( 262 ) 



VïTT 



COS <p 



I'. 



ƒ■ 



Xn (r) cos (p. 



sin "— V 4 Sn—l 



In the field corresponding to this in the elliptic space, all force lines 

 move from the positive to the negative pole of the double point; a 

 part cuts the pole Sj),!—! of the origin : these force lines are unilateral 

 in the meridian plane ; the remaining do not cut it ; these are bilateral 

 in the meridian plane. 



The two boundary force lines forming together a double point in 

 the pole Spn—], have the equation : 



I r . ) 



sin "— 'yi Jsin "—V -|- [n — 1) cot r I sin "— 'r dr\ = dr 1. 

 ' %J ) 



r 



The Sjin—i of zero potential consists of the pole Spn—\ and the 

 equator Sp,.—i of the double point; its line of intersection with the 

 meridian plane has a double point in the force lines doublepoint. All 

 potential curves in the meridian plane are bilateral. 



V. For the fictitious "field of a single agens point" the potential is 

 j A„ (r) dr. It is rational to let it become in the pole S}^—] ; so 

 we find : 



Xn{r)dr = F,{r), 

 r 



and for the arbitrary gradient distribution holds : 



72 



IX = ^ C^^F,{r)dT (/) 



We could also have found F^ {r) out of the differential equation 

 {H) of F § III, which it must satisfy on the same grounds as have 

 been assei-ted there. For the elliptic aS/>« also we find: 



dF, 



c . 



I sin " — V dr 



dr sin " — V 



But here in the pole Spn—x, Ijhig symmetrically with respect to 



the centre of the field, the force, thus I sin^^—'^rdr must be 0; so 



that we find : 



