Clifford's **biquaternions** are quantities Eq+nr, where q, r are quaternions, and E, n are symbols (commutative with quaternions) obeying the laws E 2 = E, n 2 =,g, = 1 j E=0 (cf.

Clifford, on **Biquaternions**, Proc. L.

Clifford's **biquaternions** and G.

(Note that the z here occurring is only required to ensure harmony with tri-quaternions of which our present **biquaternions**, as also octonions, are particular cases.) The point whose position vector is Vrq i is on the axis and may be called the centre of the bi-quaternion; it is the centre of a sphere of radius Srq i with reference to which the point and plane are in the proper quaternion sense polar reciprocals, that is, the position vector of the point relative to the centre is Srg i.