Roever — Geometrical Properties of Lines of Force. 285 

 or if we consider equation (3) put for the 



!■* asymptote cu = 



of ** « = (n,— .1) w 



then for the n^ asymptote equation (3) becomes 



«. = («« — 1)- -hx, (24), 



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



X a \ 

 n. = 1 equation (23) becomes x. = = ac,, which is the 



same as equation (Ifi). ¥orn„-=l equation (24) becomes 



x^ = Xq. Equations (23) and (24) show that aj«= (1 ), 



in which a is the angle which the tangent at O 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 Xq = equation ( 24) 



X 

 becomes xj = ( n, — 1 ) - In which x'^ is the distance from O 



to the nf asymptote of the dashed curve. 



( b ) 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 perpendicular to the electrified plane; one line having a 

 motion of rotation about the electrified point and the other a 

 motion of translation perpendicular to itself and parallel to the 

 electrified plane. The rotation is such that the versine of the 

 angle lohich the rotating line makes with O F {a line which 

 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 moving line were the meridian line of a 



