In a recently published paper (Proc. R.S., Dec. 1919) Mr W. J. Johnston makes a brilliant use of Clifford's extension of Hamilton's quaternions to the case of four (or more) variables. He proceeds, by adding a fourth independent and real unit vector and making the corresponding tensor imaginary, to modify the quaternionic ∇ so as to make it applicable to physical problems on the basis of relativity. In this respect his vectors are simply the direct extension of Hamilton's bivectors.