# Denoting Sentence Examples

- A waitress wearing a lace cap
**denoting**her Pennsylvania Dutch heritage seated him at a small corner table by the window. - His advisors and mates dressed in well-made clothing edged with silver,
**denoting**their rank among the shouting crowd in rags. - Concordatum, agreed upon, from con-, together, and cor, heart), a term originally
**denoting**an agreement between ecclesiastical persons or secular persons, but later applied to a pact concluded between the ecclesiastical authority and the secular authority on ecclesiastical matters which concern both, and, more specially, to a pact concluded between the pope, as head of the Catholic Church, and a temporal sovereign for the regulation of ecclesiastical affairs in the territory of such sovereign. - With Descartes the use of exponents as now employed for
**denoting**the powers of a quantity becomes systematic; and without some such step by which the homogeneity of successive powers is at once recognized, the binomial theorem could scarcely have been detected. - Arnaout),
**denoting**the people, and Arbenia or Arberia, the land, are also, though less frequently, used by the Albanians. - METHODISM, a term'
**denoting**the religious organizations which trace their origin to the evangelistic teaching of John Wesley. - Toller) describes a thegn as "one engaged in a king's or a queen's service, whether in the household or in the country," and adds, "the word in this case seems gradually to acquire a technical meaning, and to become a term
**denoting**a class, containing, however, several degrees." - The plant formation may be designated in technical language ph the termination -ion added to a stem
**denoting**the habitat. - The figure
**denoting**the general average yield per acre of any class of crop needs readjustment after every successive harvest. - The term " futures " is used broadly and narrowly: broadly it is a generic term
**denoting**" futures " in the Futures. - Typical formulae are (R
**denoting**0, S or NH): Isomers are possible, for the condensation may be effected on the two carbon atoms symmetrically placed to the hetero-atom; these isomers, however, are more of the nature of internal anhydrides. - If we express the pressure, volume and temperature as fractions of the critical constants, then, calling these fractions the " reduced " pressure, volume and temperature, and
**denoting**them by 7r, 0 and 0 respectively, the characteristic equation becomes (7+3/0 2)(30-i) =80; which has the same form for all substances. - -
**Denoting**the atomic weight by W and the specific heat by s, Dulong and Petit's law states that 6.4 = Ws. - The word is commonly used in the Alexandrian Greek translation of the Old Testament (Septuagint) for the Hebrew word (ger) which is derived from a root (gur)
**denoting**to sojourn. - For if u, v, w be the polynomials of orders m, n, p respectively, the Jacobian is (u 1 v 2 w3), and by Euler's theorem of homogeneous functions xu i +yu 2 +zu 3 = mu xv1 +yv2 +zv3 = /IV xw 1+y w 2+ zw 3 = pw;
**denoting**now the reciprocal determinant by (U 1 V2 W3) we obtain Jx =muUi+nvVi+pwWi; Jy=ï¿½.., Jz=..., and it appears that the vanishing of u, v, and w implies the vanishing of J. - In terms of dl, d 2, d 3, ..., products
**denoting**successive operations, by the same law which expresses the ele mentary function a s in terms of the sums of powers s l, s 2, s3,... - All symmetric functions are expressible in terms of the quantities ap g in a rational integral form; from this property they are termed elementary functions; further they are said to be single-unitary since each part of the partition
**denoting**ap q involves but a single unit. - The partitions being taken as
**denoting**symmetric functions we have complete correspondence between the algebras of quantity and operation, and from any algebraic formula we can at once write down an operation formula. - 1 Ze An Expression Which Also Enumerates The Asyzygetic Seminvariants, We May Regard The Form, Written, As
**Denoting**The General Form Of Asyzygetic Seminvariant; A Very Important Conclusion. - Restricted Substitutions We may regard the factors of a binary n ip equated to zero as
**denoting**n straight lines through the origin, the co-ordinates being Cartesian and the axes inclined at any angle. **Denoting**the two pairs of magnetic poles by N, S and N', S', there is attraction between N and S', and between S and N'; repulsion between N and N', and between S and S'.**Denoting**its mean value by Hti, and that of the demagnetizing factor by N, we have H=Ho-Hti=Ho-NI.