A contribution to the rotation of a galaxy, due to internal structure
alone, is discussed in the context of a generalized version of the the
ory of general relativity, whereby the space-time metric has a quatern
ion structure. The radial dependences of the angular momentum of a con
stituent star of a galaxy, relative to the remainder of its host galax
y, are determined and compared in regard to the classical Newtonian th
eory, Einstein's tenser form of general relativity, and the generalize
d quaternion formulation of the latter theory of gravitation. The resu
lts are subject to possible observational tests.