Wf- (';iti <;k\>I'<'MH (liiH (»ro|>''rly u\h(} ;im CoIIowm: ;i.II IIm! liiM-.iM)!' Hahi- 

 ruliori paHhiiij^ (liroiij^li .'i, |»ouil O of tlic ■ (nno'l.il Ium-, Ioik'Ii <';m'Ii 

 ollif'j' in llii> (ifHiil O. 



W(; }iuv'! Hravvn llic ciirv*; rO^/ ifi li{j;, ) iii üijcIi u way Hial, tin; 

 larig<;nt ^-^ K inl'ü'Hfjcls lli»; H|>ino<]al liti*- in O Tlml lliih in (rn*- in 

 goriomi 'm ovidffjt IVorn iIm; loliowinp;. 



Til»; f,()n;tfion of Üio Hpino'lal liri'; 'm: 



()'z iVz /(Vz y 



I T-: o (H) 



ir now w<; «•alf-nlal'; on( f^l 'ly Ihr; valn';H of' , an'l , 



(Iv'' <)ij'' O/inli/ 



aHor liaviri}^ (mjI ificm c^-zri) ari<l 6',, O, w<; (in<l (o; (H)', 



(2c, 1 Ori,>^ I 2<// i ...)iU,,n |-(W,,y f . .) (2./,.; 1.2/i.:y | ..,)' , -: 0. 



Ah 6', JH nol. '//Cro, w<; lin'l hy firhl approxiniulion lor Ih'- ''rjinition 

 of' il)'; Hpirjo'lal lin<; ; 



2./,-/; I i'„l^y i) ('j^ 



l'forn lliin civnuoy, Ifjorefon; llial fh'; lan^jr/'Jit Jf> ''y lo lic; H(>inoMa) 

 liru; (i(fl, lorrriH an angU; wilh l}i<; linf; O K, ijrij<;w d^ O, 



If' however d^:=z(), ll)f;ri if follows fVoiri fJ^y lliul ll<'; I/ui{^<J)I ir» 

 ^y lo lijf; K(»if)0'lal line <'oinc,i<]<;H willi llie line (fV. h-6 Ihen ;U Ihe 

 Hame li/ne 



6', = O, c, ~ O anO (l, i) 

 poini O nn'lr;r r'oriHiWerafJon JH a plailpoini ';, Woawa*: only in a 

 j>lail[)oinl tljc Kpitio'ial line an'l ll)«; 'Move of' fonla'-r of' a '-on'; <an 

 toueli ('/.u:\ï (A\n',r. 



I Ia.'/- l*'>i'ii't O l.H tl. plfutjfifmt. 

 \h c, = o, c,=:() afMJ d,^ '--. ()''j, Ihe e^juaiioji of' ihe 'Mirve of 



2c^x I d,y* 1- ...:=0 (10) 



So all Ihe eurven of ^'onljjU'i \niHm\% through (he plaifpoJnf touch 



(iiU'h olher ihere an'J f heir furvafure JH Jn<Je|M;n<Jenl of the iWniam'M 



hom Ihe warUtx I* of ihe e^>ne to the plaitpoinl. 



Thai Ihih fturvature 'm alM> in'JefMjndent of Ihe 'lireetion of ihe line 



()!' and therefore rjuife independent of ihe hilujition of /' will b^>i>n 



J>e evident. 



From ''8; follows for ihe e'juation of ihe b|>in^/'Jal line: 



») D. J. KoHTKWK^i Arch. N<}<>rl. Hj 24 ^X) 08^^ J). 

 2j D. J. KoBTKWf/i. J.c. 0:i (1>/^J). 



