,transcrib]'s ,notes3 ,und]scores 80 be=e & aft] a ^w or phrase indicate italics 9 ! orig9al text4 ,equal signs 80 be=e & aft] a ^w or phrase indicate bold 9 ! orig9al text4 ,small capitals h be5 conv]t$ to ,,solid capitals4 ,typographical errors h be5 sil5tly correct$4 ,vol4 ,i4 ,,octob]1 #ahib ,no4 #b4 ,,! ,,kansas ,,univ]sity ,,qu>t]ly ,,cont5ts ,,unicursal ,,curves ,,by ,,me?od ,,( ,,inv]sion1 ,h4 ,b4 ,newson ,,=eign ,,settlem5ts ,,9 ,,kansas1 ,w4 ,h4 ,c>ru? ,,! ,,great ,,_s ,,spr+ ,,m\nd1 ,r4 ,h4 ,s4 ,bailey ,,on ,,pascal',s ,,lima,,on ,,& ,,! ,,c>dioid1 ,h4 ,c4 ,riggs ,,dialect ,,^w-,,li/1 ,w4 ,h4 ,c>ru? ,,publi%$ ,,by ,,! ,,univ]sity ,,lawr5ce1 ,,kansas ,price ( ?is numb]1 #ej c5ts ,ent]$ at ! ,po/-(fice 9 ,lawr5ce z ,second-class matt]4 ,,committee ,,( ,,publication ,e4 ,h4 ,s4 ,,bailey ,f4 ,w4 ,,blackm> ,w4 ,h4 ,,c>ru? ,c4 ,g4 ,,dunlap ,e4 ,,mill] ,s4 ,w4 ,,willi/on ,v4 ,l4 ,,kellogg1 ,,manag+ ,,editor ,,j\rnal ,,publi%+ ,,h\se ,,lawr5ce1 ,,kansas #ahib ,,kansas ,,univ]sity ,,qu>t]ly4 ,,vol4 ,i4 ,,octob]1 #ahib4 ,,no4 #b4 ,unicursal ,curves by ,me?od ( ,inv]sion4 ,,by ,,h5ry ,,byron ,,newson4 ,?is pap] conta9s a summ>y ( ! "w done dur+ ! la/ s*ool ye> by my class 9 ,mod]n ,geometry4 ,s9ce _m ( ! results 7 sugge/$ or entirely wr\ght out by class-room discussion1 x becomes practically impossible to assign to ea* memb] ( ! class 8 sep>ate portion4 ,_m ( ! results 7 contribut$ by ,messrs4 ,m4 ,e4 ,rice1 ,a4 ,l4 ,c&y1 ,h4 ,c4 ,riggs1 & ,miss ,annie ,l4 ,mac,kinnon4 ,! read] :o is n famili> ) ! me?od ( ,geometric ,inv]sion %\ld read ,t[ns5d's ,mod]n ,geometry1 *apt]s ,,ix & ,,xxiv2 or a rec5t monograph entitl$1 8,das ,pr9cep d] ,reziprok5 ,radi510 by ,c4 ,wolff1 ( ,erlang54 ,:5 a conic is inv]t$ f a po9t on ! curve1 ! inv]se curve is a nodal1 circul> cubic4 ,?is is %[n analytically z foll[s3 let ! equation ( ! conic be writt5 ax #b;hxy by #b;gx #b;fy #j2 :i* %[s t ! orig9 is a po9t on ! curve4 ,sub/itut+ = x y x & y ------------------ & ---------------- 1 x y 7x y7 we h z ! equation ( ! inv]se curve ax #b;hxy by #b7;gx fy77x y7 #j4 ,! t]ms ( ! second degree %[ t ! orig9 is a d\ble po9t on ! cubic2 & is a crunode1 acnode1 or cusp1 accord+ z ! conic is a hyp]bola1 ellipse1 or p>abola4 ,! t]ms ( ! ?ird degree break up into ?ree l9e> factors1 viz3 gx fy1 x iy1 & x - iy1 :i* are ! equations ( ! ?ree l9es jo9+ ! orig9 to ! ?ree po9ts :]e ! l9e at inf9ity cuts ! cubic2 ?us %[+ t ! cubic passes ?r\gh ! imag9>y circul> po9ts at inf9ity4 ,s9ce ! above trans=mation is rational1 x foll[s t !re is a 7#a1 #a7 correspond5ce betwe5 ! conic & ! cubic4 ,?is fact is also evid5t f ! nature ( ! me?od ( inv]sion4 ,! cubic has its maximum numb] ( d\ble po9ts1 viz3 "o2 & h5ce is unicursal4 ,?is unicursal circul> cubic may be project$ into ! mo/ g5]al =m ( unicursal cubic2 ! cuspidal v>iety1 h[ev]1 always rema9+ cuspidal4 ,by apply+ ! me?od ( inv]sion to _m ( ! well kn[n !orems ( conics1 new !orems are obta9$ = unicursal1 circul> cubics4 ,if "o ( ^! new !orems /ates a projective prop]ty1 x may at once by ! me?od ( projection be ext5d$ to all unicursal cubics4 ,examples w be giv5 bel[4 ,! foll[+ me?od ( g5]at+ a unicursal cubic is (t5 useful4 ,giv5 two projective p5cils ( rays hav+ _! v]tices at ,a & ,b2 ! locus ( ! int]section ( correspond+ rays is a conic ?r\gh ,a & ,b4 ,inv]t ! :ole sy/em f ,a4 ,! p5cil ?r\gh ,a rema9s z a :ole un*ang$1 :ile ! p5cil ?r\gh ,b inv]ts into a sy/em ( co-axial circles ?r\gh ,a & ,b1 & ! g5]at$ conic becomes a circul> cubic ?r\gh ,a & ,b1 hav+ a node at ,a4 ,n[ project ! :ole figure & we h ! foll[+3--giv5 a sy/em ( conics ?r\gh f\r fix$ po9ts & a p5cil ( rays projective ) x & hav+ its v]tex at "o ( ! fix$ po9ts1 ! locus ( ! int]section ( correspond+ elem5ts ( ! two sy/ems is a unicursal cubic1 hav+ its node at ! v]tex ( ! p5cil1 & pass+ ?r\gh ! ?ree o!r fix$ po9ts4 ,unicursal cubics are divisible into two di/9ct v>ieties1 nodal & cuspidal4 ,! nodal v>iety is a curve ( ! f\r? class & has ?ree po9ts ( inflection1 "o ( :i* is always real4 ,! cuspidal v>iety is ( ! ?ird class & has "o po9t ( inflection 7,salmon1 ,h4 ,p4 ,c41 ,art4 #adg74 ,ea* ( ^! v>ieties =ms a gr\p projective )9 itself2 t is to say1 any nodal cubic may be project$ into e o!r possible nodal cubic1 & ! same is true ) reg>d to ! cuspidal4 ,b a nodal cubic c n be project$ into a cuspidal & vice v]sa4 ,9 apply+ ?is me?od ( inve/igation to ! v>i\s =ms ( unicursal cubics & qu>tics1 only a limit$ numb] ( !orems are giv5 9 ea* case4 ,x w be at once evid5t t _m m !orems might be add$1 b en\gh are giv5 9 ea* case to illu/rate ! me?od & %[ ! range ( its application4 ,x is n necess>y to "w out all ! details1 z ?is pap] is int5d$ to be sugge/ive r ?an exhau/ive4 ,,nodal ,,cubics4 ,if an ellipse be inv]t$ f "o ( its v]tices1 ! inv]se curve is symmetrical ) respect to ! axis2 x has "o po9t ( inflection at inf9ity & ! asymptote is an inflectional tang5t4 ,?is asymptote is ! inv]se ( ! circle ( curvature at ! v]tex4 ,! cubic has two o!r po9ts ( inflection situat$ symmetrically ) respect to ! axis4 ,h5ce ! ?ree po9ts ( inflection lie on a "r l9e1 a projective !orem :i* is consequ5tly true ( all nodal cubics4 ,! axis is evid5tly ! h>monic pol> ( ! po9t ( inflection at inf9ity4 ,s9ce ! axis bisects ! angle betwe5 ! tang5ts at ! node1 x foll[s t ! l9e jo9+ a po9t ( inflection to ! node1 ! two tang5ts at ! node1 & ! h>monic pol> ( ! po9t ( inflection1 =m a h>monic p5cil4 ,!re are ?ree su* l9es1 "o to ea* node1 & ?ree h>monic pol>s2 ^! =m a p5cil 9 involution1 ! tang5ts at ! node be+ ! foci4 ,s9ce ! asymptote is p]p5dicul> to ! axis1 we h by projection ! foll[+ !orem3--?r\gh a po9t ( inflection ,i1 draw any l9e cutt+ ! cubic 9 ,b & ,c4 ,?r\gh ,p ! po9t ( int]section ( ! h>monic pol> & inflectional tang5t ( ,i1 draw two l9es to ,b & ,c4 ,! f\r l9es meet+ 9 ,p =m a h>monic p5cil4 ,! po9t ( contact ( ! tang5t f ,i to ! cubic is on ! h>monic pol> ( ,i4 ,any two inflectional tang5ts meet on ! h>monic pol> ( ! ?ird po9t ( inflection4 ,! locus ( ! foot ( ! p]p5dicul> f ! focus ( a conic on a tang5t is ! auxili>y circle4 ,inv]t+ f ! v]tex1 !re are two po9ts1 ,a & ,b1 on ! axis ( ! curve1 su* t if a circle be drawn ?r\gh "o ( !m & ! node1 cutt+ at "r angles a tang5t circle ?r\gh ! node1 _! po9t ( int]section w be on ! tang5t to ! curve :]e x is cut by ! axis4 ,project+3--?r\gh a po9t ( inflection ,i ( a nodal cubic draw a l9e cutt+ ! cubic 9 ,p & ,q2 !re are two det]m9ate po9ts on ! h>monic pol> ( ,i1 :i* h ! foll[+ prop]ty3--draw a conic ?r\gh ,p1 ,q1 & ! node t\*+ ! cubic2 draw ano!r conic ?r\gh "o ( ^! po9ts1 ,p1 ,q1 & ! node cutt+ ! =m]1 s t _! tang5ts at _! po9t ( int]section1 toge!r ) ! l9es f x to ,p & ,q =m a h>monic p5cil2 ! locus ( su* a po9t ( int]section is ! tang5t f ,i to ! cubic4 ,if ?ree conics circumscribe ! same quadrilat]al1 ! common tang5t to any two is cut h>monically by ! ?ird4 ,inv]t+ f "o ( ! v]tices ( ! quadrilat]al3 if ?ree nodal1 circul> cubics h a common d\ble po9t & pass ?r\gh ?ree o!r fix$ po9ts1 ! common tang5t circle ?r\gh ! common node to any two ( ! cubics is cut h>monically by ! ?ird2 i4 e41 s t ! p5cil f ! node to ! two po9ts ( int]section & ! po9ts ( contact is h>monic4 ,project+ ?is3--giv5 ?ree nodal cubics hav+ a common node & pass+ ?r\gh five o!r fix$ po9ts2 let a conic be pass$ ?r\gh ! common node & two ( ! fix$ po9ts1 t\*+ two ( ! cubics4 ,! p5cil f ! common node to ! po9ts ( contact & ! po9t :]e ! conic cuts ! ?ird cubic is h>monic4 ,! foll[+ !orem may be prov$ 9 simil> mann]3--giv5 a sy/em ( cubics hav+ a common node & pass+ ?r\gh five o!r fix$ po9ts2 let a conic be drawn ?r\gh ! common node & two ( ! fix$ po9ts2 ! l9es drawn f ! po9ts :]e x cuts ! cubics to ! common node =m a p5cil 9 involution4 ,a v>iable *ord drawn ?r\gh a fix$ po9t ,p to a conic subt5ds a p5cil 9 involution at any po9t ,o on ! conic4 ,inv]t+ f ,o3--a sy/em ( circles ?r\gh ! d\ble po9t ( a nodal circul> cubic & any o!r fix$ po9t ,p1 is cut by ! cubic 9 pairs ( po9ts :i* det]m9e at ! node a p5cil 9 involution4 ,project+3--a sy/em ( conics ?r\gh ! node ( a unicursal cubic1 two fix$ po9ts on ! curve1 & any f\r? fix$ po9t1 is cut by ! cubic 9 pairs ( po9ts :i* det]m9e at ! node a p5cil 9 involution4 ,we give ano!r pro( ( ! !orem t ! ?ree po9ts ( inflection ( a nodal cubic lie on a "r l9e4 ,?is is easily %[n by inv]sion & is a beautiful example ( ! me?od4 ,!re are ?ree po9ts on a conic ^: osculat+ circles pass ?r\gh a giv5 po9t on ! conic2 ^! ?ree po9ts lie on a circle pass+ ?r\gh ! giv5 po9t4#a 7,salmon's ,conics1 ,art4 #bdd1 ,ex4 #e47 ,by inv]t+ f ! giv5 po9t & !n project+1 we readily see t !re are ?ree po9ts ( inflection on a nodal cubic :i* lie on a "r l9e4 ,if ! above conic be an ellipse1 ! ?ree osculat+ circles are all real2 b if x be a hyp]bola1 "o only is real4 ,h5ce an acnodal cubic has ?ree real po9ts ( inflection1 :ile a crunodal "o has "o real & two imag9>y4 ,! reciprocals ( _m ( ! !orems ( ?is section are ( int]e/ & w be giv5 "u ,qu>tics4 ,,cuspidal ,,cubics4#b ,inv]t+ ! p>abola f its v]tex we obta9 ! ,cissoid ( ,diocles4 ,! focus ( ! p>abola inv]ts into a po9t on ! cuspidal tang5t :i* ,i %all call ! focus ( ! cissoid4 ,! circle ( curvature at ! v]tex ( ! p>abola inv]ts into ! asymptote ( ! cissoid4 ,?is asymptote is also pla9ly ! inflectional tang5t1 & ! po9t at inf9ity is ! po9t ( inflection4 ,! directrix ( ! p>abola inv]ts into a circle ?r\gh ! cusp ( ! cissoid hav+ ! cuspidal tang5t = a diamet]4 ,hall calls ?is ! directrix circle4 ,! d\ble ord9ate ( ! p>abola :i* is tang5t to ! circle ( curvature ( ! v]tex inv]ts into ! circle usually call$ ! base circle ( ! cissoid4#c ,! cissoid may fairly be call$ ! simple/ =m ( ! cuspidal cubic4 ,its projection & pol> reciprocal are bo? cuspidal cubics4 ,i %all n[ d$uce f ! p>abola a few simple propositions = ! cissoid1 & !n ext5d !m to all cuspidal cubics4 7#a7 ,x is kn[n t ! locus ( ! int]section ( tang5ts to ! p>abola :i* are at "r angles to "o ano!r1 is ! directrix4 ,inv]t+3--! locus ( ! int]section ( tang5t circles to ! cissoid ?r\gh ! cusp & at "r angles to ea* o!r is ! directrix circle4 7#b7 ,= ! p>abola1 two "r l9es ,o ,p & ,o ,q1 are drawn ?r\gh ! v]tex ( ! p>abola at "r angles to "o ano!r1 meet+ ! curve 9 ,p & ,q2 ! l9e ,p ,q cuts ! axis at a fix$ po9t1 ^: abscissa is equal to its ord9ate4 ,inv]t+3--two "r l9es1 ,o ,p & ,o ,q1 are drawn at "r angles to "o ano!r ?r\gh ! cusp ( ! cissoid1 meet+ ! curve 9 ,p & ,q2 ! circle ,o ,p ,q passes ?r\gh ! int]section ( ! axis & asymptote4 7#c7 ,if ! normals at ! po9ts ,p1 ,o1 ,r1 ( a p>abola meet at a po9t1 ! circle ?r\gh ,p ,o ,r w pass ?r\gh ! v]tex4 ,inv]t+3--?r\gh a fix$ po9t & ! cusp ( a cissoid1 ?ree & only ?ree circles c be pass$1 cutt+ ! cissoid at "r angles2 ^! ?ree po9ts ( int]section are coll9e>4 ,f ! geometry ( ! cissoid we see t if any l9e be drawn p>allel to ! asymptote1 cutt+ ! curve 9 two po9ts1 ,b & ,c1 ! segm5t ,b ,c is bisect$ by ! axis4 ,h5ce1 project+ ! curve we h ! foll[+ !orem3--any l9e drawn ?r\gh ! po9t ( inflection is cut h>monically by ! po9t ( inflection1 ! curve1 & ! cuspidal tang5t4 ,?us ! cuspidal tang5t is ! h>monic pol> ( ! po9t ( inflection4 ,! pol> reciprocal ( ?is la/ !orem reads z foll[s3--if f any po9t on ! cuspidal tang5t ! two o!r tang5t l9es be drawn to ! curve1 & a l9e to ! po9t ( inflection1 ^! f\r l9es =m a h>monic p5cil4 ,^! are fundam5tal propositions 9 ! !ory ( cuspidal cubics4 7#d7 ,project+ proposition 7#a7 above1 we h ! g5]aliz$ !orem3--?r\gh ! po9t ( inflection draw any l9e cutt+ ! cubic 9 ,b & ,c2 ?r\gh ,b1 ,c1 & ! cusp draw two conics tang5t to ! cubic1 & int]sect+ 9 a f\r? po9t su* t ! two tang5ts to ! conics at _! po9t ( int]section1 toge!r ) ! two l9es f x to ,b & ,c1 =m a h>monic p5cil2 ! locus ( all su* int]sections is a conic ?r\gh ,b1 ,c1 & ! cusp hav+ ! po9t ( inflection & ! cuspidal tang5t = pole & pol>4 7#e7 ,reciprocat+ 7#d7 we h3--?r\gh any po9t on ! cuspidal tang5t draw ! two o!r tang5ts1 ,b & ,c1 to ! cubic4 ,t\*+ ,b1 ,c1 & ! inflectional tang5t draw two conics1 su* t ! po9ts ( contact ( _! common tang5t1 toge!r ) ! po9ts :]e _! common tang5t cuts ! tang5ts ,b & ,c1 =m a h>monic range2 ! envelope ( su* common tang5ts is a conic hav+ ! cuspidal tang5t & ! po9t ( inflection = pol> & pole4 7#f7 ,project+ 7#b7 we obta9 ! foll[+3--?r\gh ! po9t ( inflection draw any l9e cutt+ ! curve 9 ,b & ,c2 take any o!r two po9ts on ! cubic su* t ! p5cil f ! cusp1 ,o1 ,o 7,b ,p ,c ,q7 is h>monic2 ! conic pass+ ?r\gh ,o ,b ,p ,c ,q w pass ?r\gh ! int]section ( ! cuspidal & inflectional tang5ts4 7#g7 ,reciprocat+ 7#f73--;f any po9t on ! cuspidal tang5t draw two o!r tang5ts1 ,b & ,c1 to ! cubic2 take any two o!r tang5ts1 ,p & ,q1 su* t ! range cut f ! inflectional tang5t by ,b1 ,c1 ,p1 ,q1 is h>monic2 ! conic t\*+ ,b1 ,c1 ,p1 ,q1 & ! inflectional tang5t w also t\* ! l9e jo9+ ! po9t ( inflection & ! cusp4 7#h7 ,project+ 7#c73--?r\gh ! po9t ( inflection draw any l9e cutt+ ! cubic 9 ,b & ,c2 ?r\gh ! cusp ,o & ! po9ts ,b & ,c on ! cubic & any o!r fix$ po9t ,p1 ?ree1 & only ?ree1 conics c be pass$1 su* t ! tang5t to ! conic & cubic at _! rema9+ po9t ( int]section1 toge!r ) ! l9es f x to ,b & ,c1 =m a h>monic p5cil2 ^! ?ree po9ts ( int]section are coll9e>4 ,,sy/ems ,,( ,,cubics ,,?r\gh ,,n9e ,,po9ts4 ,let ,u & ,v be ! equations ( two giv5 cubics1 !n ,u k,v is ! equation ( a sy/em ( cubics ?r\gh _! n9e po9ts ( int]section4 ,twelve cubics ( ?is sy/em are unicursal1 & ! twelve nodes are call$ ! twelve critic c5tres ( ! sy/em4 7,see ,salmon's ,h4 ,p4 ,c41 ,art4 #aij47 ,let ! equation ( ! sy/em be writt5 briefly a ka 7b kb7 x 7c kc7 y u u #j2 "o1 & only "o1 value ( k makes ! absolute t]m vani%2 h5ce "o1 & only "o1 curve ( ! sy/em passes ?r\gh ! orig91 :i* may be any po9t 9 ! plane4 ,make ! equation ( ! sy/em homog5e\s by means ( z1 & diff]5tiate twice ) respect to z2 we obta9 ?us ! equations ( ! pol> conics & pol> l9es ( ! orig9 ) respect to ! sy/em4 ,! pol> conics ( ! orig9 are giv5 by #c7;a ka7 #b 7b kb7 x 7c kc7y u #j2 ?us %[+ t ! pol> conics ( any po9t1 ) respect to ! sy/em ( cubics1 =m a sy/em ?r\gh f\r po9ts4 ,! pol> l9es ( ! orig9 are giv5 by #c7;a ka7 7b kb7 x 7c kc7y #j1 :i* repres5ts a p5cil ( l9es ?r\gh a po9t4 ,suppose n[ ! orig9 to be at "o ( ! critic c5tres2 !n = a p>ticul> value1 k1 all t]ms l[] ?an ! second degree mu/ vani%1 s t a b c #j4 a b c ,! factors ( ! t]ms ( u1 :i* involves k1 repres5t ! tang5ts at ! d\ble po9t to ! nodal cubic1 & also ! pol> conic ( ! orig9 ) respect to ?is nodal cubic4 ,h5ce a critic c5tre is at "o ( ! v]tices ( ! self-pol> triangle ( its sy/em ( pol> conics4 ,! opposite side ( ?is triangle is ! common pol> l9e ( ! critic c5tre ) respect to its sy/em ( pol> conics1 & h5ce x is also ! common pol> l9e ( ! critic c5tre ) respect to ! sy/em ( cubics4 ,! f\r basal po9ts ( ! sy/em ( pol> conics lie two & two ^u ! tang5ts at ! d\ble po9t ( ! nodal cubic4 ,:5 ! orig9 is tak5 at "o ( ! n9e basal po9ts ( ! sy/em ( cubics1 a & a bo? vani%4 ,h5ce x is readily se5 t a basal po9t ( a sy/em ( cubics is also a basal po9t ( its sy/em ( pol> conics & ! v]tex ( its p5cil ( pol> l9es4 ,suppose two ( ! basal po9ts ( ! sy/em ( cubics to co9cide1 !n e cubic ( ! sy/em1 9 ord] to pass ?r\gh two co9cid5t po9ts1 mu/ t\* a common tang5t at a fix$ po9t4 ,! common tang5t is ! common pol> ( its po9t ( contact1 bo? ) respect to ! sy/em ( cubics & to its sy/em ( pol> conics4 ,h5ce ! union ( two basal po9ts gives rise to a critic c5tre4 ,! self-pol> triangle ( its sy/em ( pol> conics "h r$uces to a limit$ portion ( ! common tang5t4 ,?is l9e is n a tang5t to ! nodal cubic1 b only passes ?r\gh its d\ble po9t4 ,suppose ?ree ( ! basal po9ts ( a sy/em ( cubics to co9cide1 su* a po9t w !n be a po9t ( inflection on ea* cubic ( ! sy/em4 ,=1 9 ! la/ case1 if a l9e be drawn f ! po9t ( contact ( ! common tang5t to a ?ird basal po9t ( ! sy/em1 su* a l9e w be a common *ord ( ! sy/em ( cubics4 ,suppose1 n[1 ?is ?ird basal po9t be mov$ along ! curves until x co9cides ) ! o!r two2 !n ! common *ord becomes a common tang5t1 :i* cuts e cubic ( ! sy/em 9 ?ree co9cid5t po9ts1 & h5ce is a common inflectional tang5t4 ,s9ce ! pol> conic ( a po9t ( inflection on a cubic consi/s ( ! inflectional tang5t & ! h>monic pol> ( ! po9t1 & s9ce ! pol> conics ( a fix$ po9t ) respect to a sy/em ( cubics pass ?r\gh f\r fix$ po9ts1 x foll[s t 9 a sy/em ( cubics hav+ a common po9t ( inflection & a common inflectional tang5t ! h>monic pol>s ( ! common po9t ( inflection meet 9 a po9t4 ,s9ce ! common inflectional tang5t is ! common pol> l9e ( ! common po9t ( inflection1 x foll[s t su* a po9t is a critic c5tre ( ! sy/em ( cubics4 ,"o cubic ( ! sy/em !n has a node at ! common po9t ( inflection ( ! sy/em1 & =ms an exception4 ,! l9e :i* is ! common inflectional tang5t to ! o!r cubics ( ! sy/em cuts ?is also 9 ?ree po9ts1 b is "o ( ! tang5ts at ! d\ble po9t2 ! o!r tang5t at ! d\ble po9t goes ?r\gh ! v]tex ( ! p5cil ( h>monic pol>s4 ,x is evid5t t ! n9e basal po9ts ( a sy/em ( conics may unite into ?ree gr\ps ( ?ree ea*4 ,! cubics w !n all h ?ree common po9ts ( inflection1 & at ^! po9ts ?ree common inflectional tang5ts4 ,^! ?ree po9ts all lie on a l9e4 ,:5 f\r basal po9ts ( ! sy/em ( cubics co9cide1 su* a po9t is a d\ble po9t on e cubic ( ! sy/em4 ,?is is easily %[n z foll[s1 us+ ! me?od ( inv]sion4 ,let a sy/em ( conics ?r\gh f\r po9ts be inv]t$ f "o ( ! f\r po9ts4 ,! sy/em ( conics inv]ts into a sy/em ( cubics1 hav+ a common node & pass+ ?r\gh ?ree o!r f9ite fix$ po9ts & ! two circul> po9ts at inf9ity4 ,s9ce ! common node c\nts z f\r po9ts ( int]section1 x foll[s t any two cubics ( ! sy/em1 & h5ce all ( !m1 int]sect 9 n9e po9ts4 ,?is sy/em c be project$ into a sy/em hav+ a common d\ble po9t & pass+ ?r\gh any five o!r fix$ po9ts4 ,a numb] ( !orems conc]n+ ! sy/em ( cubics c easily be inf]r$ f kn[n !orems conc]n+ ! sy/em ( conics4 ,s9ce two conics ( ! sy/em are p>abolas1 x foll[s t two cubics ( ! sy/em are cuspidal4 ,s9ce ?ree conics ( ! sy/em break up into pairs ( "r l9es1 x foll[s t ?ree cubics ( ! sy/em break up into a "r l9e & a conic4 ,ea* "r l9e & its correspond+ conic int]sect 9 ! common d\ble po9t4 ,! l9e at inf9ity cuts ! sy/em ( conics 9 pairs ( po9ts 9 involution1 ! po9ts ( contact ( ! two