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dv

For by (30) do = dv, and by (2) dv is proportional to ds.

10The heat absorbed in isothermal expansion from vo to v at a temperature 0 is equal to the work done by equation (8) (since d0 =o, and 0(dp/d0)dv =pdv), and both are given by the expression RO log e (v/vo).

10dv, Velar area or cephalic dome.

00dv, vessel.

00dv, dorsal vessel passing into central sinus (bs).

00tsm l, Tergo-sternal muscle (labelled dv in fig.

00dv' to dv s, Dorso-ventral muscles (same as the series labelled tsm in fig.

00tsm, Tergo-sternal muscles, six pairs as in Scorpio (labelled dv in fig.

00From the series for G and H just obtained it is easy to verify that dH = - 7rvG, dv av - dG _ 7rvH -1.

00Ignoring 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.

00dp dpu dpv dpw -z)' reducing to the first line, the second line vanishing in consequence of the equation of continuity; and so the equation of motion may be written in the more usual form du du du du d dt +udx+vdy +wdz =X -n dx' with the two others dv dv dv dv i dp dt +u dx +v dy +w dz - Y -P d y' dw dw dw Z w dw i d p dt +u dx +v dy +wd - -P dz.

00(5) (8) (I) The components of acceleration of a particle of fluid are consequently Du dudu du du dt = dt +u dx +v dy + wdz' Dr dv dv dv dv dt -dt+udx+vdy+wdz' dt v = dtJ+udx+vdy +w dx' leading to the equations of motion above.

00Eliminating 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.

00Taking the axis of x for an instant in the normal through a point on the surface H = constant, this makes u = o, = o; and in steady motion the equations reduce to dH/dv=2q-2wn = 2gco sin e, (4) where B is the angle between the stream line and vortex line; and this holds for their projection on any plane to which dv is drawn perpendicular.

00if r denotes the radius of curvature of the stream line, so that I dp + dV - dH _ dq 2 q2 (6) p dv dv dv dv - r ' the normal acceleration.

00- In the uniplanar motion of a homogeneous liquid the equation of continuity reduces to du dv dx' dy-O' u= -d,y/dy, v = d i t/dx, (2) surface containing so that we can put _ (6) (9) we have (I) (2) (5) (I) where 4 is a function of x, y, called the streamor current-function; interpreted physically, 4-4c, the difference of the value of 4, at a fixed point A and a variable point P is the flow, in ft.

00The 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?

00,In a fluid, the circulation round an elementary area dxdy is equal to dv du udx + (v+dx) dy- (u+dy) dx-vdy= () dxdy, so that the component spin is dv du (5) 2 dx - dy) in the previous notation of § 24; so also for the other two components and n.

00ZI /t = - (a - s) M'Q 2 sine cos ° - EQ sin() =[ - (a - (3)M'U+E]V (8) Now suppose the cylinder is free; the additional forces acting on the body are the components of kinetic reaction of the liquid - aM' (Ç_vR), - (3M' (-- E -FUR), - EC' dR, (9) so that its equations of motion are M (Ç - vR) _ - aM' (_vR) - (a - $) M'VR, (io) M (Ç+uR) = - OM' (dV+U R) - (a - ()M'UR - R, '(II) C dR = dR + (a - Q)M'UV+0V; (12) and putting as before M+aM'=ci, M+13M' = c2, C+EC'=C3, ci dU - c2VR=o, dV +(c1U+E)R=o, c 3 dR - (c 1 U+ - c 2 U)V =o; showing the modification of the equations of plane motion, due to the component E of the circulation.

00Let V be the potential at the centre of the prism, then the normal forces on the two faces of area dy.dx are respectively RI dx2 d xl and (dx 2 d x), dV d2 and similar expressions for the normal forces to the other pairs of faces dx.dy, dz.dx.

00Hence the total flux through the surface considered is - {(dV i /dn l)-}-(dV 2 /dn 2)}dS, and this by a previous theorem must be equal to 47radS, or the total included electric quantity.

00Hence we have - dV /dn = 4lra or a = - (1 /47r) dV /dn = E/42r.

00Then bearing in mind that a= (I/4x1-)dV/dn, and p =-(1/4xr)VV, we have finally E 2 c/v=2 f f v.-dS+ 2J J J Vp dv.

00We thus obtain the expressions dH = sdo +0 (dp I dO) dv = Sd0 - o (dv/do) dp..

