The theory given in a previous paper is extended and refined. The restriction of collinear spins is lifted and the idea of local random canting as suggested by Geller is introduced. It is assumed that when a magnetic ion has only one magnetic nearest neighbor, its spin need not be collinear with the total magnetization. The angle by which these spins are canted is treated as an adjustable parameter. This refinement of the theory makes it possible to reproduce in addition to the substitution dependence of the magnetic moments at 0°K, also the substitution dependence of the transition temperatures for a large variety of ferrimagnetic‐substituted garnet systems. All of this agreement is obtained with a single adjustable parameter. When substitution is in the octahedral site, canting occurs in the tetrahedral site, and vice versa. It was found that spins in the ``d'' site having only one nearest magnetic neighbor are canted by about 60° when substitution is performed in the ``a'' site. Very small canting, if any at all, occurs in the ``a'' site when the substitution is in the ``d'' site. In double‐substituted systems there is also no canting in the ``a'' site and the canting angles in the ``d'' site are ∼0° in Mg‐substituted systems, ∼50° in Sc‐substituted systems, and ∼75° in Zr‐substituted systems.