# Ds Sentence Examples

- The one D's looking for?
- This is one of D's compounds.
- C or cz is pronounced as English ts; cs as English ch;
**ds**as English j; zs as French j; gy as dy. - If the primary wave at 0 be cos kat, the effect of the secondary wave proceeding from the element
**dS**at Q is**dS**1**dS**- p cos k(at - p+ 4 A) = - -- sin k(at - p). - If
**dS**=27rxdx, we have for the whole effect 27r œ sin k(at - p)x dx, f P ' or, since xdx = pdp, k = 27r/A, - k fr' sin k(at - p)dp= [- cos k(at - p)]°° r. - 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. - In the applications with which we are concerned, t, n are very small quantities; and we may take P = x yn - At the same time
**dS**may be identified with dxdy, and in the de nominator p may be treated as constant and equal to f. - The path of a ray from the wave-surface AoBo to A or B is determined by the con dition that the optical distance, µ
**ds**, is a minimum; and, as AB is by supposition a wave-surface, this optical distance is the same for both points. - Thus f t2
**ds**(for A) = f A**ds**(for B).. - Accordingly, the optical distance from AoBo to A is represented by f (A +S/c)
**ds**, the integration being along the original path Ao. - In virtue of (4) the difference of the optical distances to A and B is f Sµ
**ds**(along Bo. - B) - f S,u
**ds**(along The new wave-surface is formed in such a position that the optical distance is constant; and therefore the dispersion, or the angle through which the wave-surface is turned by the change of refrangibility, is found simply by dividing (5) by the distance AB. - If, as in common flint-glass spectroscopes, there is only one dispersing substance, f Sy
**ds**= Sµ.s, where s is simply the thickness traversed by the ray. - Taking as the standard phase that of the secondary wave from A, we may represent the effect of PQ by cos 27r (_) .
**ds**, where, l = BP - AP is the retardation at B of the wave from P relatively to that from A. - The intensity may be expressed by 12= (2+Cv) 2 +(2+Sv) 2 and the maxima and minima occur when dC
**dS**(z+Cv)a`j+(2+Sv)dV=0, whence sin rV 2 +cos27rV 2 =G.. - " Let E = o,7 7 = o, =f (bt - x) be the displacements corresponding to the incident light; let O l be any point in the plane P (of the wave-front),
**dS**an element of that plane adjacent to 01; and consider the disturbance due to that portion only of the incident disturbance which passes continually across**dS**. - It is then verified that, after integration with respect to
**dS**, (6) gives the same disturbance as if the primary wave had been supposed to pass on unbroken. - The conception of the lamina leads immediately to two schemes, according to which a primary wave may be supposed to be broken up. In the first of these the element
**dS**, the effect of which is to be estimated, is supposed to execute its actual motion, while every other element of the plane lamina is maintained at rest. - 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. - Under these circumstances the double differentiation with respect to t of any quantity is equivalent to multiplication by the factor - n 2, and thus our equations take the form (b 2 v 2 + n2)E+(a2 - b2)
**ds**(b2 2 + n2)n +(a2 - b2 y =0 (7). - (16), secondary disturbance corresponding to the element
**dS**of the plane may be supposed to be that caused by a force of the above magnitude acting over**dS**and vanishing elsewhere; and it only remains to examine what the result of such a force would be. - According to (18), the effect of the force acting at
**dS**parallel to OZ, and of amount equal to 2b2kD**dS**cos nt, will be a disturbance -**dS**sin cos (nt - kr) (20), regard being had to (12). - Taking the fixed direction parallel to the axis of x, the time-rate of increase of momentum, due to the fluid which crosses the surface, is - f'fpuq cos OdS = - f f (lpu 2 -+mpuv+npuw)
**dS**, (1) which by Green's transformation is (d(uiu 2) dy dz dxdydz. - Eliminating H between (5) and (6)
**DS**du dv dw (du dv d1zv dt u dx n dx udx' 5 -, dzi =°' and combining this with the equation of continuity Dp du dv dw p iit dx+dy+ dz = °' (10) D i du n dv dw_ dt (p p dx p dx p dx - o, with two similar equations. - Thus if d,/ is the increase of 4, due to a displacement from P to P', and k is the component of velocity normal to PP', the flow across PP' is d4 = k.PP'; and taking PP' parallel to Ox, d,, = vdx; and similarly d/ ' = -udy with PP' parallel to Oy; and generally d4,/
**ds**is the velocity across**ds**, in a direction turned through a right angle forward, against the clock. - Uniplanar Motion of a Liquid due to the Passage of a Cylinder through it.