Clifford considers an **octonion** p+wq as the quotient of two motors p+wv, p'+wo'.

Thus, in place of his general tri-quaternion we might deal with products of an odd number of point-plane-scalars (of form, uq+wr) which are themselves point-plane-scalars; and products of an even number which are **octonions**; the quotient of two point-plane-scalars would be an **octonion**, of two **octonions** an **octonion**, of an **octonion** by a point-plane-scalar or the inverse a point-plane-scalar.

Again a unit point p. may be regarded as by multiplication changing (a) from **octonion** to point-plane-scalar, (b) from point-plane-scalar to **octonion**, (c) from plane-scalar to linear element, (d) from linear element to plane-scalar.