( 346 ) 



of intersection of P^ and O,,, one of eacli of the points of inter- 

 section of II ^ and ((„ widi ( \, is pdinl of (•(Uitacl : so on n^ as well 

 as on a., anodier node is siliialed. ( )f each of die jxtiiils of inkT- 

 section of h^ and ^i willi (', one is point of coniacl, die odier is 

 also j)oint of inlerscrdoii of </,, and C.^. So tiie jioinls of inlcixM-doii 

 /vj, 6'i, n^, ti., iiiiitiiaUy are left as nodes: these aix' live in nuniher 

 besides die point of intersection connted already ^/i^/^ l»elonj;in,U' lo r/^,. 

 So the entire nuniher of liie nodes of the section of ()^_ and P, nol 

 lying on </"., ainonnts lo 7. From this ensues thai ^>„ has besides r/^, 

 another doni)le cnr\e of order seven. If we make a plane lo pass lliroui:li 

 a generatrix O^ and if we in\esligale how many right lines aie 

 situated in il, we shall liiid the number to be '.^ cin-responding to 

 former results. 



The nodal curxe of oi-der sexen is thus intersected thice limes 

 by the right lines of (f^.. 



8. The closei' in\estigali(»ii of die surface ( K, as well as ihal of 

 ^>^ and the other possible forms aj>pearing by \aiiously assuming 

 the pencil of surfaces. gi\es rise to very extensive (•(»nsideralions. 

 which are not to be included in this communicalion, as for the 

 present its aim was bul to show die general properties of the 

 discussed locus. 



Physics. - ••Sliiiiilll'li'il Di-dnclinu nf llii' F'li-ld mill tlir Forci'S iif 

 nil l-]li'rlroii. iiiiiniiij hi ninj ijlreii n'lii/.' Vi\ Prof. A. So.M.MEKFELD. 

 (Coinuiiuiicak'fl bv Prof. 11. A. I.(jki;.ntz). 



§ J. Sniniiuirij. 



In the "Grtttinger xS'achricliten" ^) 1 communicated a general ropre- 

 sentation of the field of an electron, moving in any given xvay. 

 which seems to be .simpler than the formulae, hitherto Iviiown. which 

 are liased on ihe work of II. A. Lokentz. This is the ditference: 

 My formulae expi-ess the [>oteiitials Iw a simjilr intt't/ral, eMemlimj 

 ovin- the jufst thru' and containing only the varying distances of the 

 point in (piestion from thi' ceitfn' of fhr i'lectroïi, sujiposed lo be 

 spherical, whereas the formulae hitherto known are iloiihli- or Irijih' 

 Integrah, extending over the simcc, charged with electricity, and 

 containing the distance of the |)oint in question fnuii tin' jinsition of 

 the ehnrye nt n n-rtnin for nier time. It may \\o remarked, that 



1) Nachrichten d. K. Geseli.scliaft d. Wisscnschaltcn I'.iOi Heft 2: in the folio- 

 wing lo be cited us "lirsl pajier". 



