Eoever — Geometrical Constructions of Lines of Force. 219 



head BC which moves the line AP, has a linear velocity m^, 



and the crosshead B'C which moves line A'P, has a velocity 



771' 

 m',, such that — ^ = K, a constant. If the crossheads move in 



the same direction, (as shown in the figure by the arrows) and 

 B'C starts from the beginning JS' of its stroke when BC 

 starts from a position /S at a distance BS from the begin- 

 ning of its stroke, and D and D' are the respective positions 

 of the crossheads for a general point P, 

 then, from the figure, 



U'D' = K [ED — ES 



Ied — esY 



or 



AB' versin PA'X = ~ AB (versin PAX — versin GAX\ 



m' / N 



6(1 — cos 00') = b — 1(1 — cos CO ) — (1 — cos a)u 



in which 



co' =^ PAX, oi = ^ PAX, 



a = ^ GAX, and b = AB = AB'. 



The above equation reduces to 



w'j (1 — cos (o) — m^ (1 — cos co') = m\ (1 — cos a). .(26). 



When the crossheads move so as to make the lines rotate in 

 opposite directions, the locus of the point of intersection P' is 



m'^ (1 — cos CO ) + m^ (1 — cos co') = m'^ (1 — cos a). .(27). 



Equations (24) and (26) have the same form, but the 

 primed constants are interchanged. This shows that the 

 curve representing a line of force proceeding from a system 

 consisting of two electrified points having charges of opposite 

 algebraic sign, is the locus of the intersection of two straight 

 lines rotating in the same plane about parallel axes (passing 