-A stream-function 4, must be determined to satisfy the conditions v24 =o, throughout the liquid; (I) I =constant, over any fixed boundary; (2) d,t/
**ds**= normal velocity reversed over a solid boundary, (3) so that, if the solid is moving with velocity U in the direction Ox, d4y1ds=-Udy/**ds**, or 0 +Uy =constant over the moving cylinder; and 4,+Uy=41' is the stream function of the relative motion of the liquid past the cylinder, and similarly 4,-Vx for the component velocity V along Oy; and generally 1,1'= +Uy -Vx (4) is the relative stream-function, constant over a solid boundary moving with components U and V of velocity. - If the liquid is stirred up by the rotation R of a cylindrical body, d4lds = normal velocity reversed dy = - Rx- Ry
**ds**(5)**ds**4' + 2 R (x2 + y2) = Y, (6) a constant over the boundary; and 4,' is the current-function of the relative motion past the cylinder, but now V 2 4,'+2R =o, (7) throughout the liquid. - Along the path of a particle, defined by the of (3), _ c) sine 2e, - x 2 + y2 = y a 2 ' (Io) sin B' de' _ 2y-c dy 2
**ds****ds**' on the radius of curvature is 4a 2 /(ylc), which shows that the curve is an Elastica or Lintearia. - Along the path of a particle, defined by the of (3), _ c) sine 2e, - x 2 + y2 = y a 2 ' (Io) sin B' de' _ 2y-c dy 2
**ds****ds**' on the radius of curvature is 4a 2 /(ylc), which shows that the curve is an Elastica or Lintearia. - Trans., 1892); and dly/yds is the component velocity across
**ds**in a direction turned through a right angle forward. - 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? - Again, since d4)/dv =d /
**ds**, d4)/**ds**= - d4y/dv, (13) T = 1 p f(1 9 d = - 2 p f4' d (14) With the Stokes' function, y for motion symmetrical about an axis. - T =140 y d 27r y
**ds**=7rp f c, 5 4 . - Flow, Circulation, and Vortex Motion.-The line integral of the tangential velocity along a curve from one point to another, defined by s v as + u'a s)
**ds**=f (udx+vdy-}-zdz), (I) is called the " flux " along the curve from the first to the second point; and if the curve closes in on itself the line integral round the curve is called the " circulation " in the curve. - For in a rigid body, rotating about Oz with angular velocity the circulation round a curve in the plane xy is x
**ds**yds)**ds**= times twice the area. - 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. - Iju -a' a-u a-b
**ds****ds**d? - 5, I ch S2 = u a, sh C2= ' u (I) (I and along the jet APJ, oo > u=aerslc>a, sh S2=i sin 0 =iu=ie zrs/o, (2) PM sin 0
**ds**= f e**ds**= 1 = 1 sin 0, (3) cos 272a - cos 2n0 = 2Q - ?ib L a b2 s i n' 27ta u-b A (a- (u -a.u -b') sin 2110 - 2 a-a .u-b ?l (u -a.u -a') = s in 2na u-b 2n b) A (ab.ba') p l u -bJ (u -a.u -a') sh nS2=i sin 110=i then the radius sin 2170 (30) A', cos nO= i, sin n0=o, n 1 ' b-a' ch nS2= ch log (9) = Va -a' n shnS2= shlog (Q) q _ o> u>a'. - (I) Over the jet surface 4'=m, q=Q, u=-e rr,lm= -berslc, ch SZ=cos n0= e>rsle+I, shS2 =i sin ins =tan
**ds**2n (3) e2 =tan nO, - c dB sin 2,10' For a jet impinging normally on an infinite plane, as in fig. - U -b' Along a jet surface, q=Q, and ch S2= cos 0 =cos a-i sin2a(a-a')/(u-b), (5) if 0 =-a at the source x of the jet xB, where u = co; and supposing 0=0,13 at the end of the streams where u =j, j', u-b i sin 2 a u - j cos 0-cos /3 i a -a cos a sin a -cos 0' aa' - 2 (cos a -cos (3) (cos a-cos 0)' u-j' 1 2 cos 0-cos, (6) a -a' - 2 S i n a (cos a -cos (3') (cos a -cos B)' and 4' being constant along a stream line d4 - dw
**ds**_d8 d4 _ dw du du du' d- -dud0' 7rQ ds_ it**ds**(cos a-cos /3) (cos a -cos (3') sin 0 m+m' dB c d0 - (cos a-cos B) (cos 0-cos /3) (cos 0 -cos /3')' _ sin 0 cos a-cos 13 sin 0 - cos a-cos B + cos 0-cos (3' cos 0-cos 13 cos a -cos $ sin 6 cos (3-cos /3' cos 0-cos 0" giving the intrinsic equation of the surface of a jet, with proper attention to the sign. - From A to B, a>u >b, 0=0, ch S2= ch log Q=cos a-i sin 2a a-b I sh S2= sh log Q= I (a u-b-a/) s i n a Q = (u-b) cos a-2(a-a') sin 2 a+1,/ (a-u.u- a')sin a (8) u-b
**ds**_**ds**d4 _ Q dw Q du - Q d 4) du q du (u-b) cos a-2(a- a') sin 2 a (a-u.0 - a') sin a (9) it j- -j' AB _f a(2b - a - a')(u-b)-2(a-b)(b-a')+2V (a - b. - 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? - = 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. - "D's coming soon, Jule," Dusty said quietly.
- D's at some meeting.
- If you weren't D's, I'd kiss you.
- From meta-brombenzoicacid two nitrobrombenzoic ac i
**ds**are obtained on direct nitration; elimination of the bromine atom and the reduction of the nitro to an amino group in these two acids results in the formation of the same ortho-aminobenzoic acid. - If the magnet is not uni - form, the magnetization at any point is the ratio of the moment of an element of volume at that point to the volume itself, or I = m.
**ds**/dv. - Where
**ds**is the length of the element. - Forces acting on a Small Body in the Magnetic Field.-If a small magnet of length
**ds**and pole-strength m is brought into a magnetic field such that the values of the magnetic potential at the negative and positive poles respectively are V 1 and the work done upon the magnet, and therefore its potential energy, will be W =m(V2-Vi) =mdV, which may be written W =m d s- = M d v= - MHo = - vIHo,**ds****ds**where M is the moment of the magnet, v the volume, I the magnetization, and Ho the magnetic force along**ds**. - When the secondary disturbance thus obtained is integrated with respect to
**dS**over the entire plane of the lamina, the result is necessarily the same as would have been obtained had the primary wave been supposed to pass on without resolution, for this is precisely the motion generated when every element of the lamina vibrates with a common motion, equal to that attributed to**dS**. - Do I have D's number? a warm, male voice on the other end said.