Anx2, and 52 takes the simpler form dd d d aodal+alda2+a2da,1--...
Inside the sphere d I d'd rd?
= dx ?+xd%y ds ds ds ds +2 l dd, so that the velocity of the liquid may be resolved into a component -41 parallel to Ox, and -2(a 2 +X)ld4/dX along the normal of the ellipsoid; and the liquid flows over an ellipsoid along a line of slope with respect to Ox, treated as the vertical.
We have by partial integration ff1 fV dd - ' 2 dy JJ dx y JJ y dxd dz = V - d dzdxd dz, and Itwo (similar equations in y and z.
The difference 90-E is represented by the area 9"DdO to the left of the isometric Dd under the isothermal B"D.
Then, if we take ordinates Kb, Lg, Mc, Nd, Pf, equal to B'B, GG', C'C, D'D, FF', the figure abgcdfe will be the equivalent trapezoid, and any ordinate drawn from the base to the a LM N P e X top of this trapezoid will be equal to the portion of this ordinate (produced) which falls within the original figure.
Panem nostrum super -substantiale[m] dd nobis hodie.
16) in which this wonderful process is carried out is a huge retort, lined with clay, dolomite or other refractory material, hung aloft and turned on trunnions, DD, through the right-hand one of which the blast is carried to the gooseneck E, which in turn delivers it to the tuyeres Q at the bottom.
He had now three distinct space-units, i, j, k; and the following conditions regulated their combination by multiplication: - I T = 12 '=' 2 = _ 1, ij= - ji=k, jk= - kj=i, ki= - ik =j.3 And now the product of two quaternions could be at once expressed as a third quaternion, thus (a+ib+jc+kd) (a'+ib'+jc'+kd') = A+iB+jC+kD, where A=aa' - bb' - cc' - dd', B = ab'+ba'+cd' - dc', C = ac'+ca'+db' - bd', D =ad' +da'+bc' - cb'.
Hence these displacements are proportional to, JD, JC, and A therefore to DD, CC, where ~ CD is any line drawn FIG.
The instantaneous centre of CD will be at the intersection of AD, BC, and if CD be drawn parallel to CD, the lines CC, DD may be taken to represent the virtual velocities of C, D turned each through B a right angle.
Moreover, if we draw DE parallel to DE, and EF B D parallel to EF, the lines CC, DD, EE, FF will represent on the same P ~, scale the virtual velocities of the, v~.._ points C, D, E, F, respectively,, ,.~ .--..~_ turned each through a right angle.
88), where aa, bb, cc, dd represent plane a joints.
While the stroke of A is ACa, extending to equal distances on either side of C, and equal to twice the chord of the arc Dd, the stroke of B is only equal to twice the sagitta; and thus A is guided through a comparatively long stroke by the sliding of B through a comparatively short stroke, and by rotatory motions at the joints C, D, B.
A, Cavity surrounding fin ray; a', fin ray; b, muscular tissue of myotome; c, nervecord; d, notochord; c, left aorta; f, thickened ridges of epithelium of praeoral chamber (Rader organ); g, coiled tube lying in a coelomic space on right side of praeoral hood, apparently an artery; h, cuticle of notochord; i, connective-tissue sheath of notochord; k, median ridge of skeletal canal of nerve-cord; 1, skeletal canal protecting nerve-cord; m, inter-segmental skeletal septum of myotome; n, subcutaneous skeletal connective tissue; o, ditto of metapleur (this should be relatively thicker than it is); q, subcutaneous connective tissue of ventral surface of atrial wall (not a canal, as supposed by Stieda and others); r, epiblastic epithelium; s, gonad-sac containing ova; t, pharyngeal bar in section, one of the "tongue" bars alternating with the main bars and devoid of pharyngo-pleural fold and coelom; v, atrio-coelomic funnel; w, socalled "dorsal" coelom; x, lymphatic space or canal of metapleur; y, sub-pharyngeal vascular trunk; z, blood-vessel (portal vein) on wall of hepatic caecum; aa, space of atrial or branchial chamber; bb, ventral groove of pharynx (anteriorly this takes the form of a ridge); cc, hyperbranchial groove of pharynx; dd, lumen or space of hepatic caecum; ee, narrow coelomic space surrounding hepatic caecum; $, lining cell-layer of hepatic caecum; gg, inner face of a pharyngeal bar clothed with hypoblast, the outer face covered with epiblast (represented black); hh, a main pharyngeal bar with projecting pharyngeal fold (on which the reference line rests) in section, showing coelomic space beneath the black epiblast; ii, transverse ventral muscle of epipleura; kk, raphe or plane of fusion of two down-grown epipleura; 11, space and nucleated cells on dorsal face of notochord; mm, similar space and cells on its ventral face.
V); dd (= Eng.
- (1) Between two vowels, or a vowel and a liquid, the seven consonants p, t, c, b, d, g, in, became respectively b, d, g, f, dd, -, f, where "-" represents the lost voiced spirant y.
A consonant occurring medially is, generally speaking, invariable in the present language; thus the p and d of cupidus are b and dd in cybydd; but with the initial consonant the case is different.
These are old stem endings left after the loss of the original -es; thus latro gives lleidr, latrones gives lladron; the forms having dd represent i stems, i becoming dd in certain positions.