Projection on a plane

FIG. 6-57 Drag coefficients for spheres, disks, and cylinders =area of particle projected on a plane normal to direction of motion C = over-... 

A = Total area, in ft, projected on a plane, perpendicular to the direction of the wind, except that the exposed areas of two opposite sides of the mast or derrick shall be used. 

Figure 6.42 Crystal structure of HMTTF-TCNQ. (a) Projection on the plane perpendicular to the stacking axis and (b) projection on a plane containing the stacking axis. (After Greene et ai, 1976.)...

Apr = the area of the particle projected on a plane normal to the direction of flow (projected area perpendicular to flow) ula. = the terminal velocity CD = an empirical drag coefficient. 

FIG. 6-57 Drag coefficients for spheres, disks, and cylinders A = area of particle projected on a plane normal to direction of motion C = overall drag coefficient, dimensionless Dp - diameter of particle Fd = drag or resistance to motion of body in fluid Re = Reynolds number, dimensionless u = relative velocity between particle and main body of fluid (I = fluid viscosity and p = fluid density. (From Lapple and Shepherd, Ind. Eng. Chem., 32, 60S [1940].)... 

The usual description of this situation is in terms of the dihedral angle between the H-C-C-H bonds. The dihedral angle is obvious in the Newman projection as it is the angle between the two C-H bonds projected on a plane orthogonal to the C-C bond. In a Newman projection this plane is the plane of the paper, and here the angle is 180°. 

Angle between the 2p7i orbital and the C-H i bond projected on a plane perpendicular to the C-C bond direction. 

These angles are shown stereographically in Fig. 9-10, projected, on a plane normal to the incident beam. The (111) pole figure in (a) consists simply of two arcs which are the paths traced out by 111 poles during rotation of a single crystal about [100]. In (b), this pole figure has been superposed on a projection of the reflection circle in order to find the locations of the reflecting plane normals. Radii drawn... 

Figure 2.7 A projection of a a-helix on a plane that contains the axis of the hehx in a hall and sticks representation (left) and in a conventional representation (right), with a rihhon added to mimic the helix (upper diagrams). The bottom diagram (balls and sticks) is the same hehx as above but projected on a plane perpendicular to the axis of the hehx.

FIGURE 5.12 Brownian motion. Projection on a plane of the trajectory of a gamboge particle, taking observations at constant time intervals. The right-hand side shows the same trajectory, but the time interval is 10 times shorter than at the left-hand side. After observations by Perrin. See text. 

It will be clear from the above discussion that if the ternary eutectic curves are projected on a plane parallel with the face BC of the prism, that is, if we express the composition of the solutions in accordance with the formula xA, yB, (100 ) C, then it will be possible to state, from the form of the curve obtained, whether or not the two components present in varying amount crystallise out pure or combine with each other to form a compound. It will be apparent that the projections of the ternary eutectic curves in the manner indicated, will yield a series of curves similar to the binary curves given in Figs. 33, 37, and 43, pp, 103, 109 and 119. 

Fig. 7.01. Plan of the unit cell of the orthorhombic structure of iodine projected on a plane perpendicular to the y axis. In (a) atomic centres are shown and the heights of the atoms are indicated in units of b. In (6) the atoms are assigned their correct van der Waals radii to emphasize the packing.

Fig. 7.05. Plan of a single sheet of the rhombohedral structure of arsenic projected on a plane perpendicular to the principal axis. The atoms are at two different heights, as shown, and the structure as a whole is formed by the superposition of identical sheets in such a way that the lower atoms of each sheet fall vertically above the holes in the sheet beneath.

Fig. 8.02. (a) Plan of the unit cell of the hexagonal structure of nickel arsenide, NiAs, projected on a plane perpendicular to the z axis, (b) Clinographic projection of the same structure. The two As atoms represented by heavy circles are those within the unit cell the others lie outside the cell but have been added to show the co-ordination about the Ni atom at o, o,... 

Fig. 8.08. Plan of a single layer of the structures of cadmium chloride, CdCl2, and cadmium iodide, Cdl2, projected on a plane perpendicular to the z azis. The unit cell of cadmium iodide is indicated.

Fig. 11.04. Plan of the idealized orthorhombic structure of forsterite, Mg2Si04, projected on a plane perpendicular to the x axis. The silicon atoms lie at the centres of the tetrahedra of oxygen atoms, and are not shown.

Fig. 11.07. Plan of the idealized monoclinic structure ofdiopside,CaMg(Si03)3, projected on a plane perpendicular to the z axis. The chains of fig. x 1.06 a are here seen end-on.

Fig. 12.06. Schematic plan of the unit cell of the tetragonal structure of potassium dihydrogen phosphate, KH2P04, projected on a plane perpendicular to the z axis. The phosphorus atoms lie at the centres of the tetrahedra of oxygen atoms, and the potassium atoms (not shown) lie midway between pairs of tetrahedra in the z direction. The heights of the phosphorus and oxygen atoms are indicated in units of c. Hydrogen bonds are represented by broken lines. The comers of the unit cell coincide with the phosphorus atoms at height o.

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