Solid angle orientation formula_9, and distance from the viewer as: where the surface area of a sphere is . The solid angle of a cone with its apex at the apex of the solid angle, and with apex angle 2, is the area of a spherical cap on a unit sphere For small such that , this reduces to the area of a circle . The above is found by computing the following double integral using the unit surface element in spherical coordinates: This formula can also be derived without the use of calculus. Over 2200 years ago Archimedes proved that the
Specific surface area a particle size distribution, making some assumption about the particle shape. This method, however, fails to account for surface associated with the surface texture of the particles. The SSA can be measured by adsorption using the BET isotherm. This has the advantage of measuring the surface of fine structures and deep texture on the particles. However, the results can differ markedly depending on the substance adsorbed. This depends upon a relationship between the specific surface area and the resistance to gas-flow of a porous bed of powder. The method is simple and quick, and yields a result that often correlates