2 to 4 in.
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  • Gypsophila elegans: hardy, t z ft., pale rose; branched very gracefully.
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  • Petunia violacea hybrida: half-hardy, I z ft., various colours; sow in heat.
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  • C. spectabile, I z to 2 ft., white and rose colour, in June, is a lovely species, as is C. Calceolus, i ft., yellow and brown, in May; all are full of interest and beauty.
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  • Ruyschianum, I z ft., with its var.
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  • The "Victory of Samothrace," set up by Demetrius Poliorcetes c. 305 B.C., was discovered in the z 8 Samovar Sampierdarena island in 1863, and is now in the Louvre.
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  • The most cell (z) have arisen.
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  • Perhaps the most interesting of these consonantal interchanges is that occurring between n and the sibilants sh and z; ner = slier; na=za, which by some scholars has been declared to be phonetically impossible, but its existence is well established between the modern Chinese colloquial idioms. For example, Pekingese then, Hakka nyin, Fuchow niing, Ningpo zhing and nying, WOnchow zang and Hang all =" man."
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  • The early abbey was probably destroyed by the Danes in the reign of i z Ethelred the Unready (978-1015), for in 1043 Edward the Confessor founded here a college of secular canons.
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  • Like all the precious stones, the diamond was credited with many marvellous virtues; among others the power of averting insanity, and of rendering poison harmless; and in the middle ' Diamonds are invariably weighed in carats and in z, 4, a, 1, s, of a carat.
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  • If Y and Z are groups which behave very differently, then there is apparently no tautomerism and a definite formula can be given to the compound.
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  • Neglecting the external heat-loss, and the variation of the thermal and electric conductivities k and k', we obtain, as before, for the difference of temperature between the centre and ends, the equation O, Tho z Go = C 2 R1/8qk = ECl/8qk = E 2 k'/8k, (11) where E is the difference of electric potential between the ends.
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  • An imperial guarantee of interest was obtained in 1905 for the construction of a railway from Hickory to Bayong, a place z oo m.
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  • (ix.) Onchnesoma, with 2 species, and (x.) Tylosoma, with z species, have no tentacles, only one brown tube, and only one retractor muscle.
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  • O Sakkara a 0 El Azizia d Mith o a Walda Pala z.
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  • *~, wz, command, is regularly written~ ~ ~,wz(w);butj, liz, white, is written ~ ~ 111(z).
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  • It is clear that this (z) implicitly considers truth as a value, and so connects it with the conception of good, and (2) openly raises the question - What is truth, and how is it to be distinguished from error ?
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  • Steamers ply to Rustchuk, 2 z m.
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  • When the correspondence of the commissioners was sent to the United States Congress the letters "X," "Y" and "Z," were inserted in place of the names of the French agents with whom the commission treated - hence the "X Y Z Correspondence," famous in American history.
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  • Trending in a south-easterly to northwesterly direction, the lake has a length of 13 Z m.
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  • Mace contains a similar volatile oil, macene, boiling at 160° C., which is said by Cloi z to differ from that of nutmegs in yielding a solid compound when treated with hydrochloric acid gas.
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  • It is chiefly remarkable for its finely preserved fortifications constructed of tetrahedral and polygonal blocks of local limestone well jointed, with maximum dimensions of about 3 by i z ft.; the outer circuit of the city wall measures about 22 m.
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  • A temple was excavated in 1889 about z m.
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  • Memans wear (z) a gold embroidered skull-cap, (2) a long kamis fastened at the neck with 3 or 4 buttons on a gold chain, (3) sadariya, i.e.
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  • Under Mahommedan influence Hindu clothing developed into " suits," consisting of five pieces for men, hence called pancho tuk kapra - (z) head-dress, (2) dhoti, (3) coat, (4) chaddar or sheet, (5) bathing cloth; and three for women, hence called tin tuk - (i) dhoti, (2) jacket, (3) shawl.
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  • Let it be supposed that two positive lenses of equal curvature powers are made out of these two glasses, then in order to represent the combined dispersion of the two together the two 0µ's for each spectral region may be added together to form 0'µ as in the line below, and then, on again expressing the partial z'µ in terms of L'µ (C to F) we get the new figures in the bottom row beneath the asterisks.
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  • In z goo West Orange was chartered as a town.
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  • By Ohm'S Law, And By The Definition Of Difference Of Electric Pressure Or Potential, We Obtain The Following Alternative Expressions For The Quantity Of Heat H In Joules Generated In A Time T Seconds By A Current Of C Amperes Flowing In A Wire Of Resistance R Ohms, The Difference Of Potential Between The Ends Of The Wire Being E = Cr Volts: H=Ect=Crt=E Z T/R.
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  • Moreover, the solar period (II years) is far outside the limits of the periods of 1 Variable stars (except those sufficiently bright to have received special names) are denoted by the capital letters R to Z followed by the name of the constellation.
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  • This point brings us to consider the matter-of-fact conditions of the villeins during the feudal period, especially in the z 2th, 13th and r4th centuries.
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  • (t) in conversion, when we must think that all men are some animals, in order to judge that some animals are men; (2) in syllogisms of the 3rd figure, when the predicate of the minor premise must be particularly quantified in thought in order to become the particularly quantified subject of the conclusion; (3) in identical propositions including definitions, where we must think both that i -{- i are 2 and 2 are z -}- r.
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