**Denoting**the distance AM by d 1, BM by d2, and AB by 1, we have for the force at M due to the magnetism of the rod H P =d 12 - horizontal component (dla - d 2 3).**Denoting**by W the work in ergs done upon a cubic centimetre of the metal (=_fHdB or f HdI), he finds W =nips approximately, where n 47r is a number, called the hysteretic constant, depending upon the metal, and B is the maximum induction.**Denoting**the root by a, and the number 2222222 in this scale by N, we have N = 2222222.- An expression
**denoting**that two or more monomials are to be added or subtracted is a multinomial or polynomial, each of the monomials being a term of it. - In the graphic method of representation the sign - may be taken as
**denoting**a reversal of direction, so that, if + 3 represents a length of 3 units measured in one direction,-3 represents a length of 3 units measured in the other direction. **Denoting**these convergents by Po/Qo, P1/Q1, P2/Q2, ...**Denoting**them by x, y, so that AB is axis of y and a perpendicular through A the axis of x, and rationalizing (26), we have 2 ax 2 - V 2 Xy 2 - V 2 aAy = o, which represents a hyperbola with vertices at 0 and A.- - 47rb 2 dr (r / '
**denoting**the angle between r and z. - 05v050s), a term
**denoting**an assembly of ecclesiastical officials legally convoked to discuss and decide points of faith, discipline and morals. - In this case the thrust at the lower end B must exceed the thrust at A, the upper end, by the weight of the prism of liquid; so that,
**denoting**the cross section of the prism by a ft. - In the more general case of the convective equilibrium of a spherical atmosphere surrounding the earth, of radius a, (1-1?-=(n+ I) Po --a 2 dr, (12) gravity varying inversely as the square of the distance r from the centre; so that, k = po/po,
**denoting**the height of the homogeneous atmosphere at the surface, 0 is given by (n+I)k(I -9/6 0) =a(I -a/r), (13) or if c denotes the distance where 0=o, 0 _a (14) 0 r c -a' When the compressibility of water is taken into account in a deep ocean, an experimental law must be employed, such as p - po=k(P - Po), or P/po=I+(p-p0)/A, A=kpo, (15) so that A is the pressure due to a head k of the liquid at density under atmospheric pressure po; and it is the gauge pressure required on this law to double the density. - (9) Turning the axes to make them coincide with the principal axes of the area A, thus making f f xydA = o, xh = - a 2 cos a, y h = - b 2 sin a, (io) where ffx2dA=Aa2, ffy 2 dA= Ab 2, (II) a and b
**denoting**the semi-axes of the momental ellipse of the area. - Suppose the ship turns about an axis through F in the water-line area, perpendicular to the plane of the paper;
**denoting**by y the distance of an element dA if the water-line area from the axis of rotation, the change of displacement is EydA tan 8, so that there is no change of displacement if EydA = o, that is, if the axis passes through the C.G. - Of the fluid, equal to the weight vertically upward through the movement of a weight P through a distance c will cause the ship to heel through an angle 0 about an axis FF' through F, which is conjugate to the direction of the movement of P with respect to an ellipse, not the momental ellipse of the water-line area A, but a confocal to it, of squared semi-axes a 2 -hV/A, b 2 - hV/A, (I) h
**denoting**the vertical height BG between C.G. - To determine the component acceleration of a particle, suppose F to denote any function of x, y, z, t, and investigate the time rate of F for a moving particle;
**denoting**the change by DF/dt, DF = 1t F(x+uSt, y+vIt, z+wSt, t+St) - F(x, y, z, t) dt at = d + u dx +v dy+ w dz and D/dt is called particle differentiation, because it follows the rate of change of a particle as it leaves the point x, y, z; but dF/dt, dF/dx, dF/dy, dF/dz (2) represent the rate of change of F at the time t, at the point, x, y, z, fixed in space. - The kinetic energy of the liquid inside a surface S due to the velocity function 4' f i (s given by T=2p + (d) 2+ (t) dxdydz, pff f 75 4 dS (I) by Green's transformation, dv
**denoting**an elementary step along the normal to the exterior of the surface; so that d4ldv = o over the surface makes T = o, and then (d4 2 d4) 2 'x) + (dy) + (= O, dd? **Denoting**the cross-section a of a filament by dS and its mass by dm, the quantity wdS/dm is called the vorticity; this is the same at all points of a filament, and it does not change during the motion; and the vorticity is given by w cos edS/dm, if dS is the oblique section of which the normal makes an angle e with the filament, while the aggregate vorticity of a mass M inside a surface S is M - l fw cos edS.