476 PROCEEDINGS OF THE AMERICAN ACADEMY. 



from simple geometrical premises to conclusions of so purely physical 

 a character. Of course it is to be noted that while our values of e and 

 h are identical in mathematical form with equations for electric and 

 magnetic force, we should need some additional assumptions before 

 actually identifying these quantities. 



50. Our next step will be to show that the values of e and h derived 

 from the 2-vector O^^^ — ^ ^^'6 identical with the expressions for 

 electric and magnetic force in the general case in which the electron 

 is no longer restricted to uniform motion. We have from (94) 



M = eP = — ^3 (Ixwxc) -1 — ^ Ixw. (101) 



Thus, assuming some time-axis, we see from (43) that 



wxc = wxv/ (1 — r). 



Then 



Hence 



M 



e 



M = -B. — ^r^i iisix". (103) 



Is • V IsXV , R IsXV 1 e IsXV 



r L'VLxy R Isxy "1 



€ r is'Vd — /4V)xk4 i?/iVxk4 ~1 _ e (h — ky^ki 



(104) 



R'L (l-r^)^ l-«^2j R' (l-j;2)? 



Hence, if again we use r = Is — /4V and r' = /^ — Is'V = i? (1 — ?^-)2, 

 we have 



ri-v /4V . i-7'2 -| 



e = E.k4 = e |^-,3 r - ^ + ^:^^J 



(105) 

 , __ , ris-vrxv , Lxv (1 — t>^)rxv -| 



If we look at the form in l, — /4V (104) we observe that 



H= |^l,xe, E = — exk4. (106) 



Hence 



M = ^" 1, + k4 jxe = ^ Ixe. (107) 