p>abolas ( ! sy/em be+ ! foci2 x foll[s on inv]sion t ! pairs ( tang5ts to ! cubics at _! common node =m a p5cil 9 involution1 ! two cuspidal tang5ts be+ ! foci4 ,if ! f\r basal po9ts ( ! sy/em ( conics lie on a circle1 ?is circle inv]ts into a "r l9e1 & "o cubic !n consi/s ( ?is "r l9e & ! l9es jo9+ ! c5tre ( inv]sion to ! circul> po9ts at inf9ity4 ,?is !orem may be /at$ = ! sy/em ( cubics z foll[s3 if ! conic det]m9$ by ! five basal po9ts ( ! sy/em ( cubics 7n c\nt+ ! common d\ble po9ts71 break up into "r l9es1 ! l9e pass+ ?r\gh ?ree ( ! five po9ts1 toge!r ) ! l9es jo9+ ! o!r two po9ts to ! common node1 con/itute a cubic ( ! sy/em4 ,if ?ree ( ! f\r basal po9ts ( ! sy/em ( conics lie on a l9e1 ! conics consi/ ( ?is l9e & a p5cil ( l9es ?r\gh ! f\r? basal po9t4 ,inv]t+ f ?is f\r? po9t & !n project+1 we h a sy/em ( cubics consi/+ ( a p5cil ( l9es & a conic ?r\gh ! v]tex & ! f\r o!r fix$ po9ts4 ,h5ce1 :5 ! five fix$ po9ts ( su* a sy/em ( cubics lie on a conic ?r\gh ! common node1 ?is conic is a "p ( e cubic ( ! sy/em4 ,if we inv]t ! above sy/em ( conics f "o ( ! ?ree po9ts on ! "r l9e1 & !n project1 we obta9 a sy/em ( cubics :i* consi/s ( a sy/em ( conics ?r\gh f\r fix$ po9ts1 & a fix$ "r l9e ?r\gh "o ( ^! f\r po9ts4 ,h5ce1 if two ( ! five basal po9ts ( su* a sy/em ( cubics be on a l9e ?r\gh ! common node1 ?is l9e is a "p ( e cubic ( ! sy/em4 ,if a sy/em ( conics hav+ "o basal po9t at inf9ity be inv]t$ f "o ( ! rema9+ basal po9ts1 ?is po9t at inf9ity inv]ts to ! c5t] ( inv]sion1 & we obta9 a sy/em ( cubics hav+ five co9cid5t basal po9ts & h5ce pass+ ?r\gh only f\r o!rs4 ,! sy/em ( cubics is n[ s arrang$ t "o tang5t at _! common d\ble po9t is common to all4 ,only "o cubic ( ! sy/em is cuspidal4 ,z be=e ?ree cubics break up into a "r l9e & conic4 ,if two ( ?ree basal po9ts ( ! sy/em ( conics be at inf9ity1 ! sy/em ( cubics obta9$ by projection & inv]sion has six co9cid5t basal po9ts & h5ce only ?ree o!rs4 ,?is sy/em has bo? tang5ts at ! common node common to all cubics ( ! sy/em4 ,if ! two basal po9ts at inf9ity 9 ! sy/em ( conics be co9cid5t1 all ! conics are p>abolas1 & h5ce all ! cubics ( ! sy/em are cuspidal & h a common cuspidal tang5t4 ,if ?ree ( ! basal po9ts ( ! sy/em ( conics be at inf9ity1 ! conics consi/ ( ! l9e at inf9ity & a p5cil ( l9es ?r\gh ! f9ite basal po9t4 ,inv]t+ f ! latt]1 we obta9 a sy/em ( cubics ) sev5 co9cid5t basal po9ts4 ,?is sy/em is made up ( a p5cil ( l9es meet+ 9 ! sev5 co9cid5t basal po9ts toge!r ) ! two l9es jo9+ ?is to ! o!r two basal po9ts ( ! sy/em4 ,^! two l9es are "p ( e cubic ( ! sy/em4 ,if "o ( ! rema9+ basal po9ts be mov$ up to jo9 ! sev5 co9cid5t ones1 "o ( ^! fix$ l9es becomes indet]m9ate1 & ! sy/em ( cubics ?r\gh eight co9cid5t po9ts consi/s ( a fix$ l9e ?r\gh ! eight co9cid5t po9ts & ! n9? fix$ po9t toge!r ) any two l9es ( ! p5cil ?r\gh ! eight po9ts4 ,if ! n9e basal po9ts co9cide1 any ?ree l9es ?r\gh x =m a cubic ( ! sy/em4 ,,unicursal ,,qu>tics4 ,! inv]se ( a conic f any po9t n on ! curve is a nodal bicircul> qu>tic4 ,?is is %[n by inv]t+ ! g5]al equation ( ! conic ax #b;hxy by #b;gx #b;fy c #j2 x y by sub/itut+ = x & y1 ------------------ & -------------------- 1 7x y7 7x y7 we get ! equation ax #b;hxy by #b7;gx fy77x y7 c7x y7 #j4 ,! orig9 is evid5tly a d\ble po9t on ! curve1 & is a crunode1 acnode1 or cusp accord+ z ! conic is a hyp]bola1 ellipse1 or p>abola4 ,! factors ( ! t]ms ( ! f\r? degree1 viz3 7x iy7 7x iy7 7x - iy7 7x - iy71 %[ t ! two imag9>y circul> po9ts at inf9ity are d\ble po9ts on ! qu>tic1 :i* is ?us tr9odal4 ,h5ce ?is nodal1 bicircul> qu>tic c be project$ into ! mo/ g5]al =m ( ! tr9odal qu>tic4 ,tr9odal qu>tics are unicursal4 ,if ! conic :i* we inv]t be a p>abola1 ! qu>tic has two nodes & "o cusp4 ,if ! conic be inv]t$ f a focus1 ! qu>tic has ! two circul> po9ts at inf9ity = cusps4 ,?is is be/ %[n analytically z foll[s3 let ! equation ( ! conic1 orig9 be+ at ! focus1 be writt5 x y #b;aex b ------ ------ -------- - ------ #j4 a b a a ,inv]t+ ?is we h x y #b;aex7x y7 b7x y7 ------ ------ ------------------------------ - -------------------------------- #j4 a b a a ,n[ trans=m ?is equation s t ! l9es jo9+ ! orig9 to ! circul> po9ts at inf9ity %all be ! axes ( ref]5ce4 ,to d ?is let x iy x & x - iy y2 x y x - y x ---------------- & y ---------------- 4 #b #b;i4 ,mak+ ^! sub/itutions & r$uc+ we h 7dropp+ ! subscripts71 7x #bxy y7 7x - #bxy y7 #d;aexy7x y7 bxy ---------------------------------- - ---------------------------------- - ------------------------ - ------------------ #j4 a b a a ,mak+ ?is equation homog5e\s by means ( z1 we h 7x #bxy y7 7x - #bxy y7 #d;aexyz7x y7 bxy z -------------------------------- - -------------------------------- - -------------------------- - ------------------ a b a a #d;aexyz7x y7 bxy - -------------------------- - ------------------ #j1 a a :i* is ! equation ( ! qu>tic ref]r$ to ! triangle =m$ by ! ?ree nodes4 ,we are n[ able to det]m9e ! nature ( ! node at ! v]tex 7y1 z74 ,factor x out ( all ! t]ms :i* conta9 x2 & arrange ?us3 z z #d;aeyz by yz yz #b;aeyz x ------ - ------ - ---------- - ------------ #bx -------- -------- - -------------- a b a a a b a yz yz ------------ - ------------ #j4 a b ,! quantity :i* multiplies x repres5ts ! two tang5ts at ! d\ble po9t 7y1 z72 b ?is quantity is a p]fect squ>e & h5ce we h a cusp4 ,9 ?is way ! po9t 7x1 z7 may be %[n to be a cusp4 ,la/ly1 :5 a p>abola is inv]t$ f ! focus1 we obta9 a tricuspidal qu>tic4 ,! tr9odal qu>tic c be g5]at$ 9 a mann] analog\s to t %[n = ! nodal cubic4 ,let two projective p5cils ( rays h _! v]tices at ,a & ,b1 ! locus ( int]section ( correspond+ rays is a conic ?r\gh ,a & ,b4 ,inv]t f any po9t ,o 9 ! plane1 & we obta9 two sy/ems ( co-axial circles1 ,o ,a be+ ! axis ( "o & ,o ,b ( ! o!r4 ,! locus ( int]section ( correspond+ circles is a bicircul> qu>tic hav+ a node at ,o4 ,project+ ! :ole figure we h ! foll[+ !orem3--two projective sy/ems ( conics ?r\gh ,o ,p ,q ,a & ,o ,p ,q ,b g5]ate by _! correspond+ int]sections a tr9odal qu>tic hav+ its nodes at ,o1 ,p1 & ,q1 & pass+ ?r\gh ,a & ,b4 ,x is evid5t t ! qu>tic g5]at$ 9 ?is way may h ?ree nodes1 "o node & two cusps1 two nodes & "o cusp1 or ?ree cusps1 dep5d+ ^u ! nature ( ! conic inv]t$ & ! c5tre ( inv]sion4 ,mak+ ?is ! basis ( classification we ?us di/+ui% f\r v>ieties ( unicursal qu>tics4 ,to ^! mu/ be add$ a fif? v>iety1 viz3 ! qu>tic ) a triple po9t4 ,ea* ( ^! v>ieties w be consid]$ sep>ately4 ,! me?od ( treat+ unicursal qu>tics giv5 9 ?is & ! next f\r sections is 9 "s respects simil> to t sugge/$ by ,cayley 9 ,salmon's ,high] ,plane ,curves4 ,b ! me?od "h sket*$ out is v diff]5t 9 its po9t ( view & mu* wid] 9 its application1 yield+ a multitude ( new !orems n sugge/$ by ,cayley's me?od4 ,,tr9odal ,,qu>tics4 ,! qu>tic ) ?ree d\ble po9ts is a curve ( ! six? class hav+ f\r d\ble tang5ts & six cusps 7,salmon's ,h4 ,p4 ,c4 ,art4 #bdc74 ,h5ce its reciprocal is ( ! six? degree ) f\r d\ble po9ts1 six cusps1 ?ree d\ble tang5ts1 & no po9ts ( inflection4 ,! locus ( int]section ( tang5ts to a conic at "r angles to "o ano!r is a circle4 ,inv]t+3--! locus ( int]section ( circles ?r\gh ! node & tang5t a nodal1 bicircul> qu>tic & at "r angles to "o ano!r is a circle4 ,project+3--?r\gh ! ?ree nodes ( a qu>tic draw two conics1 ea* t\*+ ! qu>tic & int]sect+ s t ! two tang5ts to ! conics at _! po9t ( int]section1 toge!r ) ! l9es f x to two ( ! nodes1 =m a h>monic p5cil2 ! locus ( all su* int]sections is a conic ?r\gh ^! two nodes4 ,:5ev] ! two tang5ts to ! qu>tic f ! ?ird node1 toge!r ) ! l9es f x to ! o!r two nodes1 =m a h>monic p5cil1 ?is la/ conic breaks up into two "r l9es4 ,any *ord ( a conic ?r\gh ,o is cut h>monically by ! conic & ! pol> ( ,o4 ,inv]t+ f ,o & project+3--f "o ( ! nodes ( a tr9odal qu>tic draw ! two tang5ts to ! qu>tic 7n tang5ts at ! node72 draw ! conic ?r\gh ^! two po9ts ( contact & ! ?ree nodes2 any l9e ?r\gh ! fir/ m5tion$ node is cut h>monically by ?is conic1 ! qu>tic & ! l9e jo9+ ! o!r two nodes4 ,if a triangle circumscribe a conic1 ! ?ree l9es f ! angul> po9ts ( ! triangle to ! po9ts ( contact ( ! opposite sides int]sect 9 a po9t4 ,inv]t+ & project+3--?r\gh ! ?ree nodes ( a qu>tic draw ?ree conics t\*+ ! qu>tic2 ?r\gh ! po9t ( int]section ( two ( ^! conics1 ! po9t ( contact ( ! ?ird1 & ! ?ree nodes draw a conic2 ?ree su* conics c be drawn & !y pass ?r\gh a fix$ po9t4 ,! eight po9ts ( contact ( two conics ) _! f\r common tang5ts lie on a conic1 :i* is ! locus ( a po9t1 ! pairs ( tang5ts f :i* to ! two giv5 conics =m a h>monic p5cil4 ,inv]t+ & project+3--two connodal tr9odal qu>tics h f\r common tang5t conics ?r\gh ! ?ree nodes2 _! eight po9ts ( contact lie on ano!r connodal tr9odal qu>tic2 if f any po9t on ! la/ qu>tic f\r conics be drawn ?r\gh ! nodes & tang5t 9 pairs to ! fir/ qu>tics1 any l9e ?r\gh a node is cut h>monically by ^! f\r conics4 ,! eight common tang5ts to two conics at _! common po9ts all t\* a conic4 ,inv]t+ & project+3--two connodal tr9odal qu>tics int]sect 9 f\r o!r po9ts2 eight conics c be drawn ?r\gh ! ?ree nodes tang5t to ! qu>tics at ^! po9ts ( int]section2 ^! eight conics all t\* ano!r