Roever — Geometrical Properties of Lines of Force. 285 



or if we consider equation (3) put for the 



1'* asymptote w = 

 njf ** (o — {n^ — 1) TT 



then for the n^'' asymptote equation (3) becomes 



^.= {na-l)\+x, (24), 



in which x^ is the distance from O to the n^ asymptote. For 

 n„=\ equation ( 23 ) becomes x. = = a:,, which is the 



same as equation (Ifi). For n„ = 1 equation (24) becomes 



X a 

 Xa = x^. Equations (23) and (24) show that 0;^= (1 ), 



in which a is the angle which the tangent at makes with 

 OF. The dashed curve (Fig. 5) is a portion of the com- 

 plete curve of which the critical line is a part. For a = 



\ 

 equation (23) becomes x\ = n^ and for x^ — O equation (24) 



X 

 becomes x^ — (n^ — 1) -In which x\\% the distance from O 



to the n^a asymptote of the dashed curve. 



( h ) The curve representing a line of force proceeding from 

 a system consisting of an electrified plane and an electrified 

 point, is the locus of the intersection of tioo straight lines having 

 motions in a plane which passes through the electrified point 

 and is perpendicidar to the electrified plane; one line having a 

 motion of rotation about the electrified point and the otlier a 

 motion of translation perpendicular to itself and parallel to the 

 electrified plane. The 7'otation is such that the versine of the 

 angle which the rotating line makes with Y {a line lohich 

 passes through the electrified point and is perpendicular to the 

 electrified plane) changes at a uniform rate, and the transla- 

 tion is such that if the 7noving line were the meridian line of a 



