486 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



vector m on the chosen space and time are the ordinary "retarded" 

 potentials. 



If (Figure 28)^^ we draw the backward hypercone from the point at 

 which the potential m is to be determined, and if this backward hjper- 

 cone cuts an elementary tube of the field q in the vector volume rfS, 

 then R is the perpendicular interval from the point in question to w 

 or w produced (where w is the direction of q at the point where the 

 tube cuts the cone). That part of the additive potential vector m 

 which is due to this particular tube is 



w 



dm = (f/Sxq)* „ = — r/S**q 



w 

 R 



(132) 



Evidently the integration of dm is to be taken over the whole three 

 dimensional spread produced by the intersection of the backward 

 hypercone with the whole assemblage of infinitesimal tubes. 



Figure 29. 



Now if (Figure 29) we construct anj^ planoid through the point in 

 question, the retarded potentials are calculated as follows. This 

 planoid, which we may regard as our space, is divided into elements 

 of volume d'B' (corresponding to dS' in the figure). We consider the 



52 Figure 28 and Figure 29 are drawn and lettered for one dimension lower. 



