( 486 ) 



is Sjilislicd. 



lil llic lallcr CISC the ;is\ iii|>tulic coiic possesses as is known x' 

 h'ipicis of ninlnaliv |>er|>eii(licnlar laiiiiciil planes. 



2. When in tlie (M|nati(»n 



wc siil)sliliile Uil- -\- )■ l>;i- lor (ijj., llie jiew e((iiali()li re|)reseiils llie 

 svsleni of llie spheres of M()N(;i'. heh)iminü- lo ihe (pia<h'alic sni-races 

 (>r a jK'iicil. 



The (Mpiatiini i> a ciihie oik' in ).-. so \\\v indicated spliei-es jonn 

 a svsleiii wilh index .'), ihal is, ihronnh each poinl three s|ihei-cs j»ass. 



Il' l'ur hrexilv's sake wc re|»resent the lorinnla 



•'^' + //' + r,.''- i 'l,.!l + '■,. 

 I»v ('i-. llie cnliic (Mpiation is 



The p(t\ver of a point with i-es|»ect to the sphere (>.j is Iheii cfjiial to 



This expression hecoDies iiidepeiideiit of A loj- the cenli-(> of llio 

 s|)liere cntlinu' the four spheres ()^. oi-thoiiiinallv : ((II tin' sp/ti'/fs 

 oj' till' iitdicdtfd sijstciii ni'i' intrrst'cti'd at rnjlit hikiIi's hi/ a fi.ri'd siiln-iw. 



()ii this Diiliixidiiiil siilhi-c the point-spheres of the svslein are of 

 coni-sc sitnated: so it contains in the lirsl |)laee the /vvy/rr.v of the four 

 co/ii's, in the second place the Ci-ntn's of the two ('ij^iihitcnil liiijh'rlm- 

 Io'kIs^) helon.uiiiii' to the pencil. 



b'roiii this ensues that the locus of the c(Mitres of the spheres is 

 a skew cnhic. 'J'liis is inoreoxcr conlii-ined l>\ the oliser\alion that in 



■=\r--^.. 



'l..:^lu 



ƒ/ I, ^Ijj.^A,, , ~|l -•'.11 • ^'11 



the i.uineralors and the deiKMuinators are ciihie forms in ).. 



The s<piare of the radius heiiiu' repi'eseiiled l»v the (piotieni oftxNO 

 forihs of order six in ).. the svsleni eonhiins six spheres with ,ni\(Mi 

 radius. 



'<\. The (piadralic surface indicate(l hv lh(> erpiatioii in tangential 

 eoordinates ^. >;. ^ 



1) Their parameters are deterinined hv 