00If we put dH=o in equations (8), we obtain the relations between dv and do, or dp and do, under the condition of no heat-supply, i.e.

00The change of energy at constant volume is simply sdo, the change at constant temperature is (odp/de - p)dv, which may be written dE/de (v const) =s, dE/dv (0 const) =odp/do - p .

00The equation to these lines in terms of v and 0 is obtained by integrating dE=sd0+(Odp/de - p)dv = o .

00For the simplest case of polarized waves travelling parallel to the axis of x, with the magnetic oscillation y along z and the electric oscillation Q along y, all the quantities are functions of x and t alone; the total current is along y and given with respect to our moving axes by __ (d_ d Q+vy d K-1 Q, dt dx) 47rc 2 + dt (4?rc 2) ' also the circuital relations here reduce to _ dydQ _dy _ dx 47rv ' _ dt ' d 2 Q dv dx 2 -417t giving, on substitution for v, d 2 Q d 2 Q d2Q (c2-v2)(7372 = K dt 2 2u dxdt ' For a simple wave-train, Q varies as sin m(x-Vt), leading on substitution to the velocity of propagation V relative to the moving material, by means of the equation KV 2 + 2 uV = c 2 v2; this gives, to the first order of v/c, V = c/K i - v/K, which is in accordance with Fresnel's law.

00The calculation can be carried out in each region of velocity from the formulae: (25) T(V) - T(v) =k f vvm dv, S(V)-S(v) =k f vvm+ldv I (V)-I(v)=gk v vv m-ldv, and the corresponding integration.

00dv, The ductus venosus.

00According to Maxwell's law, however, the number of molecules having a velocity in the line of sight lying between v and vd-dv is proportional to e-1 3v2 dv, where (3 is equal to 312u 2; for v=u, we have therefore the ratio in the number of molecules having velocity u to those having no velocity in the line of sight e-0/1 2 =-- e-z = 22.

00units per unit concentration, L the latent heat as 79 4X 4.184 X Io 7 in the corresponding units, and dv the volume change in the solution for unit mass of solvent added we get for the quantity dT/c, where is the concentration of the solution, the value 1.857° C. per unit concentration.

00It is generally known as the Dvenos inscription, from the name of the maker who wrote on the vessel from right to left the in scription, part of which is DV E N OS MED F E C E D (= fecit).

00DV S1 k ?

00If X, Y, Z are the components of force, then considering the changes in an infinitely short time 3t we have, by projection on the co-ordinate axes, i3(mu) =Xi5t, and so on, or du dv dw m-~jj=X, m~=Y, m~=Z.

00Since dv dv ds dv d,t~ d~ ds v2

00If the axes of x and y be drawn horizontal and vertical (upwards), and if ~ be the inclination of the tangent to the horizontal, we have dv.

00If P be the acceleration towards 0, we have dv dr v~=P~,, (3)

00The component accelerations at P in these directions are therefore du do dir /dO\f dv do idfdO\ .14

00dt dt~di ~L duM dv N dt di ~

00dv ~- (12)

00The article (6, ?, in Homer is chiefly used as an independent pronoun (he, she, it), a use which in Attic appears only in a few combinations (such as o dv ...

00If we suppose a normal v less than E to be drawn from the surface S into the liquid, we may divide the shell into elementary shells whose thickness is dv, in each of which the density and other properties of the liquid will be constant.

00This shows that f E (x - xo) p dv must be negative for water in contact with glass.

00The volume of the sphere is V = 3 irr3, and the increment of volume is dV = 4lrr2dr Now if we suppose a quantity of air already at the pressure II+p, the work done in forcing it into the bubble is p dV.

00Hence the equation of work and energy is p dV = Tds (6) 41rpr 2 dr = 8zrrdrT (7) p = 2T/r (8) This, therefore, is the excess of the pressure of the air within the bubble over that of the external air, and it is due to the action of the inner and outer surfaces of the bubble.

00Hence, whereas his predecessors had confounded that which is universally existent with that which is not universally existent, he proposed to distinguish carefully between that which is universally existent and that which is not universally existent, between dv and /lien,.

00In particular, Plato taxes Parmenides with his inconsistency in attributing (as he certainly did) to the fundamental unity extension and sphericity, so that "the worshipped dv is after all a pitiful j.) " (W.

