# Dz Sentence Examples

These equations can be made to represent the state of convective equilibrium of the atmosphere, depending on the gas-equation p = pk =RA (6) where 0 denotes the absolute temperature; and then d9 d p R

**dz**-**dz**(p) n+ 1' so that the temperature-gradient deldz is constant, as in convective equilibrium in (I I).The time rate of increase of momentum of the fluid inside S is )dxdydz; (5) and (5) is the sum of (I), (2), (3), (4), so that /if (dpu+dpu2+dpuv +dpuw_ +d p j d xdyd z = o, (b)` dt dx dy

**dz**dx / leading to the differential equation of motion dpu dpu 2 dpuv dpuv _ X_ (7) dt + dx + dy +**dz**with two similar equations.These equations may be simplified slightly, using the equation of continuity (5) § for dpu dpu 2 dpuv dpuw dt dx + dy +

**dz**=p Cat +uax+vay+waz?Let us apply the above theorem to the case of a small parallelepipedon or rectangular prism having sides dx, dy,

**dz**respectively, its centre having co-ordinates (x, y, z).Let this rectangular prism be supposed to be wholly filled up with electricity of density p; then the total quantity in it is p dx dy

**dz**.Hence the total flux is - (+ d2V d 2 V d2V dye + dz2) dy

**dz**, dx2 and by the previous theorem this must be equal to 4'rrp dxdydz.Consider the integral W dx dy

**dz**.I by the whole area B"

**DZ**'VO under the isothermal 9"D and the adiabatic**DZ**', bounded by the axes of pressure and volume.Here, then, is a case specially adapted to the isotropy of the quaternion system; and Hamilton easily saw that the expression i d x +j - + k

**dz**could be, like ix+jy+ kz, effectively expressed by a single letter.If we take the axis of z normal to either surface of the film, the radius of curvature of which we suppose to be very great compared with its thickness c, and if p is the density, and x the energy of unit of mass at depth z, then o- = f o

**dz**, (16) and e = f a xpdz,.AdvertisementThe surface-density of this stratum is a = cp. The energy per unit of area is e = f xpdz=cp(X' -4lrpe(o))+27rp'f c 0(z)

**dz**+27rp fee(c - z)**dz**.Hence the surface-tension =e - =47rp 2 (f 0(z)

**dz**- ce(c)).Integrating the first term within brackets by parts, it becomes - fo de Remembering that 0(o) is a finite quantity, and that Viz = - (z), we find T = 4 7rp f a, /.(z)

**dz**(27) When c is greater than e this is equivalent to 2H in the equation of Laplace.If the density be a, the attraction between the whole of one side and a layer upon the other distant z from the plane and of thickness

**dz**is 27r6 2 P(z)**dz**, reckoned per unit of area.The expression for the intrinsic pressure is thus simply K= 2 iro 2 f 1,G(z)

**dz**(28) In Laplace's investigation o- is supposed to be unity.AdvertisementWe may call the value which (28) then assumes Ko, so that as above Ko =27rf (z)

**dz**.If a i, a 2 represent the densities of the two infinite solids, their mutual attraction at distance z is per unit of area 21ra l a fZ '(z)

**dz**, (30) or 27ra l 02 0(z), if we write f 4,(z)**dz**=0(z) (31) The work required to produce the separation in question is thus 2 7ru l a o 0 (z)**dz**; (32) and for the tension of a liquid of density a we have T = a f o 0 (z)**dz**.In all cases to which it is necessary to have regard the integrated terms vanish at both limits, and we may write f o (z)

**dz**= 3f2' z 3 4(z)**dz**, f o z(z)**dz**= 'a' z4 cb(z)d z; (36) so that Ko = 3 f o z3 ?(z)**dz**, To = $?Remember to do the three checks; Airspace, Alti and

**DZ**, before starting any exercises and to respect all other canopy flyers.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.AdvertisementThe osculating plane of a stream line in steady motion contains the resultant acceleration, the direction ratios of which are du du, du d i g d g 2 _ dH dx +v dy +

**dz**- 2v?One class g g of polyps, the dactylozoids of branching in the Plumularia-type; (

**dz**), lose their mouth and compare with fig.According to this notation, the three equations of motion are dt2 = b2v2E + (a2 - b2) d.s dt =b2v2rj+(a2 - b2) dy d2 CIF - b2p2+(a2_b2)

**dz**It is to be observed that denotes the dilatation of volume of the element situated at (x, y, z).If we suppose that the force impressed upon the element of mass D dx dy

**dz**is**DZ**dx dy**dz**, being everywhere parallel to the axis of Z, the only change required in our equations (I), (2) is the addition of the term Z to the second member of the third equation (2).