Unfortunately he didn't use quaternions in his initial formulation (that was all split into xyz coordinates) and in his later revision he took apart the quatern

Unfortunately he didn't use quaternions in his initial formulation (that was all split into xyz coordinates) and in his later revision he took apart the quaternions into scalar and vectors parts. It could have been so much prettier....but luckily we have geometric algebra for that today. On the other hand he did derive the electric and magnetic fields from a scalar and potential field. In that sense Heaviside made a step backwards.