Conway — Application of Quaternions to Electrical Theory. 9 



As a last example of quateinion treatment we consider an interesting 

 extension of the relativity principle by Bateman and Cunningham.* 

 Consider the transformation 



q' = qs 



which gives 



d(( = - CL-Wqq-' and q' = q(7(c[) 



where we denote by a bracket a quantity which is not operated on by (j. 



a = q'ff'Cq')- 



If we put (T = q'"'cr'c['m, where m is some scalar function of q, we have 



(j(j = q'(7'(q')q'"''T'q'™ = q'fr'c'q'wi + 4(T'q' 

 = in(^{(l'a')(( + q'((7''"')<'"'q' + m4(T'q"'j 

 since 0^(0^' = *^- 



Hence the " relativity " form is attained if q'(j'™ + 4?;i = 0. Hence m is 

 obviously a function of Tq'. 



— = - -- /S'rfq'ff'm = 4,S'rfq'q'-' = 4:dT(({Tf()-\ so that m = {TqJ. 

 * Proceedings of the London Maih. Society, series ii, vol. viii, Nos, 1, 2, 3, and 4. 



R.I. A. PROC, VOL. X.XIX., SECT. A. [2J 



