Thus every quaternion may be written in the form q = Sq+Vq, where either Sq or Vq may separately vanish; so that ordinary algebraic quantities (or scalars, as we shall call them) and pure vectors may each be regarded as special cases of quaternions.
When Clerk Maxwell pointed out the way to the common origin of optical and electrical phenomena, these equations naturally came to repose on an electric basis, the connexion having been first definitely exhibited by FitzGerald in 1878; and according as the independent variable was one or other of the vectors which represent electric force, magnetic force or electric polarity, they took the form appropriate to one or other of the elastic theories above mentioned.
In modern language, forces are compounded by vector-addition; thus, if we draw in succession vectors ~--~
-, HK be vectors representing the given forces, the resultant will be given by AK.
For if 0, A, B be any three points, and m, n any scalar quantities, we have in vectors m.~+n.~=(m+n)O~, (I)