^{page 225 note *} Recent Researches, chap, i; Electricity and Matter, chap. i.

^{page 225 note †} [Heaviside's vector notation is a modification of Hamilton's quaternion notation, the main difference being that the quaternion product of two vectors AB is not used in Hamilton's sense but is used to mean the scalar of the complete product—that is, Heaviside's AB is equivalent to Hamilton's –SAB, and may be defined geometrically as equal to AB cos θ, where A, B are the lengths of A, B, and θ the angle between them. As in other non-associative vector algebras, the square of a vector is equal to the square of its length; in quaternions A²= – A². The notation introduced by Gordon Brown in equations (9), (10), etc.,has been suggested by others but generally discarded. Burali-Forti and Marcolongo, however, make it a feature of their system of vector analysis. As a notation it is misleading; as an operator it is inferior to the quaternion ∇-—C. G. K.]

^{page 231 note *} Electrical Papers, vol. ii, pp. 521 et seq.; also Phil. Trans., A, 1892.

^{page 238 note *} Phil. Mag., Nov. 1915, p. 723.

^{page 238 note †} Phil. Mag. (6), xxvi, p. 792.

^{page 238 note ‡} Jeans, , “Report on Quantum Theories,” Proc. Loud. Phys. Soc., 1915.Google Scholar