00If the Inspector has requested an agreed apportionment the DV should seek the information from the taxpayer (or agent ).

00The DV should not suggest the parties make an application under this Rule without first having obtained the concurrence of the IR Solicitor.

00The DV should not however agree alternative valuations without the prior concurrence of the RD/CV(S) and the legal adviser to the authority.

00I'm using it as a handy convertor between DV and composite and vise versa, which is a bit of a shame!

00oriental darter Anhinga melanogaster KR, DV Frigatebird sp.

00Jones edits the footage himself using Avid Express DV on his laptop.

00The contribution of the garrison may not exceed the DV + EW; any extra garrison troops don't count.

00This module is a thorough introduction to the preparation and shooting of material on DV.

00In television, I have used linear editing and Avid editing software, and have a working knowledge of DV Cams.

00medical examiners of divers may be obtained from either the HSE or DV Diving.

00A current list of approved medical examiners of divers may be obtained from either the HSE or DV Diving.

00Excellent ideas for making a low-budget dramatic feature on DV, and obtaining a deal to get it transferred to 35mm for theatrical release.

00DIGIC DV II helps to ensure low noise, a wide dynamic range, and accurate color reproduction for both video and photos.

00From the nauseating Blair Witch Project to the impressive auto-biopic tarnation, low-budget DV filmmaking has taken mainstream cinema by storm.

00The DV format actually helps to bring the story across because we become voyeurs on their private movies and fantasies.

00dv, Velar area or cephalic dome.

00dv, vessel.

00dv, dorsal vessel passing into central sinus (bs).

00tsm l, Tergo-sternal muscle (labelled dv in fig.

00dv' to dv s, Dorso-ventral muscles (same as the series labelled tsm in fig.

00tsm, Tergo-sternal muscles, six pairs as in Scorpio (labelled dv in fig.

00From the series for G and H just obtained it is easy to verify that dH = - 7rvG, dv av - dG _ 7rvH -1.

00For by (30) do = dv, and by (2) dv is proportional to ds.

00Ignoring 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.

00dp dpu dpv dpw -z)' reducing to the first line, the second line vanishing in consequence of the equation of continuity; and so the equation of motion may be written in the more usual form du du du du d dt +udx+vdy +wdz =X -n dx' with the two others dv dv dv dv i dp dt +u dx +v dy +w dz - Y -P d y' dw dw dw Z w dw i d p dt +u dx +v dy +wd - -P dz.

00(5) (8) (I) The components of acceleration of a particle of fluid are consequently Du dudu du du dt = dt +u dx +v dy + wdz' Dr dv dv dv dv dt -dt+udx+vdy+wdz' dt v = dtJ+udx+vdy +w dx' leading to the equations of motion above.

00To integrate the equations of motion, suppose the impressed force is due to a potential V, such that the force in any direction is the rate of diminution of V, or its downward gradient; and then X= -dV/dx, Y= -dV/dy, Z= -dV/dz; (I) and putting dw dv du dw dv du Ty - dz -2 ' dz - dx -2n ' dx - dy2?, d -{- d ' v ?

00Eliminating H between (5) and (6) DS du dv dw (du dv d1zv dt u dx n dx udx' 5 -, dzi =Ã‚°' and combining this with the equation of continuity Dp du dv dw p iit dx+dy+ dz = Ã‚°' (10) D i du n dv dw_ dt (p p dx p dx p dx - o, with two similar equations.

00Taking the axis of x for an instant in the normal through a point on the surface H = constant, this makes u = o, = o; and in steady motion the equations reduce to dH/dv=2q-2wn = 2gco sin e, (4) where B is the angle between the stream line and vortex line; and this holds for their projection on any plane to which dv is drawn perpendicular.

00if r denotes the radius of curvature of the stream line, so that I dp + dV - dH _ dq 2 q2 (6) p dv dv dv dv - r ' the normal acceleration.

00- In the uniplanar motion of a homogeneous liquid the equation of continuity reduces to du dv dx' dy-O' u= -d,y/dy, v = d i t/dx, (2) surface containing so that we can put _ (6) (9) we have (I) (2) (5) (I) where 4 is a function of x, y, called the streamor current-function; interpreted physically, 4-4c, the difference of the value of 4, at a fixed point A and a variable point P is the flow, in ft.

