Solid angle is much, much farther away. The solid angle subtended by the complete ()-dimensional spherical surface of the unit sphere in -dimensional Euclidean space can be defined in any number of dimensions . One often needs this solid angle factor in calculations with spherical symmetry. It is given by the formula where is the gamma function. When is an integer, the gamma function can be computed explicitly. It follows that This gives the expected results of 4 steradians for the 3D sphere bounded by a surface of area and 2 radians for the 2D circle bounded by a circumference of length
Capillary surface and other energy potentials absent, the energy of the system is where the subscripts formula_40, formula_41, and formula_42 respectively indicate the liquid–gas, solid–gas, and solid–liquid interfaces. Note that inclusion of gravity would require consideration of the volume enclosed by the capillary surface and the solid walls. Typically the surface tension values between the solid–gas and solid–liquid interfaces are not known. This does not pose a problem; since only changes in energy are of primary interest. If the net solid area formula_43 is a constant, and the contact angle is known, it may be shown that (again, for two different fluids