- (12) Along the stream line xBAPJ, t ' =0, u=ae-" c bl, n; (13) and over the jet surface JPA, where the skin velocity is Q, - q = - Q, u = ae rs Q /m = ae rs lc, (14) ds
**denoting**the arc AP by s, starting at u = a; a ' ch nS2=cos nB= -a' u u - - a b' (15) a l a - b l u - a' a-a' u-b' co > u = ae'" S " c > a, and this gives the intrinsic equation of the jet, and of curvature ds '&1) _ i dw i dw dS2 P= - dO = Q a0 - Q as2 = Q c u-b d (u -a.u -a') _ ? - Beginning with a single body in liquid extending to infinity, and
**denoting**by U, V, W, P, Q, R the components of linear and angular velocity with respect to axes fixed in the body, the velocity function takes the form = Ucb1+V42+W43+ P xi+Qx2+Rx3, (I) where the 0's and x's are functions of x, y, z depending on the shape of the body; interpreted dynamically, C -p0 represents the impulsive pressure required to stop the motion, or C +p4) to start it again from rest. - The terms of 0 may be determined one at a time, and this problem is purely kinematical; thus to determine 4)1, the component U alone is taken to exist, and then 1, m, n,
**denoting**the direction cosines of the normal of the surface drawn into the exterior liquid, the function 01 must be determined to satisfy the conditions v 2 0 1 = o, throughout the liquid; (ii.) ' = -1, the gradient of 0 down the normal at the surface of the moving solid; 1 =0, over a fixed boundary, or at infinity; similarly for 02 and 03. - Over the ellipsoid, p
**denoting**the length of the perpendicular from the centre on a tangent plane, px _ pv _ _ pz 1= a2+X' b +A' n c2+A p2x2 + p2y2 p2z2 I (a2 - + X)2 (b 2 +x)2 + (0+X)2, p 2 = (a2+A)12+(b2+X)m2+(c2+X)n2, = a 2 1 2 +b 2 m 2 +c 2 n 2 +X, 2p d = ds; (8) Thence d? **Denoting**the effective inertia of the liquid parallel to Ox by aW' the momentum aW'U = 4)0W' (24) _ U i -AO' 25) in this way the air drag was calculated by Green for an ellipsoida pendulum.- These equations are proved by taking a line fixed in space, whose direction cosines are 1, then dt=mR-nQ,' d'-t = nP =lQ-mP. (5) If P denotes the resultant linear impulse or momentum in this direction P =lxl+mx2+nx3, ' dP dt xl+, d y t x2' x3 +1 dtl dt 2 +n dt3, =1 ('+m (dt2-x3P+x1R) ' +n ('-x1Q-{-x2P) ' '= IX +mY+nZ, / (7) for all values of 1, Next, taking a fixed origin and axes parallel to Ox, Oy, Oz through 0, and
**denoting**by x, y, z the coordinates of 0, and by G the component angular momentum about 1"2 in the direction (1, G =1(yi-x2z+x3y) m 2-+xlz) n(y(y 3x 1 x3x y + x 2 x) (8) Differentiating with respect to t, and afterwards moving the fixed. - The effect of an external circulation of vortex motion on the motion of a cylinder has been investigated in § 29; a similar procedure will show the influence of circulation through a hole in a solid, taking as the simplest illustration a ring-shaped figure, with uniplanar motion, and
**denoting**by the resultant axial linear momentum of the circulation. - In the second of the above books his idea of religion is somewhat of an anachronism; as he himself confessed, he " used the word in the sense which it invariably bore half a century ago," as
**denoting**" belief in an ever-living God, a divine mind and will ruling the universe and holding moral relations with mankind." - Root ac-, sharp; acere, to be sour), the name loosely applied to any sour substance; in chemistry it has a more precise meaning,
**denoting**a substance containing hydrogen which may be replaced by metals with the formation of salts. **Denoting**by So, so, these constant limiting values at p=o, we may obtain the values at any pressure by integrating the expressions (27) and (28) from co to v and from o to p respectively.- Under external migration are comprised emigration and immigration,
**denoting**simply direction from and to. - In reckoning years from any fixed epoch in constant succession, the number
**denoting**the years is necessarily always on the increase. - Each of these periods, which is denominated a tsee, is subdivided into two equal portions called chung-ki and tsie-ki, the chung-ki
**denoting**the first half of the tse, and the tsie-ki the latter half. - In modern botany it is a technical term sometimes
**denoting**the lower part of the capsule called pyxidium, attached to the flower stalk in the form of an urn. **Denoting**the constant ratio by fir, the area of a circle is ira 2, where a is the radius, and ir=3.14159 approximately.