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.
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.
For small supplies such a well may be perfectly successful; but however small the quantity drawn, it must obviously have the effect of diminishing the volume of fresh water, which contributes to the maintenance of the level of saturation above the sea-level; and with further pumping the fresh water would be so far drawn upon that the mean level of saturation would sink, first to a curved figure - a cone of depression - such as that represented by the new level of saturation dd, and later to the figure represented by the lines ee, in which the level of saturation has everywhere been drawn below the mean sea-level.