Moever — Geometrical Properties of Lines of Force. 285 

 or if we consider equation (3) put for the 

 l Bt asymptote <u = 



2 nd " CO — 7T 



nf " co - (n B — 1) 7T 



then for the n^ asymptote equation (3) becomes 



*a=(* a -l)^+* (24), 



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



«„= 1 equation (23) becomes ac a = = x., which is the 



same as equation (IB). For n a = 1 equation (24) becomes 



x a = x„. Equations (23) and (24) show that cc= - (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' a = n a and for x = equation ( 24) 



\ 

 becomes x' — (n. — 1) —In which x' is the distance from 



to the nj, h 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 two 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 which the rotating line makes with O Y [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 



