Solid angle to the unit sphere with center P, which can be calculated as the surface integral: where formula_5 is the unit vector corresponding to formula_6, the position vector of an infinitesimal area of surface with respect to point P, and where formula_7 represents the unit normal vector to . Even if the projection on the unit sphere to the surface S is not isomorphic, the multiple folds are correctly considered according to the surface orientation described by the sign of the scalar product formula_8. Thus one can approximate the solid angle subtended by a small facet having flat surface area ,
BET theory physical adsorption of gas molecules. The total surface area formula_19 and the specific surface area formula_20 are given by where formula_5 is in units of volume which are also the units of the monolayer volume of the adsorbate gas, formula_24 is Avogadro's number, formula_25 the adsorption cross section of the adsorbing species, formula_26 the molar volume of the adsorbate gas, and formula_27 the mass of the solid sample or adsorbent. The BET theory can be derived similarly to the Langmuir theory, but by considering multilayered gas molecule adsorption, where it is not required for a layer to be completed before