connodal tr9odal qu>tic4 ,a s]ies ( conics ?r\gh f\r fix$ po9ts is cut by any transv]sal 9 a range ( po9ts 9 involution4 ,inv]t+ & project+3--a s]ies ( connodal tr9odal qu>tics c be pass$ ?r\gh f\r o!r fix$ po9ts2 any conic ?r\gh ! ?ree nodes cuts ! s]ies ( qu>tics 9 pairs ( po9ts :i* det]m9e at a node a p5cil 9 involution4 ,! conic t\*es two ( ! qu>tics & ! l9es to ! po9ts ( contact are ! foci ( ! p5cil4 ,if ! sides ( two triangles t\* a giv5 conic1 _! six angul> po9ts w lie on ano!r conic4 ,inv]t+ & project+3--if two gr\ps ( ?ree conics ea* be pass$ ?r\gh ?ree nodes & tang5t to ! qu>tic1 _! six po9ts ( int]section 7?ree ( ea* gr\p7 lie on ano!r connodal tr9odal qu>tic4 ,if ! two triangles are inscrib$ 9 a conic1 _! six sides t\* ano!r conic4 ,inv]t+ & project+3--if two gr\ps ( ?ree conics ea* be pass$ ?r\gh ! ?ree nodes ( a qu>tic s t ! ?ree po9ts ( int]section ( ea* gr\p lie on ! qu>tic1 ^! six conics all t\* ano!r connodal tr9odal qu>tic4 ,a triangle is circumscrib$ ab\t "o conic1 & two ( its angul> po9ts are on a second conic2 ! locus ( its ?ird angul> po9t is a conic4--,inv]t+ & project+3--if ?ree conics be drawn ?r\gh ! ?ree nodes ( two connodal tr9odal qu>tics s t !y all t\* "o ( ! qu>tics & two ( _! po9ts ( int]section are on ! o!r qu>tic1 ! locus ( _! ?ird po9t ( int]section is a connodal tr9odal qu>tic4 ,a triangle is inscrib$ 9 "o conic & two ( its sides t\* a second conic2 ! envelope ( its ?ird side is a conic4 ,inv]t+ & project+3--if ?ree conics be drawn ?r\gh ! ?ree nodes ( two connodal tr9odal qu>tics s t _! ?ree po9ts ( int]section lie on "o ( ! qu>tics & two ( !m t\* ! o!r qu>tic1 ! envelope ( ! ?ird conic is ano!r connodal tr9odal qu>tic4 ,! !orems ( ?is section are /at$ 9 ! mo/ g5]al t]ms & are /ill true :5 "o or m ( ! nodes are *ang$ into cusps4 ,x is !re=e n necess>y to give sep>ate !orems = ! case ( "o cusp & two nodes4 ,,nodal ,,bicuspidal ,,qu>tics4 ,a qu>tic ) "o node & two cusps is a curve ( ! f\r? class1 hav+ "o d\ble tang5t & two po9ts ( inflection 7see ,salmon74 ,h5ce its reciprocal is also a nodal bicuspidal qu>tic1 a fact ( :i* frequ5t note w be made 9 ?is section4 ,! inv]se ( a conic ) respect to a focus is a curve call$ ,pascal's ,limaon4 ,f ! pol> equation ( a conic1 ! focus be+ ! pole1 x is evid5t t ! pol> equation ( ! limaon may be writt5 9 ! =m3 e #a r ---- cosx ---- 2 p p :]e e & p are con/ants1 be+ respectively ! ecc5tricity & semi-latus rectum ( ! conic4 ,f ! above equation x is readily se5 t ! curve may be trac$ by draw+ f a fix$ po9t ,o on a circle any numb] ( *ords & lay+ (f a con/ant l5g? on ea* ( ^! l9es1 measur$ f ! circumf]5ce ( ! circle4 ,! po9t ,o is ! node ( ! limaon2 & ! fix$ circle1 :i* ,i %all call ! base circle1 is ! inv]se ( ! directrix ( ! conic4 ,?is is readily %[n z foll[s3--! pol> equation ( ! directrix is r p_/7e cosx74 ,h5ce ! equation ( its inv]se is r 7e cosx7_/p1 :i* is ! equation ( ! base circle ( ! limaon4 ,! envelope ( circles on ! focal radii ( a conic z diamet]s is ! auxili>y circle4 ,inv]t+3--! envelope ( p]p5dicul>s at ! extremities ( ! nodal radii ( a limaon is a circle ) its c5tre on ! axis & hav+ d\ble contact ) ! limaon4 ,project+3--f any po9t on a nodal bicuspidal qu>tic draw l9es to ! ?ree nodes & a f\r? l9e =m+ ) !m a h>monic p5cil2 ! envelope ( all su* l9es is a conic ?r\gh ! two cusps & hav+ d\ble contact ) ! qu>tic2 ! *ord ( contact passes ?r\gh ! node & cuts ! l9e jo9+ ! cusps s t ?is po9t ( int]section1 ! two cusps1 & int]section ( ! d\ble tang5t ) ! cuspidal l9e =m a h>monic range4 ,reciprocat+3--on any tang5t to a nodal bicircul> qu>tic take ! ?ree po9ts :]e x cuts ! two inflectional tang5ts & ! d\ble tang5t1 & a f\r? po9t =m+ ) ^! a h>monic range2 ! locus ( all su* po9ts is a conic t\*+ ! two inflectional tang5ts & hav+ d\ble contact ) ! qu>tic2 ! pole ( ! *ord ( contact is on ! d\ble tang5t2 jo9 ?is la/ po9t to ! int]section ( ! inflectional tang5ts & jo9 ! node ) ! same int]section2 ^! f\r l9es =m a h>moni\s p5cil4 ,if ! tang5t at any po9t ,p ( a conic meet ! directrix 9 ,q1 ! l9e ,p ,q w subt5d a "r angle at ! focus ,o2 ! circle ,p ,o ,q has ,p ,q = a diamet] & h5ce cuts ! conic at ,p at "r angles4 ,inv]t+3--f any po9t ,p on ! limaon draw ,o ,p to ! node ,o2 draw ,o ,q p]p5dicul> to ,o ,p meet+ ! base circle 9 ,q2 ,p ,q is normal to ! limaon at ,p4 ,project+3--f any po9t ,p on a nodal bicuspidal qu>tic draw l9es to ! ?ree nodes & a f\r? h>monic to ^! ?ree2 f ,o draw l9es to ! two cusps & a f\r? h>monic to ^! two & ! l9e ,o ,p2 ! locus ( ! int]section ( ! f\r? l9e ( ea* p5cil is a conic ?r\gh ! ?ree nodes4 ,call ?is ! basal conic ( ! qu>tic4 ,reciprocat+3--on any giv5 tang5t to a nodal bicuspidal qu>tic take its po9ts ( int]section ) ! d\ble tang5t & ! inflectional tang5ts1 & a f\r? po9t h>monic ) ^!2 on ! d\ble tang5t take its po9ts ( int]section ) ! giv5 tang5t & ! inflectional tang5ts1 & a f\r? po9t h>monic ) ^!2 ! envelope ( ! l9es jo9+ ! f\r? po9t ( ^! two ranges is a conic t\*+ ! d\ble & inflectional tang5ts4 ,! locus ( ! foot ( ! p]p5dicul> f ! focus on ! tang5t to a conic is ! auxili>y circle4 ,inv]t+3--draw a circle ?r\gh ! node tang5t to a limaon2 draw ! diamet] ,o ,p ( ?is circle2 ! locus ( ,p is a circle hav+ d\ble contact ) ! limaon1 ! axis be+ ! *ord ( contact4 ,cor42 ! locus ( ! c5tre ( ! tang5t circle is also a circle4 ,project+3--?r\gh ! ?ree nodes ( a nodal bicuspidal qu>tic draw any conic t\*+ ! qu>tic2 ! locus ( ! pole ) respect to ?is conic ( ! l9e jo9+ ! two cusps is a conic2 draw ! *ord ,o ,p ( ! fir/ conic ?r\gh ! node ,o & ! pole ( ! l9e jo9+ ! two cusps2 ! locus ( ,p is a conic ?r\gh ! cusps1 hav+ d\ble contact ) ! qu>tic4 ,if *ords ( a conic subt5d a con/ant angle at ! focus1 ! tang5ts at ! ends ( ! *ords w meet on a fix$ conic1 & ! *ords w envelope ano!r fix$ conic2 bo? ^! conics w h ! same focus & directrix z ! giv5 conic4 ,inv]t+3--draw two nodal radii ( a limaon ,o ,p & ,o ,q1 mak+ a giv5 angle at ,o2 ! envelope ( ! circle ,p ,o ,q is ano!r limaon2 ! locus ( ! int]section ( circles ?r\gh ,o tang5t to ! limaon at ,p & ,q is ano!r limaon4 ,^! two limaons h ! same node & base circle z ! giv5 "o4 ,project+3--?r\gh ! node ,o ( a nodal bicuspidal qu>tic draw a p5cil ( radii 9 involution2 let ,o ,p & ,o ,q be a conjugate pair ( ^! nodal radii2 ! envelope ( ! conic ?r\gh ,p1 ,q1 & ! ?ree nodes1 is ano!r qu>tic ( ! same k9d3 also draw conics ?r\gh ! ?ree nodes tang5t to ! qu>tic at ,p & ,q2 ! locus ( _! po9t ( int]section is ano!r qu>tic ( ! same k9d4 ,^! ?ree qu>tics all h ! same node1 cusps1 & base conic4 ,e focal *ord ( a conic is cut h>monically by ! curve1 ! focus1 & directrix4 ,inv]t+3--e nodal *ord ( a limaon is bisect$ by ! base circle4 ,project+3--e nodal *ord ( a nodal bicuspidal qu>tic is cut h>monically by ! qu>tic1 ! base conic1 & ! l9e jo9+ ! two cusps4 ,reciprocat+3--f any po9t on ! d\ble tang5t ( a nodal bicuspidal qu>tic draw ! o!r two tang5ts to ! qu>tic & a l9e to ! int]section ( ! inflectional tang5ts2 ! f\r? h>monic to ^! l9es envelopes a conic4 ,s9ce ! limaon is symmetrical ) respect to ! axis1 x foll[s t ! two po9ts ( inflection are situat$ symmetrically ) respect to ! axis4 ,h5ce ! l9e jo9+ ! two po9ts ( inflection is p>allel to ! d\ble tang5t4 ,!re=e by projection we inf] ! foll[+ g5]al !orem = ! nodal bicuspidal qu>tic3 ! l9e jo9+ ! two cusps1 ! l9e jo9+ ! two po9ts ( inflection1 & ! d\ble tang5t meet 9 a po9t4 ,also ! f\r? h>monic po9ts on ea* ( ^! l9es lie on a l9e ?r\gh ! node4 ,reciprocat+3--! po9t ( int]section ( ! cuspidal tang5ts1 ! po9t ( int]section ( inflectional tang5ts1 & ! node all lie on a "r l9e4 ,f ! node draw a f\r? h>monic to ?is "r l9e & ! tang5ts at ! node2 draw a f\r? l9e h>monic to ?is "r l9e & ! inflectional tang5ts2 draw a f\r? h>monic to ! cuspidal tang5ts & ?is "r l9e2 ^! ?ree l9es all meet 9 a po9t on ! d\ble tang5t4 ,,tricuspidal ,,qu>tics4 ,a tricuspidal qu>tic is a curve ( ! ?ird class ) "o d\ble tang5t & no inflection4 ,its reciprocal is !re=e a nodal cubic4 ,we %all beg9 by reciprocat+ "s ( ! simpl] prop]ties ( nodal cubics4 ,s9ce ! ?ree po9ts ( inflection ( a nodal cubic lie on a "r l9e1 x foll[s t ! ?ree cuspidal tang5ts ( a tricuspidal qu>tic meet 9 a po9t4 ,! reciprocal ( ! h>monic pol> ( a po9t ( inflection is a po9t on ! d\ble tang5t1 f\nd by draw+ ?r\gh ! po9t ( int]section ( ! ?ree cuspidal tang5ts a l9e =m+ ) !m a h>monic p5cil4 ,?ree su* l9es c be drawn & x is n difficult to di/+ui% !m4 ,all six l9es =m a p5cil 9 involution1 ! l9es to ! po9ts ( contact ( ! d\ble tang5t be+ ! foci4 ,i %all call su* a po9t on ! d\ble tang5t ! h>monic po9t ( ! cuspidal tang5t4 ,s9ce any two inflectional tang5ts ( a nodal cubic meet on ! h>monic pol> ( ! ?ird po9t ( inflection1 x foll[s t any two cusps ( a tr9odal qu>tic & ! h>monic po9t ( ! ?ird cuspidal tang5t lie on a "r l9e4 ,s9ce ! po9t ( contact ( ! tang5ts f a po9t ( inflection ( a nodal cubic is on ! h>monic pol> ( ! po9t1 x foll[s t ! tang5t to ! tricuspidal qu>tic at ! po9t :]e x is cut by a cuspidal tang5t passes ?r\gh ! h>monic po9t ( t cuspidal tang5t4 ,! inv]se ( ! p>abola f a focus is ! c>dioid2 & ! inv]se ( ! correspond+ directrix is ! base circle ( ! c>dioid4 ,! c>dioid projects into a tricuspidal qu>tic & its base circle projects into a conic ?r\gh ! ?ree cusps :i* has ! same g5]al prop]ties z ! base conic ( ! nodal bicuspidal qu>tic4 ,! circle circumscrib+ ! triangle =m$ by ! ?ree tang5ts to a p>abola passes ?r\gh ! focus4 ,inv]t+3--?ree circles ?r\gh ! cusp1 & tang5t to a c>dioid1 int]sect 9 ?ree coll9e> po9ts4 ,project+3--?ree conics ?r\gh ! ?ree cusps ( a tricuspidal qu>tic & t\*+ ! qu>tic int]sect 9 ?ree coll9e> po9ts4 ,reciprocat+3--if ?ree conics t\* ! ?ree inflectional tang5ts ( a nodal cubic & ! cubic itself1 _! ?ree o!r common tang5ts int]sect 9 a po9t4 ,circles describ$ on ! focal radii ( a p>abola z diamet]s t\* ! tang5t ?r\gh ! v]tex4 ,inv]t+ & project+3--f a po9t on a tricuspidal qu>tic l9es are drawn to ! ?ree cusps & a f\r? l9e =m+ a h>monic p5cil2 ! envelope ( ?is f\r? l9e is a conic ?r\gh ! ?ree cusps & t\*+ ! qu>tic at ! po9t :]e ! latt] is cut by "o ( ! cuspidal tang5ts4 ,!re are ?ree su* conics1 "o correspond+ to ea* cusp4 ,at any cusp ! tang5t to its correspond+ base conic1 ! cuspidal tang5t1 & ! l9es to ! o!r two cusps =m a h>monic p5cil4 ,reciprocat+3--on any tang5t to a nodal cubic take ! ?ree po9ts ( int]section ) ! inflectional tang5ts & a f\r? po9t =m+ ) ^! a h>monic range2 ! locus ( ?is f\r? po9t is a conic t\*+ ! ?ree inflectional tang5ts & ! cubic4 ,! tang5t to ! cubic :]e x is t\*$ by ! conic goes ?r\gh a po9t ( inflection4 ,on any inflectional tang5t ! po9t ( contact ( ?is conic1 ! po9t ( inflection1 & ! po9ts ( int]section ( ! o!r two inflectional tang5ts =m a h>monic range4 ,! circle describ$ on any focal *ord ( a p>abola z diamet] w t\* ! directrix4 ,inv]t+3--! circle describ$ on any cuspidal *ord ( a c>dioid w t\* ! base circle4 ,project+3--?r\gh a cusp ,c draw any *ord ( a tricuspidal qu>tic meet+ ! qu>tic 9 ,p & ,o2 draw a conic ?r\gh ,p1 ,o1 & ! o!r two cusps s t ! p5cil at ,p =m$ by ! tang5t to ! conic & ! l9es to ! cusps is h>monic2 all su* conics w t\* ! base conic ( ! cusp ,c4 ,reciprocat+3--f ,o1 on any inflectional tang5t ( a nodal cubic1 draw two tang5ts ,p & ,q to ! cubic2 draw a conic t\*+ ! tang5ts ,p & ,q & ! o!r two inflectional tang5ts s t ! range on "o ( ^! tang5ts =m$ by ! po9t ( contact ( ! conic & ! int]section ( ! ?ree inflectional tang5t is h>monic2 ! envelope ( all su* conics is a conic t\*+ ! ?ree inflectional tang5ts4 ,! directrix ( a p>abola is ! locus ( ! int]section ( tang5ts at "r angles to "o ano!r4 ,inv]t+ & project+3--?r\gh any po9t ,p on ! base conic ( a cusp ,c ( ! tricuspidal qu>tic1 two conics c be drawn ?r\gh ! ?ree cusps & t\*+ ! qu>tic2 _! two tang5ts at ,p & ! l9es to ! o!r two cusps =m a h>monic p5cil2 _! two po9ts ( contact lie on a l9e ?r\gh ,c4 ,reciprocat+3--f any po9t on "o ( ! inflectional tang5ts to a nodal cubic draw ! two tang5ts ,p & ,q2 draw two conics ea* t\*+ ! cubic & ! ?ree inflectional tang5ts1 "o t\*+ ,p & ! o!r ,q2 ! envelope ( _! o!r common tang5t is a conic t\*+ ! ?ree inflectional tang5ts2 ! two po9ts ( contact ( any "o ( ^! common tang5ts & ! po9ts :]e x cuts ! o!r two inflectional tang5ts =m a h>monic range4 ,any two p>abolas :i* h a common focus & _! axes 9 opposite directions cut at "r angles4 ,inv]t+3--any two c>dioids hav+ a common cusp & _! axes 9 opposite directions cut at "r angles4 ,project+3--two tricuspidal qu>tics hav+ common cusps & at "o ( ! cusps ! same cuspidal tang5t1 b ! cusps po9t$ 9 opposite directions1 cut at su* an angle t ! tang5ts at a po9t ( int]section & ! l9es to ! o!r two cusps =m a h>monic p5cil4 ,reciprocat+3--two nodal cubics h common inflectional tang5ts & on "o ( !m ! po9ts ( inflection common1 b ! bran*es ( ! curve on opposite sides ( ! l9e2 any common tang5t to ! two curves is cut h>monically by ! po9ts ( contact & ! o!r two inflectional tang5ts4 ,circles are describ$ on any two focal *ords ( a p>abola z diamet]s2 _! common *ord goes ?r\gh ! v]tex ( ! p>abola4 ,inv]t+3--circles are describ$ on any two cuspidal *ords ( a c>dioid2 ! circle ?r\gh _! po9ts ( int]section & ! cusp goes also ?r\gh ! v]tex ( ! c>dioid4 ,project+3--?r\gh "o ( ! cusps ( a tricuspidal qu>tic draw two *ords2 draw conics ?r\gh ! o!r two cusps & ! extremities ( ea* ( ^! *ords s t ! pole ( ! l9e jo9+ ! o!r two cusps ) respect to ea* ( ^! conics is on ! correspond+ *ord2 ! conic ?r\gh ! po9ts ( int]section ( ^! two conics & ! cusps passes also ?r\gh ! po9t :]e ! cuspidal tang5t ( ! fir/ m5tion$ cusp cuts ! qu>tic4 ,reciprocat+3--on "o ( ! inflectional tang5ts1 ( a nodal cubic take two po9ts ,p & ,q2 draw a pair ( tang5ts f ea* ( ^! po9ts to ! cubic2 draw two conics ea* t\*+ a pair ( ^! tang5ts & ! o!r two inflectional tang5ts1 s t ! pol>s ( ! po9t ( int]section ( ! o!r two inflectional tang5ts ) respect to ea* ( ^? conics pass respectively ?r\gh ,p & ,q2 ! conic t\*+ ! common tang5ts to ^! two conics & ! ?ree inflectional tang5ts t\*es also ! tang5t f ! fir/ m5tion$ po9t ( inflection to ! cubic4 ,,qu>tics ,,) ,a ,,triple ,,po9t4 ,s9ce a triple po9t is analytically equival5t to ?ree d\ble po9ts1 a qu>tic ) a triple po9t is unicursal4 ,su* a qu>tic is obta9$ by inv]t+ a unicursal cubic f its node4 ,! equation ( su* a cubic may be writt5 u u #j1 :]e u & u are homog5e\s functions ( ! second & ?ird degree respectively 9 x & y4 ,h5ce ! equation ( ! inv]se curve is u u 7x y71 :i* %[s t ! orig9 is a triple po9t & ! qu>tic circul>4 ,by project+ ?is all o!r =ms may be obta9$4 ,! nature ( ! triple po9t dep5ds ^u ! relation ( ! l9e at inf9ity to ! cubic be=e inv]sion4 ,?us ! l9e at inf9ity may cut ! cubic 9 ?ree di/9ct po9ts all real1 or "o real & two imag9>y1 9 "o real & two co9cid5t po9ts 7an ord9>y tang5t71 or 9 ?ree co9cid5t po9ts 7an inflectional tang5t74 ,h5ce ! qu>tic may h at ! triple po9t ?ree di/9ct tang5ts all real1 or "o real & two imag9>y1 "o real & two co9cid5t1 or all co9cid5t4 ,?is qu>tic may be g5]at$ 9 a mann] simil> to t us$ = ! curves already discuss$4 ,we %[$ 9 ! section on nodal cubics t a sy/em ( conics ?r\gh ,a1 ,b1 ,c1 ,d1 & a projective p5cil ( rays ) its v]tex at ,a g5]ate by ! int]section ( correspond+ elem5ts a cubic ) a node at ,a4 ,inv]t ! :ole figure f ,a & !n project3--! p5cil ( rays rema9s a p5cil2 ! sy/em ( conics becomes a sy/em ( unicursal cubics hav+ a common node at ,a & pass+ ?r\gh five o!r common po9ts2 ! cubic inv]ts & projects into a qu>tic ) a triple po9t at ,a1 pass+ ?r\gh ! five o!r common po9ts ( ! sy/em ( cubics4 ,! ?ree po9ts ( inflection ( a nodal cubic lie on a "r l9e4 ,inv]t+3--!re are ?ree po9ts on a circul> qu>tic ) a triple po9t ^: osculat+ circles pass ?r\gh ! triple po9t1 & ^! ?ree po9ts lie on a circle ?r\gh ! triple po9t4 ,let ^! ?ree po9ts be designat$ by ,a1 ,b1 & ,c4 ,! l9es f ! triple po9t ,o to ! po9ts ,a1 ,b1 ,c1 & ! common *ord ( ! osculat+ circles at two ( !m =m a h>monic p5cil4 ,?r\gh "o ( ^! po9ts1 ,a1 & ! triple po9t draw a circle t\*+ ! qu>tic2 ! po9t ( contact is on ! common *ord ( ! osculat+ circles at ,b & ,c4 ,f !orems :i* we h already prov$ = a sy/em ( cubics hav+ a common node & pass+ ?r\gh five o!rs fix$ po9ts1 we c inf] o!r !orems = a sy/em ( qu>tics hav+ a common triple po9t & pass+ ?r\gh sev5 o!r fix$ po9ts4 ,= example1 any conic ?r\gh ! common d\ble po9t & two ( ! fix$ po9ts is cut by ! cubics 9 pairs ( po9ts :i* det]m9e at ! node a p5cil 9 involution4 ,h5ce any cubic hav+ its node at ! common triple po9t & pass+ ?r\gh any f\r ( ! fix$ po9ts is cut by ! qu>tics 9 pairs ( po9ts :i* det]m9e at ! common triple po9t a p5cil 9 involution4 ,aga91 ! pairs ( tang5ts to ! cubics at ! common d\ble po9t =m a p5cil 9 involution1 ! two cuspidal tang5ts be+ ! foci ( ! p5cil4 ,inv]t+3--! l9e at inf9ity 7:i* passes ?r\gh two ( ! fix$ po9ts1 i4 e4 ! circul> po9ts7 cuts ! sy/em ( circul> qu>tics 9 pairs ( po9ts 9 involution4 ,project+3--a l9e ?r\gh any two ( ! sev5 fix$ po9ts cuts ! sy/em ( qu>tics 9 pairs ( po9ts 9 involution4 ,s9ce ! l9e at inf9ity t\*es ! inv]se ( a cuspidal cubic1 x foll[s t any l9e ?r\gh two ( ! fix$ po9ts w t\* two ( ! qu>tics ( ! sy/em2 ^! po9ts ( contact are !re=e ! foci ( ! involution4 ,o!r !orems on su* a sy/em ( qu>tics w be giv5 9 ! next section4 ,,sy/ems ,,( ,,qu>tics ,,?r\gh ,,sixte5 ,,po9ts4 ,let ,u & ,v repres5t a sy/em ( qu>tics ?r\gh sixte5 po9ts4 ,s9ce ! discrim9ant ( qu>tic is ( ! #bg? degree 9 ! coeffici5ts x foll[s t !re are #bg values ( k = :i* ! discrim9ant vani%es1 & h5ce #bg qu>tics ( ! sy/em :i* h d\ble po9ts4 ,z 9 case ( cubics ^! #bg po9ts are call$ ! critic c5tres ( ! sy/em4 ,let ! equation ( ! sy/em ( qu>tics be writt5 u u u u u #j4 ,9 a mann] simil> to t employ$ = cubics1 we f9d ! equation ( ! pol> cubics ( ! orig9 ) respect to ! sy/em to be u #bu #cu #du #j4 ,! pol> conics ( ! orig9 are giv5 by u #cu #fu #j2 & ! pol> l9es ( ! orig91 by u #du #j4 ,! orig9 may be any po9t 9 ! plane & h5ce we conclude t only "o qu>tic ( ! sy/em passes ?r\gh a giv5 po9t & t ! pol> cubics ( any po9t =m a sy/em ?r\gh n9e po9ts4 ,! pol> conics ( any po9t =m a sy/em ?r\gh f\r po9ts & ! pol> l9es meet 9 a po9t4 ,if "o ( ! critic c5tres be tak5 = orig91 we c readily see t su* a po9t is also a critic c5tre on ea* ( its sy/ems ( pol> curves4 ,x is ?us at a v]tex ( ! self-pol> triangle ( its sy/em ( pol> conics & ! opposite side ( ! triangle is ! common pol> l9e ( ! critic c5tre ) respect to ea* ( ! sy/ems ( curves4 ,! tang5ts at ! node ( ! nodal qu>tic co9cide ) ^? ( its pol> cubic & ^! we "k co9cide ) ! l9es :i* con/itute its pol> conic4 ,if two ( ! sixte5 basal po9ts co9cide1 su* a po9t is a critic c5tre4 ,! argum5t is ! same z = a sy/em ( cubics4 ,we c also see t two ( ! basal po9ts ( ea* ( its sy/ems ( pol> curves co9cide at ! critic c5tre4 ,! sixte5 basal po9ts ( ! sy/em ( qu>tics may unite two & two s t x is possible to draw a sy/em ( qu>tics t\*+ eight giv5 l9es ea* at a fix$ po9t4 ,if ?ree ( ! basal po9ts ( our sy/em ( qu>tics co9cide1 all ! qu>tics h at su* a po9t a common po9t ( inflection & a common inflectional tang5t4 ,! demon/ration is ! same z t already giv5 = cubics4 ,! sy/em ( pol> cubics ( su* a po9t also h ?is po9t = a common po9t if inflection & ! same tang5t = a common inflectional tang5t4 ,i pref] to %[ ?is analytically = ! sake ( ! me?od4 ,! equation ( ! sy/em ( qu>tics hav+ ! orig9 = a common po9t ( inflection & ! axis ( y = a common inflectional tang5t may be writt5 u u 7,b k,b7xy 7,c k,c7y 7,a k,a7y #j4 ,! equation ( ! pol> cubics ( ! orig9 is !re=e1 u #b7;,b k,b7xy 7,c k,c7y #c7;,a k,a7y #j1 :i* proves ! proposition4 ,! prop]ties ( ! sy/em ( pol> conics ( su* a po9t are !re=e ! same z ^? already prov$ = cubics4 ,"o qu>tic ( ! sy/em has a d\ble po9t at ! common po9t ( inflection ( ! o!rs4 ,:5 f\r basal po9ts co9cide !y give rise ei!r to a common po9t ( undulation or a common d\ble po9t on all ! qu>tics ( ! sy/em4 ,! equation ( ! sy/em hav+ a common po9t ( undulation may be writt5 u 7,a k,a7xy 7,b k,b7xy 7,c k,c7y 7,d k,d7xy 7,e k,e7y 7,f k,f7y #j4 ,!re is "o value ( k = :i* ! la/ t]m vani%es1 & h5ce ! orig9 is a critic c5tre4 ,! pol> cubics ( ! po9t ( undulation break up into a sy/em ( conics ?r\gh f\r po9ts & ! common tang5t at ! common po9t ( undulation4 ,= ! equation ( ! pol> cubics is y7,a k,a7x 7,b k,k7xy 7,c k,c7y #b7;,d k,d7x #b7;,e k,e7y 7,f k,f7 #j4 ,! sy/em ( pol> conics ( ! orig9 consequ5tly breaks up into ! l9e y #j & a p5cil meet+ 9 a po9t4 ,! common tang5t at ! common po9t ( undulation is also ! common pol> l9e ( ! po9t ( undulation4 ,:5 ! f\r co9cid5t basal po9ts =m a common d\ble po9t on ! qu>tic1 x is n difficult to %[ t two ( ! qu>tics are cuspidal at ?is po9t4 ,! pol> cubics ( ! common d\ble po9t =m a sy/em hav+ ! same po9t = common d\ble po9t4 ,! tang5ts to ! qu>tics at ! common node con/itute ! sy/em ( pol> conics & =m a p5cil 9 involution4 ,twelve ( ! sixte5 basal po9ts may unite 9 ?ree gr\ps ( f\r ea* & ! sy/em ( qu>tics is !n tr9odal & passes ?r\gh f\r o!r fix$ po9ts4 ,?is is ! sy/em obta9$ by inv]t+ a sy/em ( conics ?r\gh f\r po9ts & !n project+4 ,a few special cases %\ld be notic$ "h4 ,if ! f\r fix$ po9ts & two ( ! nodes lie on a conic1 ?is conic toge!r ) ! two l9es f ! ?ird node to ! fir/ two con/itute a qu>tic ( ! sy/em4 ,if ! f\r fix$ po9ts lie on a l9e1 ! qu>tic !n consi/s ( ?is l9e & ! sides ( ! triangle =m$ by ! nodes4 ,if ! ?ree nodes & ?ree ( ! fix$ po9ts lie on a conic1 ! sy/em ( qu>tics !n consi/s ( ?is conic & a sy/em ( conics ?r\gh ! ?ree nodes & ! f\r? fix$ po9t4 ,a special case ( a sy/em ( qu>tics ) ?ree nodes is a sy/em ( cubics hav+ a common node & pass+ ?r\gh five o!r fix$ po9ts toge!r ) a l9e ?r\gh two ( !m4 ,if a fif? basal po9t be mov$ up to jo9 ! f\r at ! common node1 ! qu>tics h "o tang5t at ! common node common to all4 ,if six basal po9ts co9cide !y h bo? tang5ts at ! node common to all4 ,9 ?is case "o ( ! qu>tics has a triple po9t at ! common node ( ! o!rs4 ,if sev5 basal po9ts co9cide1 "o ( ^! tang5ts is an inflectional tang5t z well4 ,if eight po9ts co9cide1 bo? are inflectional tang5ts4 ,:5 n9e ( ! basal po9ts ( a sy/em ( qu>tics co9cide1 ! qu>tics h a common triple po9t4 ,?is is nicely %[n by inv]t+ a sy/em ( nodal cubics f ! common node4 ,! inv]se curves =m a sy/em ( qu>tics hav+ a triple po9t & pass+ ?r\gh sev5 o!r fix$ po9ts4 ,! common triple po9t on two qu>tics c\nts = n9e po9ts ( int]section & ! sev5 o!rs make ! requisite sixte54 ,f our k ( a sy/em ( cubics hav+ a common node x is readily inf]r$ t ?ree ( ! qu>tics mu/ ea* break up into a nodal cubic & a "r l9e ?r\gh ! node4 ,if ! sev5 fix$ po9ts ( ! sy/em ( qu>tics lie on a cubic hav+ a node at ! common triple po9t1 ! sy/em ( qu>tics !n consi/s ( ?is cubic & a p5cil ( l9es ?r\gh ! node4 ,if two ( ! sev5 fix$ po9ts lie on a l9e ?r\gh ! common triple po9t1 ! sy/em ( qu>tics !n consi/s ( ?is "r l9e & a sy/em ( cubics ?r\gh ! o!r five po9ts & hav+ a common node at ! common triple po9t4 ,! sy/em ( cubics hav+ a common node may h "o1 two1 or ?ree ( ! o!r basal po9ts at inf9ity2 & ^! may be all di/9ct or two or ?ree ( !m co9cid5t4 ,:5ce we inf] t if ! sy/em ( qu>tics h t5 co9cid5t basal po9ts1 "o ( ! tang5ts at ! triple po9t is common to all ! qu>tics ( ! sy/em4 ,if elev5 basal po9ts co9cide1 two ( ! triple-po9t tang5ts are common to all ! qu>tics4 ,if twelve co9cide1 all ?ree triple-po9t tang5ts are common4 ,^! triple-po9t tang5ts may be all di/9ct1 two co9cid5t1 or all ?ree co9cid5t4 ,if ?irte5 basal po9ts co9cide1 ! sy/em ( qu>tics !n consi/s ( ! ?ree fix$ l9es jo9+ ! multiple po9t to ! o!r ?ree1 toge!r ) a p5cil ( l9es ?r\gh ! multiple po9t4 ,if f\rte5 po9ts co9cide1 two l9es are fix$ & ^! ) any two l9es ( ! p5cil =m a qu>tic ( ! sy/em4 ,if fifte5 po9ts co9cide1 only "o l9e is fix$ & ea* qu>tic consi/s ( ?is l9e & any o!r ?ree ( ! p5cil4 ,:5 all sixte5 po9ts co9cide1 any f\r l9es ?r\gh x =m a qu>tic ( ! sy/em4 ,9 ?is pap] cubic & qu>tic curves only are consid]$4 ,i expect 9 a future pap] to ext5d ! me?ods h]e9 develop$ to curves ( /ill high] degrees4 ,_m ( ! pres5t results c be g5]aliz$ & /at$ = a unicursal curve ( ! n? degree4 ,i h purposely omitt$ all consid]ation ( focal prop]ties ( ^! curves4 ,!re are also _m special =ms ( int]e/ :i* d n prop]ly belong to a g5]al treatm5t ( ! subject4 ,,note ,a4 ,! !orem conc]n+ ! ?ree po9ts on a conic ,a1 ,b1 & ,c1 ^: osculat+ circles pass ?r\gh a f\r? po9t ,o on ! conic1 is due to ,/e9]4 ,f ! prop]ties ( ! h>monic pol>s ( ! po9ts ( inflection on a nodal cubic we may inf] _m o!r !orems conc]n+ ! po9ts ,a1 ,b1 & ,c on a conic4 ,let ! cubic be project$ into a circul> cubic & !n inv]t$ f ! node4 ,its po9ts ( inflection ,a1 ,b1 ,c inv]t into ! po9ts ,a1 ,b1 & ,c4 ,! h>monic pol> ( ,a inv]ts into ! common *ord ,o ,p ( ! circles osculat+ ! conic at ,b & ,c2 & simil>ly = ! o!r h>monic pol>s4 ,! p5cil ,o ,a ,b ,p ,c is h>monic4 ,any circle ?r\gh ,a & ,o meets ! conic 9 ,s & ,t s t ! p5cil ,o ,a ,s ,p ,t is h>monic4 ,! two circles ?r\gh ,o & tang5t to ! conic at ,s & ,t int]sect on ,o ,p4 ,if two circles be drawn ?r\gh ,o & ,a int]sect+ ! conic "o 9 ,s & ,t & ! o!r 9 ,u & ,v1 ! circles ,o ,s ,u & ,o ,t ,v int]sect on ,o ,p2 s also ! circles ,o ,s ,v & ,o ,t ,u4 ,b "o circle c be drawn ?r\gh ,o & ,a & tang5t to ! conic2 its po9t ( contact is on ,o ,p4 ,let l1 m1 & n be ?ree po9ts on ! conic on a circle ?r\gh ,o4 ,draw ! circles ,o ,a l1 ,o ,a m1 & ,o ,a n int]sect+ ! conic aga9 9 l1 m1 n2 l1 m1 n1 are also on a circle ?r\gh ,o1 & ! circles ?r\gh l1 m1 n & l1 m1 n int]sect on ,o ,p4 ,,note ,b4 ,f ! fundam5tal prop]ty ( ! ,cissoid ( ,diocles we c obta9 by inv]sion an int]e/+ !orem conc]n+ ! p>abola4 ,9 ! figure ( ! ,cissoid giv5 9 ,salmon's ,h4 ,p4 ,c4 ,art4 #bad1 ,a ,m ,m ,r1 :5ce ,a ,m ,a ,r - ,a ,m2 or ,a ,r ,a ,m ,a ,m4 ,inv]t+ f ! cusp & repres5t+ ! inv]se po9ts by ! same lett]s1 we h = ! p>abola #a #a #a ------ ------ ---------- 4 ,a ,r ,a ,m ,a ,m ,?is result is int]pret$ z foll[s3--draw ! circle ( curvature at ! v]tex ( a p>abola2 ?is circle is tang5t to ! ord9ate ,b ,d :i* is equal to ! abscissa ,a ,d2 draw a l9e ?r\gh ,a cutt+ ! circle 9 ,r1 ! ord9ate ,b ,d 9 ,m1 & ! p>abola 9 ,m2 !n #a #a #a ------ ------ ---------- 4 ,a ,r ,a ,m ,a ,m ,draw ! circle ) c5tre at ,d & radius ,a ,d2 any *ord ( ! p>abola ?r\gh ! v]tex is cut h>monically by ! p>abola1 ! circle1 & ! d\ble ord9ate ?r\gh ,d4 ,footnotes3 #a ,see note ,a4 #b ,a few ( ! results ( ?is section are due to ! late ,mr4 ,h4 ,b4 ,hall4 #c ,see note ,b4 ,=eign ,settlem5ts 9 ,kansas4 ,a ,,contribution ,,to ,,dialect ,,/udy ,,9 ,,! ,,/ate4 ,explanatory4--,"s ye>s ago :5 ! subject ( dialect /udy 9 ,kansas1 or r ( ,kansas dialect1 0 m5tion$1 ,mr4 ,noble ,pr5tis1 a g5tleman :o is w>rant$ 9 speak+ ) au?ority on ,kansas1 0 incl9$ to ?9k t he settl$ ! "q 9 %ort ord] by decl>+ t !re is no ,kansas dialect4 ,probably ! majority ( intellig5t citiz5s ( ! /ate w\ld turn (f ! subject ) ! same reply4 ,9 ! s5se ( a mode ( spee* common to ! inhabitants ( ,kansas & peculi> to !m1 ,mr4 ,pr5tis 0 inde$ "r4 ,!re is no vocabul>y1 at lea/ no ext5sive vocabul>y1 by :i* ! native ( ,kansas may be recogniz$ 9 ! ,am]ican ,babel4 ,we h no di/9ctive pronunciation by :i* we may be kn[n f ! inhabitants ( ,nebraska or set ap>t f ! citiz5s ( ,miss\ri4 ,! v]b fails to agree ) its subject & ! p>ticiple is depriv$ ( its f9al #8g' ) ab\t equal frequ5cy 9 ,we/]n ,kansas & ,ea/]n ,colorado4 ,b 9 ! same s5se x is true t !re is no ,kansas flora1 no ,kansas fauna2 t is1 !re is no plant & !re is no animal f\nd q g5]ally 9 ,kansas & f\nd n[h]e outside ( ,kansas4 ,! rem>k t !re is no su* ?