00Round the cylinder r=a held fixed in the U current the liquid streams past with velocity q' =2U sin 0+m/a; (2) and the loss of head due to this increase of velocity from U to q' is q' 2 -U 2 - (2U sin e to space filled with liquid, and at rest at infinity, the cylinder will experience components of force per unit length (i.) -27rpmV, 27rpmU, due to the vortex motion; 2 dU 2dV (ii.) -71-pa 2 w,, -7rpa dt, due to the kinetic reaction of the liquid; (iii.) o, -7r(a-p)a 2 g, due to gravity, taking Oy vertically upward, and denoting the density of the cylinder by a; so that the equations of motion are 71-0-a 2 - di r = - 7pa2- -- 22rpmV, (4) aa 2 - = -7rpa 2 dV +27rpmV - 7r(cr - p) a2g, (5) 7r or, putting m = a 2 w, so that the vortex velocity is due to an angular velocity w at a radius a, (o+p)dU/dt+2pwV =o, (6) (a+ p) dV /dt - 2 pwU + (v - p)g = o.

00The 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?

00,In a fluid, the circulation round an elementary area dxdy is equal to dv du udx + (v+dx) dy- (u+dy) dx-vdy= () dxdy, so that the component spin is dv du (5) 2 dx - dy) in the previous notation of § 24; so also for the other two components and n.

00ZI /t = - (a - s) M'Q 2 sine cos Ã‚° - EQ sin() =[ - (a - (3)M'U+E]V (8) Now suppose the cylinder is free; the additional forces acting on the body are the components of kinetic reaction of the liquid - aM' (Ã‡_vR), - (3M' (-- E -FUR), - EC' dR, (9) so that its equations of motion are M (Ã‡ - vR) _ - aM' (_vR) - (a - $) M'VR, (io) M (Ã‡+uR) = - OM' (dV+U R) - (a - ()M'UR - R, '(II) C dR = dR + (a - Q)M'UV+0V; (12) and putting as before M+aM'=ci, M+13M' = c2, C+EC'=C3, ci dU - c2VR=o, dV +(c1U+E)R=o, c 3 dR - (c 1 U+ - c 2 U)V =o; showing the modification of the equations of plane motion, due to the component E of the circulation.

00Let V be the potential at the centre of the prism, then the normal forces on the two faces of area dy.dx are respectively RI dx2 d xl and (dx 2 d x), dV d2 and similar expressions for the normal forces to the other pairs of faces dx.dy, dz.dx.

00Let V i and V2 be the potentials at points just outside and inside the surface dS, and let n l and n 2 be the normals to the surface dS drawn outwards and inwards; then - dV i /dn i and - dV 2 dn 2 are the normal components of the force over the ends of the imaginary small cylinder.

00Hence the total flux through the surface considered is - {(dV i /dn l)-}-(dV 2 /dn 2)}dS, and this by a previous theorem must be equal to 47radS, or the total included electric quantity.

00Hence we have - dV /dn = 4lra or a = - (1 /47r) dV /dn = E/42r.

00Then bearing in mind that a= (I/4x1-)dV/dn, and p =-(1/4xr)VV, we have finally E 2 c/v=2 f f v.-dS+ 2J J J Vp dv.

00We thus obtain the expressions dH = sdo +0 (dp I dO) dv = Sd0 - o (dv/do) dp..

00If we put dH=o in equations (8), we obtain the relations between dv and do, or dp and do, under the condition of no heat-supply, i.e.

00The change of energy at constant volume is simply sdo, the change at constant temperature is (odp/de - p)dv, which may be written dE/de (v const) =s, dE/dv (0 const) =odp/do - p .

00The equation to these lines in terms of v and 0 is obtained by integrating dE=sd0+(Odp/de - p)dv = o .

00The heat absorbed in isothermal expansion from vo to v at a temperature 0 is equal to the work done by equation (8) (since d0 =o, and 0(dp/d0)dv =pdv), and both are given by the expression RO log e (v/vo).

00For the simplest case of polarized waves travelling parallel to the axis of x, with the magnetic oscillation y along z and the electric oscillation Q along y, all the quantities are functions of x and t alone; the total current is along y and given with respect to our moving axes by __ (d_ d Q+vy d K-1 Q, dt dx) 47rc 2 + dt (4?rc 2) ' also the circuital relations here reduce to _ dydQ _dy _ dx 47rv ' _ dt ' d 2 Q dv dx 2 -417t giving, on substitution for v, d 2 Q d 2 Q d2Q (c2-v2)(7372 = K dt 2 2u dxdt ' For a simple wave-train, Q varies as sin m(x-Vt), leading on substitution to the velocity of propagation V relative to the moving material, by means of the equation KV 2 + 2 uV = c 2 v2; this gives, to the first order of v/c, V = c/K i - v/K, which is in accordance with Fresnel's law.

