With the development of local gauge theories of gravitation, it became evident that intrinsic spin was an integral part of the theory. This gave spin a classical formulation that predicted the existence of a new kind of field, the torsion field. To date only one class of experiments has been developed to detect this field, a search for a long range dipole force. In this article, the torsion equations are de-coupled from the curved space of general relativity derived from basic principles using vector calculus and the theory of electromagnetism as a guide. The results are written in vector form so that they are readily available to experimentalists, paving the way for new kinds of experiments.