The tensor notation, which is probably best known in its application in Einstein's four-dimensional theory of gravitation, can be used in its three-dimensional form in obtaining the general equations in many branches of mathematical physics. In the present paper the various steps in the proof of the equations of motion of a viscous fluid are translated into tensor form. An attempt has been made to develop the various formulae in outline from first principles, with references where necessary to a standard work, and also to give whenever possible a geometrical interpretation of the various vector quantities met with in the course of the argument. In particular the fundamental assumptions of Stokes, on which the viscous equations are based, are stated in the form of the relation between the stress vector across an element of area and the vector element of area.

The equations of motion in tensor notation are afterwards translated into ordinary notation for the special case of orthogonal curvilinear coordinates. These can be at once reduced to the commonly useful forms of spherical polars, ellipsoidal coordinates, etc. In a final section it is shown how the tensor equations can be used to deduce the equations of viscous flow in terms of Stokes stream function for motion symmetrical about an axis. The stream function is shown to be identical with the surviving component of the covariant vector potential of which the other two components vanish.