00The calculation can be carried out in each region of velocity from the formulae: (25) T(V) - T(v) =k f vvm dv, S(V)-S(v) =k f vvm+ldv I (V)-I(v)=gk v vv m-ldv, and the corresponding integration.

00dv, The ductus venosus.

00According to Maxwell's law, however, the number of molecules having a velocity in the line of sight lying between v and vd-dv is proportional to e-1 3v2 dv, where (3 is equal to 312u 2; for v=u, we have therefore the ratio in the number of molecules having velocity u to those having no velocity in the line of sight e-0/1 2 =-- e-z = 22.

00units per unit concentration, L the latent heat as 79 4X 4.184 X Io 7 in the corresponding units, and dv the volume change in the solution for unit mass of solvent added we get for the quantity dT/c, where is the concentration of the solution, the value 1.857Ã‚° C. per unit concentration.

00It is generally known as the Dvenos inscription, from the name of the maker who wrote on the vessel from right to left the in scription, part of which is DV E N OS MED F E C E D (= fecit).

00DV S1 k ?

00If X, Y, Z are the components of force, then considering the changes in an infinitely short time 3t we have, by projection on the co-ordinate axes, i3(mu) =Xi5t, and so on, or du dv dw m-~jj=X, m~=Y, m~=Z.

00Since dv dv ds dv d,t~ d~ ds v2

00If the axes of x and y be drawn horizontal and vertical (upwards), and if ~ be the inclination of the tangent to the horizontal, we have dv.

00If P be the acceleration towards 0, we have dv dr v~=P~,, (3)

00The component accelerations at P in these directions are therefore du do dir /dO\f dv do idfdO\ .14

00dt dt~di ~L duM dv N dt di ~

00dv ~- (12)

00If the deviation be a translationthat is, an equal change of motion of all the particles of the bodythe centre of percussion is obviously the centre of gravity itself; and, according to the second law of motion, if dv be the deviation of velocity to be produced in the interval dt, and W the weight of the body, then W dv r-.~ (82)

00The article (6, ?, in Homer is chiefly used as an independent pronoun (he, she, it), a use which in Attic appears only in a few combinations (such as o dv ...

00If we suppose a normal v less than E to be drawn from the surface S into the liquid, we may divide the shell into elementary shells whose thickness is dv, in each of which the density and other properties of the liquid will be constant.

00This shows that f E (x - xo) p dv must be negative for water in contact with glass.

00The volume of the sphere is V = 3 irr3, and the increment of volume is dV = 4lrr2dr Now if we suppose a quantity of air already at the pressure II+p, the work done in forcing it into the bubble is p dV.

00Hence the equation of work and energy is p dV = Tds (6) 41rpr 2 dr = 8zrrdrT (7) p = 2T/r (8) This, therefore, is the excess of the pressure of the air within the bubble over that of the external air, and it is due to the action of the inner and outer surfaces of the bubble.

00Hence, whereas his predecessors had confounded that which is universally existent with that which is not universally existent, he proposed to distinguish carefully between that which is universally existent and that which is not universally existent, between dv and /lien,.

00In particular, Plato taxes Parmenides with his inconsistency in attributing (as he certainly did) to the fundamental unity extension and sphericity, so that "the worshipped dv is after all a pitiful j.) " (W.

00Excellent ideas for making a low-budget dramatic feature on DV, and obtaining a deal to get it transferred to 35mm for theatrical release.

00DIGIC DV II helps to ensure low noise, a wide dynamic range, and accurate color reproduction for both video and photos.

00From the nauseating Blair Witch Project to the impressive auto-biopic Tarnation, low-budget DV filmmaking has taken mainstream cinema by storm.

00The DV format actually helps to bring the story across because we become voyeurs on their private movies and fantasies.

00For example, an order of large fries sets you back 570 calories and 30 grams of fat, nearly half of the Daily Value (DV) for a person eating about 2000 calories a day.

00

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