The second order wave equations of the spinning electron

In a previous paper the author attempted to cast Dirac's wave equations into a tensorial form, but the results obtained were unsatisfactory as the first order equations (A) were expressed in terms of a third rank tensor, γμv a whose significance remained obscure. In fact, tensors of the required character are not provided by the special theory of relativity, and it is not difficult to convince one's self by actual trial that there does not exist any system of equations (for a 4-vector wave function) which is equivalent to Dirac's first order equations. It is, however, possible to construct a system of equations which is equivalent to Dirac's second order equations. This is evident from the form of the second order equations (I) of the paper cited above, for, by making the tensor βαστv antisymmetric in all four suffixes, these equations are reducible to a 4-vector form. The object of this paper is to give the general theory of a system of notation is employed in preference to tensorial notation to facilitate comparison with the procedure of electrodynamic theory.