+ z a ,kansas dialect re/s ^u a misappreh5sion ( :at is meant by ! t]m4 ,9 j ! same way t we speak ( ! flora & ! fauna ( ,kansas we may speak ( ! dialect ( ,kansas4 ,yet to avoid popul> misappreh5sion x may be bett] to speak ( dialect 9 ,kansas1 r ?an ( ,kansas dialect4 ,dialect /udy involves ! obs]vation & description ( all facts conc]n+ ! natural liv+ spee* ( m51 & especially ^? po9ts 9 :i* ! spee* ( individuals or gr\ps diff]s f t ( ! /&>d lit]>y language z repres5t$ 9 classic writ]s & classic speak]s4 ,/&>d lit]>y ,engli% is always a little beh9d ! times4 ,x is ! /uff$ & m\nt$ specim5 9 ! museum4 ,dialect is ! live animal on its native hea?4 ,mo/ p1 inde$1 w ?9k t _! spee* does n diff] mat]ially f /&>d ,engli%4 ,!y say1 8,we speak ne> en\gh alike #8= practical purposes'4 ,b a ?\s& ye>s h5ce ! pronunciation ( our c\ntry may h *ang$ s mu* t x w seem l ano!r language1 & our desc5dants w write le>n$ !ses to prove t we pron\nc$ #8c\gh' l c[ or l cuff4 ,a new language w h gr[n out ( an old "o1 b no "o "k h[ x came ab\t4 ,c>eful dialect /udy w help expla9 x40 ,kansas is a peculi>ly favorable field = dialect /udy4 ,we h "h side by side repres5tatives f ne>ly e /ate 9 ! ,union1 & f a doz5 =eign c\ntries4 ,! obs]v] has "h :at else:]e he mu/ travel ov] half ! _w to f9d4 ,9 a di/rict :]e ! p are all natives1 ! spee* is s ne>ly homog5e\s t x is difficult to f9d any "o :o recognizes ! peculi>ities ( 8 own language1 b "h ! contra/ ( /range tongues /rikes u imm$iately & we become consci\s e>ly ( ! fact t all m5 d n speak alike4 ,/udy ( dialect may be classifi$ "u ! heads ( pronunciation1 gramm> & vocabul>y4 ,( ^! ! la/ two are ! easie/1 & may be c>ri$ on by almo/ any "o ) pleasure & valuable results4 ,pronunciation is ! mo/ difficult ( ^! matt]s to /udy1 z compet5t obs]vation & reports c be made only by "o :o has made a ?or\gh /udy ( ,phonetics4 ,to ^? :o might wi% to take up ! /udy ( ?is bran* ( ! subject1 ,sweet's ,prim] ( ,phonetics1 & ,gr&g5t's 8,v[el ,measurem5ts0 & 8,g]man & ,engli% ,s\nds0 are recomm5d$4 ,9 ! /udy ( dialect vocabul>ies x may become ( ! greate/ importance to e/abli% ! exact locality ( a ^w & ! orig9 ( ! p]sons by :om x is us$4 ,= in/ance1 9 a family ( my acqua9tance ! ^w #8sl&]+' saunt]+ 0 famili>4 ,x 0 a great puzzle to me until ,i le>n$ t "s ( ! *ildr5 _h be5 9 ! c>e ( a ,g]man maid4 ,! ,g]man ^w #8s*l5d]n' sugge/$ ! unque/ionable s\rce ( ! peculi> ^w4 ,z a s\rce ( in=mation reg>d+ ! orig9 ( ! =eign elem5ts ( our population :5 _! native spee* %all h be5 =gott51 b :5 ! influ5ce ( x w be left 9 vocabul>y & pronunciation ,i h ?\ght t a map ( ! /ate ) ! location ( all ! =eign settlem5ts ( ev5 q small size w\ld be ( int]e/ & 9 "t ( great value4 ,9 ! foll[+ pages ,i transmit ! results ( my inquiries s f> z receiv$4 ,x is my int5tion to make ! report complete & to publi% ! map1 :5 z complete z x c be made1 9 colors4 ,unexpect$ difficulties h delay$ ! "w & prev5t$ its be+ complete4 ,i dep5d$ = my in=mation ^u ! ,c\nty ,sup]9t5d5ts ( ! ,/ate1 a class ( unusually intellig5t & well-in=m$ m5 & wom54 ,b 9 n a few cases !re seems to h be5 a suspicion 9 ! m9d ( my correspond5t t ,i might be a special (fic] ( ! /ate try+ to locate violations ( ! law requir+ di/rict s*ools to be conduct$ 9 ,engli%1 & h5ce in=mation reg>d+ s*ools 9 =eign tongue 0 )held or giv5 b p>tially4 ,& 9 "s cases my in=mants 7 n well po/$4 ,a sup]9t5d5t by ! "n ( ,s*au]mann 9 a c\nty conta9+ a t[n call$ ,suabia1 tells me t !re are no =eign]s 9 8 c\nty4 ,9 su* cases "t mu/ be tak5 to secure a correct result4 ,! que/ions ask$ 73 ,locate1 & give orig91 date & approximate numb]s ( any settlem5ts--six or m families--( =eign]s 9 y\r c\nty4 ,d !y /ill use _! language to any ext5t8 ,d !y h *ur* s]vice & s*ools conduct$ 9 _! native tongue8 ,9 _m replies "o or m ( ^! po9ts 0 neglect$ s t ! in=mation is n yet by any means :at ,i desire to make x4 ,h[ev]1 = ! purpose ( dialect /udy approximate correctness 9 location is ( *ief importance1 & accuracy z to numb]s q second>y4 ,?r\gh ! aid ( m9i/]s & o!rs to :om ,i h be5 ref]r$ by ! sup]9t5d5ts ,i hope to make ?is report complete 9 ! foll[+ respects3 ,! m exact limits ( ! settlem5t2 ! numb]s ( ^? =eign-born2 ! prov9ce z well z l& f :i* !y came2 ! numb] ( *ur*es2 ! numb] ( s*ools & ! l5g? ( "t ! same are conduct$4 ,i solicit ! co-op]ation ( ev]yone int]e/$ 9 ?is "w1 & also 9 ! :ole subject ( dialect /udy4 ,z intimat$ above1 int]e/$ obs]v]s c )\t especial tra9+ d a s]vice to sci5ce & at ! same "t f9d a fasc9at+ pa/ime = !mselves by mak+ collections ( words & con/ructions :i* !y believe to be unusual or new4 ,if any su* are s5t to ! writ] !y w be duly ackn[l$g$4 ,!y %\ld 9 e case be accompani$ by a /atem5t ( ! age1 condition & bir?-place ( ! p]son us+ !m4 ,i wi% "h to call att5tion to ! "w ( ! ,am]ican ,dialect ,society :i* exi/s to promote ?is /udy4 ,x desires z wide a memb]%ip z possible1 & memb]%ip is op5 to all int]e/$ 9 ! subject4 ,! publication ( ! ,society1 ,dialect ,notes1 conta9s reports ( ^w-li/s & o!r /udies1 & w be an aid to any :o wi% to und]take simil> "w4 ,subscriptions & memb]%ip fees %\ld be s5t to ,mr4 ,c4 ,h4 ,gr&g5t1 ,treas41 ,cambridge1 ,mass4 ,,reports ,,by ,,c\nties4 ,,at*ison4--,reports no =eign]s1 by ,john ,klopf5/e91 ,supt4 ,,all54--,sw$es & ,danes1 f #fjj to #gjj1 settl$ f #ahgc to #ahhj4 ,h *ur* s]vice1 & f\r to five mon?s s*ool 9 ,sw$i%4 ,grove & ,elsmore t[n%ips4 ,g]mans 9 & ar\nd ,humboldt4 ,,&]son4--,iri% 9 ,re$] t[n%ip1 #ahfj & #ahgd4 ,g]mans1 #ahfj 9 ,putman t[n%ip1 #ahhj 9 ,we/phalia t[n%ip4 ,h bo? *ur* & s*ools 9 ,g]man4 ,,b>b]4--,reports 8no =eign]s wor? mak+ acc\nt (01 by ,j4 ,o4 ,hahn1 ,sup't4 ,,b>ton4--,no report4 ,,b\rbon4--,reports no =eign]s4 ,,br[n4--,no report4 ,,butl]4--,g]mans 7,prussians71 speak+ ,l[ ,g]man1 9 ,fairm\nt & ,milton t[n%ips4 ,hold *ur* s]vices b no s*ools 9 ,g]man4 ,,*ase4--,russian ,m5nonites1 speak+ bo? ,russian & ,g]man1 9 ,diamond ,creek t[n%ip1 no *ur*1 b a portion ( s*ool+ 9 ,g]man4 ,g]mans at ,/rong ,city1 ) bo? *ur* & s*ools 9 _! native tongue4 ,,*atauqua4--,"s ,norwegians & ,sw$es1 #ahgj1 no location giv54 ,nei!r s*ools nor *ur*es 9 native tongue4 ,"o colony ( #8,russians' 7,m5nonites871 :o h also giv5 up _! language4 ,,*]okee4--,weir ,city1 ,fr5* & ,italians1 numb] consid]able4 ,scammon1 ,scot*1 also 9 l>ge numb]s4 ,! ,fr5* & ,italians h nei!r s*ools nor *ur* 9 ! native tongue4 ,g]mans 9 ,ross1 tw5ty families2 ) *ur* orig9ally ,lu!ran1 n[ ,m5nonite2 s*ool irregul>ly dur+ pa/ t5 ye>s4 ,sw$es1 a few families 9 ,*]okee t[n%ip1 h entirely giv5 up ,sw$i% language4 ,! ,scot*1 ,fr5* & ,italians 9 m9es or m9+ indu/ries4 ,,*ey5ne4--,g]mans settl$ 9 #ahhe-hf on ,hackb]ry ,creek1 #afj p]sons2 9 ! nor!a/ corn] ( ! c\nty1 #ajj2 on we/ bord] ( c\nty1 nor? ( ,republican riv]1 #abj2 all ) *ur*es & ! la/ two ) occasional s*ools4 ,sw$es are across ! ,republican adjo9+ la/ nam$ ,g]man settlem5t1 #abj1 ent]$ #ahhf1 hav+ nei!r *ur* nor s*ool 9 ,sw$i%4 ,,cl>ke4--,reports no =eign]s4 ,,clay4--,no report4 ,,cl\d4--,canadian ,fr5* are scatt]$ ov] mu* ( ! c\nty1 ) consid]able settlem5ts 9 & ar\nd ! t[ns ( ,concordia1 ,clyde1 ,/4 ,joseph & ,aurora4 ,9 all !re are *ur*es1 9 ! fir/ ?ree s*ools also conduct$ 9 ,fr5*4 ,norwegians occupy portions ( ,sibley & ,l9coln t[n%ips ) two *ur*es 9 _! own tongue4 ,!y numb] ab\t ?ree hundr$4 ,iri% occupy portions ( ,solomon & ,lyon1 ! s\? "p ( ,m]$i? & ! s\!a/ corn] ( ,grant t[n%ips4 ,,c(fey4--,g]mans 9 ,lib]ty & on bord] ( ,l]oy & ,avon t[n%ip4 ,h *ur* s]vice 9 ,g]man4 ,,coman*e4--,g]mans4 ,a few scatt]$ families4 ,,c[ley4--,a few ,sw$es & ,g]mans1 widely scatt]$4 ,,craw=d4--,iri% & ,fr5* 9 ,grant t[n%ip2 ,sw$es 9 we/ "p ( ,%]man t[n%ip1 h all giv5 up _! language4 ,italians1 ,au/rians & o!r nationalities 9 s\? "p ( ,wa%+ton1 s\!a/ "p ( ,%]idan & all ov] ,bak] t[n%ip1 especially 9 ,pittsburg1 employ$ 9 m9+ & smelt+4 ,,decatur4--,sw$es 9 ,ob]l9 t[n%ip2 ,m5nonites 9 ,prairie ,dog t[n%ip2 ,g]mans 9 & ar\nd ,dresd51 ) ,ca?olic *ur*2 ,bohemians 9 ,j5n+s & ,g>field t[n%ips4 ,,dick9son4--,g]mans1 #ejj 9 numb] settl$ 9 #ahfj 9 ,lib]ty1 ,union & ,lyon t[n%ips4 ,h ?ree *ur*es & two s*ools 9 ,g]man4 ,also 9 ,:eatl&1 ,jeff]son1 ,bonn] & ,ridge t[n%ips1 "o *ur* & a s*ool4 ,sw$es1 #ajj settl$ 9 #ahfj 9 ,c5t] & ,hayes t[n%ip1 ) two *ur*es & "o s*ool 9 ,sw$i%4 ,iri%1 sev]al hundr$ 9 s\? "p ( ,bann] t[n%ip4 ,,doniphan4--,g]mans 9 ,wayne1 ,m>ion & s\!rn "p ( ,c5t]1 ,burr ,oak & ,wa%+ton t[n%ips1 ) *ur* s]vice 9 native tongue4 ,norwegians 9 ea/]n "p ( ,wolf ,riv] t[n%ip4 ,,d\glas4--,!re are ,g]man settlem5ts 9 ,eudora t[n%ip 7#cjj71 ,m>ion t[n%ip 7#fjj71 & ,big ,spr+s t[n%ip 7#ajj71 ) *ur*es 9 all & s*ool 9 ! fir/4 ,!re are ab\t five hundr$ ,g]mans 9 ,lawr5ce1 ) ?ree ,g]man *ur*es4 ,!re are small] settlem5ts ( ,g]mans & ,sc&9avians at sev]al po9ts 9 ! c\nty4 ,,edw>ds4--,g]mans & ,sw$es 9 ,k9sley1 ,jackson & ,tr5ton t[n%ips1 h *ur* s]vice 9 _! "m tongue4 ,,elk4--,sw$es 9 ,pa9t] & ,hood t[n%ips2 ,iri% 9 ,falls t[n%ip2 ,g]mans on ! bord] ( ,elk & ,wild ,cat t[n%ips4 ,none ( ^! h *ur* or s*ool 9 ! native tongue1 b all use x at home4 ,,ellis4--,g]mans f ,russia1 settl$ ab\t #ahgf 9 ,ca!r9e1 ,h>tsook1 ,look\t1 ,:eatl& & ,fre$om t[n%ips1 ab\t #cjjj 9 numb]--"o ?ird ( ! population ( ! c\nty 9 #ahia4 ,!y are ,ca?olics1 & h bo? *ur*es & p>o*ial s*ools conduct$ 9 ,g]man4 ,!y are l>ge :eat-gr[]s4 ,,ellswor?4--,g]mans1 7,me?odi/s7 9 s\? "p ( ,valley t[n%ip2 ,g]mans 7,lu!rans7 9 nor? "p ( ,columbia & ,ellswor? t[n%ips2 ,g]mans 7,bapti/s7 f ,prussia1 9 ,gre5 ,g>d5 & s\? we/ corn] ( ,empire t[n%ips4 ,^! all h *ur* s]vice1 & ! ,lu!rans s*ools 9 _! own tongue4 ,bohemians 9 ,valley & ,noble t[n%ips4 ,,f9ney4--,reports no =eign]s4 ,,=d4--,g]mans 9 ,:eatl& & ,spe>eville t[n%ips4 ,h *ur*1 & "o s*ool conduct$ 9 ,g]man4 ,,frankl94--,no report4 ,,g>field4--,a few scatt]$ families ( ,g]mans4 ,,ge>y4--,iri% 7,connaught7 came into ,jackson1 ,jeff]son & ,lib]ty t[n%ips #ahee1 ab\t #aejj 9 numb]4 ,g]mans 7,anhalt7 ab\t #aejj came into ,jeff]son1 ,mil=d & ,lyon t[n%ips 9 #ahfb4 ,ab\t #cjj ,engli% f ,sussex settl$ 9 ,lyon t[n%ip 9 #ahgj4 ,! ,g]mans ma9ta9 bo? *ur*es & s*ools 9 ,g]man4 ,,gove4--,sw$es 9 ,lewis & s\? "p ( ,gr9nell & s\? we/ corn] ( ,gove t[n%ips4 ,,graham4--,a settlem5t ( ,canadian ,fr5* 7#fjj7 0 made 9 adjac5t p>ts ( ,wild ,horse & ,morelan t[n%ips ab\t #ahhj4 ,!y conduct *ur* s]vice b no s*ools 9 ,fr5*4 ,,grant4--,reports no =eign]s4 ,,gray4--,reports no =eign]s4 ,,greeley4--,sw$es 9 ! nor? we/ "p ( ! c\nty1 h *ur* s]vice & summ] s*ool 9 ,sw$i%4 ,,gre5wood4--,norwegians1 ab\t #bjj1 9 s\? "p ( ,salem t[n%ip1 h *ur* 9 _! own tongue4 ,g]mans 9 ,%ell ,rock t[n%ip1 ab\t #cjj1 also h *ur* 9 _! own language4 ,,hamilton4--,reports no =eign]s4 ,,h>p]4--,g]mans ab\t ! t[n ( ,h>p]4 ,hung>ians s\? ( ,bluff ,city4 ,bo? h *ur* s]vice 9 ,g]man4 ,ab\t #ajj ,fr5* 9 ,odell & ,/ohrville t[n%ips4 ,,h>vey4--,g]mans 7,russian ,m5nonites7 f ,odessa1 a few f ,prussia1 ! latt] speak+ ,l[ ,g]man4 ,!y settl$ f #ahgd to #ahgf 9 ,alta & ,g>d5 t[n%ips1 9 ,pleasant & ! ea/]n "p ( ,newton t[n%ips1 & ab\t ,hal/ead4 ,!y h *ur* & s*ool 9 ,g]man1 b speak ,russian also4 ,fr5* 9 nor? "p ( ,emma t[n%ip1 engag$ 9 rais+ silk worms4 ,,haskell4--,reports no =eign]s4 ,,hodgman4--,g]mans1 ab\t #cj families1 settl$ ab\t #ahhd 9 s\? ea/ corn] ( ,/]l+ t[n%ip2 h prea*+ 9 ,g]man4 ,sw$es 9 nor? we/ corn] ( ,m>5a t[n%ip4 ,,jackson4--,danes 9 ,netawaca & ,:it+ t[n%ips2 ,iri% 9 ,wa%+ton t[n%ip2 nei!r cont9ue to use _! native tongue4 ,,jeff]son4--,g]mans 7,swiss7 9 ,delaw>e1 ,jeff]son & ,k5tucky t[n%ips1 ma9ta9+ *ur* b no s*ools 9 ,g]man4 ,,jewell4--,sw$es1 widely scatt]$ 9 ,s9clair1 ,all51 ,ew+ & ,ezbon t[n%ips4 ,,johnson4--,no report4 ,,ke>ney4--,no report4 ,,k+man4--,a small settlem5t ( ,g]mans 9 ,pet]s t[n%ip1 n us+ ,g]man to any ext5t4 ,a few ,iri% 9 ,union t[n%ip4 ,,ki[a4--,no report4 ,,labette4--,sw$es & ,norwegians settl$ 9 ,valley & ,canada t[n%ips ab\t #ahfi4 ,/ill speak _! language1 b h nei!r *ur* nor s*ool 9 x4 ,,lane4--,reports no =eign]s4 ,,leav5wor?4--,g]man1 9 #ahgc 9 ,ea/on t[n%ip2 9 ,fair t[n%ip 9 #ahgf2 ab\t #fjj 9 ea* place4 ,!y h *ur* s]vice & s*ools 9 ,g]man4 ,,l9coln4--,danes settl$ 9 ,grant t[n%ip 9 #ahfi & s9ce1 #djj 9 numb]4 ,g]mans settl$ 9 ,pleasant t[n%ip 9 #ahgb1 ) #cjj1 & 9 ,indiana t[n%ip 9 #ahfi & lat] ) ab\t #cge4 ,danes & ,g]mans h good s*ools & *ur*es 9 native tongue4 ,bohemians 9 ,highl& t[n%ip 9 #ahgh ) ?irty families4 ,!y speak _! native tongue1 b h no s*ools or *ur*es4 ,,l9n4--,reports no =eign]s4 ,,logan4--,sw$es1 ab\t #bjj1 ab\t ,page ,city1 9 nor? "p ( c\nty4 ,h *ur* & s*ool bo? 9 ,sw$i%4 ,,lyon4--,wel%1 betwe5 #ajjj & #aejj are locat$ 9 & ab\t ,emporia1 ) ?ree *ur*es conduct$ 9 ,wel%4 ,!re is a settlem5t ( ,sc&9avians ne> ,olpe 9 ,c5tre t[n%ip4 ,,m>ion4--,g]mans 7,russian ,m5nonites71 settl$ 9 ,logan1 ,durham1 ,lehigh1 ,risley1 ,m5no1 ,we/ ,bran* & ,lib]ty t[n%ips1 f #ahgj to #ahge1 "s #ejjj 9 numb]4 ,!y speak bo? ,russian & ,g]man1 & h *ur* s]vice & s*ools 9 ! latt] tongue4 ,bohemians1 ab\t #ejj 9 numb] are settl$ 9 ,cl>k t[n%ip4 ,!y speak ,cze* & h *ur* s]vice 9 t language4 ,fr5* to ! numb] ( #bjj settl$ soon aft] #ahgj on ! bord] ( ,grant & ,doyle t[n%ips4 ,!y speak ,fr5* /ill1 b h no s*ools or *ur* s]vice 9 ! language4 ,,m>%all4--,g]mans 7,pomm]anians1 ,hanov]ians1 ,frisians7 to ! numb] ( #bjjj1 settl$ 9 ! we/ "p ( ,m>ysville t[n%ip f be=e #ahfj to #ahgj4 ,!y h bo? *ur* & s*ool 9 _! own tongue4 ,9 ! nor? "p ( ,murray & ! s\? half ( ,v]million t[n%ips are #abjj ,iri%1 :o use only ,engli% 9 *ur* & s*ool4 ,!y came be=e #ahgj4 ,bohemians 9 small numb]s occupy ! nor? "p ( ,guitt>d1 ! nor? we/ corn] ( ,wat]ville & ! s\? "p ( ,blue ,rapids t[n%ips2 ,sw$es a portion ( ! s\? "p ( ,wat]ville t[n%ip4 ,no report z to _! language4 ,,meade4--,no report4 ,,miami4--,g]mans occupy ! nor? "p ( ,wea & ! we/ "p ( ,valley t[n%ips1 ab\t #bjj 9 ea* settlem5t2 ! fir/ has a ,ca?olic1 ! second a ,lu!ran *ur*4 ,iri% occupy ! nor? "p ( ,osage t[n%ip1 also ab\t #bjj 9 numb]4 ,,mit*ell4--,g]mans to ! numb] ( #abjj occupy ,pittsburg1 ,blue ,hill1 & ,c>r ,creek t[n%ips4 ,9 ! fir/ !re is a *ur*1 & a well-att5d$ s*ool 7,ca?olic7 at ,tipton4 ,,montgom]y4--,g]mans to ! numb] ( #ajj are settl$ 9 & ab\t ,indep5d5ce4 ,!y h *ur* s]vice 9 ,g]man 7,lu!ran74 ,,morris4--,sw$es occupy ,diamond ,valley1 ! we/ "p ( ,creek1 & ! nor? "p ( ,p>k] t[n%ips4 ,!y h sev]al *ur*es & occasionally a s*ool conduct$ 9 ,sw$i%4 ,,morton4--,reports no =eign]s4 ,,mcph]son4--,sw$es settl$1 ab\t #ahgj1 9 ,union1 ,smoky ,hill1 ,h>p]1 ,new ,gottl&1 ,delmore1 & portions ( o!r t[n%ips1 9 l>ge numb]s1 sev]al ?\s&4 ,!y h sev]al *ur*es & excell5t s*ools conduct$ 9 ,sw$i%4 ,g]mans 7,russian ,m5nonites7 occupy ,sup]ior1 ,turkey ,creek1 ,m\nd1 ,lone ,tree1 ,k+ ,city1 & portions ( ,mc,pherson & o!r s\!rn t[n%ips1 ) sev]al *ur*es & s*ools4 ,! ,m5nonites numb] ab\t #ejjj & settl$ aft] #ahgf4 ,,nemaha4--,g]mans 7,swiss7 occupy ,nemaha & ,wa%+ton1 & a portion ( ,ri*mond t[n%ips1 ) ,g]man *ur*es & s*ools4 ,iri% are 9 ,cle> ,creek & nor? ea/ corn] ( ,neu*atel t[n%ips4 ,mo/ ( ,neu*atel t[n%ip is occupi$ by ,fr5* 7,swiss74 ,,neo%o4--,g]mans h a consid]able settlem5t 9 ! s\? ea/ corn] ( ,tioga t[n%ip1 ) *ur* s]vice 7,lu!ran7 9 ,g]man2 ano!r 9 ! ea/ "p ( ,l9coln t[n%ip1 :]e ! language is spok51 b )\t *ur* or s*ool4 ,sw$es h settlem5ts 9 ! nor? we/ "p ( ,tioga & ! ea/ "p ( ,big ,creek t[n%ips2 *ur* 9 ! fir/ only1 ?\gh 9 bo? ,sw$i% is spok5 almo/ exclusively4 ,,ness4--,no report4 ,,norton4--,g]mans to ! numb] ( #ajj settl$ ab\t #ahhj 9 ,grant t[n%ip4 ,!y h *ur* s]vice 9 ,g]man4 ,,osage4--,sw$es1 7#gjj 9 numb]17 settl$ 9 ,grant t[n%ip 9 #ahga1 :]e !y h f\r *ur*es conduct$ 9 ,sw$i%4 ,wel% settl$ 9 #ahfi 9 ,arvonia t[n%ip1 & o!rs 9 ! nor? "p ( ,sup]ior t[n%ip1 #gjj 9 numb]4 ,!y h six *ur*es ) s]vices 9 ,wel%4 ,g]mans are 9 ! nor? "p ( ,scranton & ,ridgway t[n%ips1 #bjj 9 numb]2 ,fr5* 9 ! c5tral "p ( ,sup]ior t[n%ip1 #bjj /rong2 ,danes1 #bjj1 9 nor? "p ( ,melv]n & ,olivet t[n%ips2 a consid]able numb] ( ,scot* & ,iri% 9 & ne> ,scranton4 ,mo/ ( ^! latt] are engag$ 9 coal m9+4 ,none ( ! =eign]s h s*ools--except ,sunday s*ools--9 _! native tongue4 ,,osborne4--,g]mans settl$ 9 ,bloom t[n%ip1 :]e !y h bo? *ur* & s*ool 9 _! "m tongue4 ,,ottawa4--,bohemians are locat$ ab\t ! bord] ( ,%]idan & ,f\nta9 t[n%ips2 ,danes 9 ! s\? "p ( ,buckeye t[n%ip2 ,iri%1 arriv$ ab\t #ahhe1 9 ! s\? "p ( ,*apman t[n%ip4 ,none ( ^! h *ur* or s*ool 9 a =eign tongue4 ,,pawnee4--,sw$es settl$ ab\t #ahgg 9 ! we/ "p ( ,g>field & ! nor? "p ( ,walnut t[n%ips1 ab\t #ejj 9 all4 ,!y speak _! native language at home almo/ exclusively1 & h prea*+ 9 x4 ,,phillips4--,g]mans occupy ,m\nd & s\? "p ( ,dayton t[n%ips1 ) prea*+ & p>o*ial s*ool 9 ,g]man4 ,dut* occupy ea/ "p ( ,prairie ,view ) adjac5t portions ( ,long ,isl&1 ,dayton1 & ,beav] t[n%ips1 ) prea*+ 9 ,dut*4 ,"s ,danes & ,sw$es 9 ,cry/al t[n%ip1 & "s scatt]$ ,poles4 ,,pottawatomie4--,g]mans1 ab\t #bejj1 9 we/ half ( ,mill ,creek & adjac5t portions ( ,%]man & ,vi5na t[n%ips1 also 9 ,pottawatomie & adjac5t portions ( ,union1 ,l\isville1 & ,/4 ,george t[n%ips4 ,!re are a few families 9 ,wamego & ,/4 ,m>y's ,mission4 ,!y h sev]al s*ools & *ur*es conduct$ 9 ,g]man4 ,sw$es occupy ! :ole ( ,blue ,valley & ! we/ bord] ( ,gre5e t[n%ips1 & h a small settlem5t 9 ,/4 ,m>y t[n%ip1 numb]+ 9 all #abjj4 ,!y h *ur* s]vice & a p>o*ial s*ool conduct$ 9 ,sw$i%4 ,iri%1 to ! numb] ( #bjjj occupy ,cle> ,creek1 ,emmet1 ,/4 ,m>y & ! bord] ( ,/4 ,cl]e t[n%ips4 ,fr5* 7,canadian71 numb]+ #bjj1 are f\nd 9 ! nor? "p ( ,mill ,creek & 9 ,union t[n%ips1 also a few ab\t ,/4 ,m>y's ,mission4 ,,pratt4--,reports no =eign]s4 ,,rawl9s4--,g]mans 9 nor? ea/ "p ( c\nty ) *ur* & s*ool 9 ,g]man4 ,sw$es 9 ea/ "p ( c\nty1 ,bohemians & ,hung>ians 9 nor? & nor? ea/ portion4 ,,r5o4--,g]mans1 ab\t #cjj1 came 9 #ahhj to nor? ea/ corn] ( ,little ,riv] t[n%ip1 & ab\t #bjj to s\? ea/ corn] ( ,sumn] t[n%ip2 also a settlem5t 9 ! we/ "p ( ,hayes t[n%ip2 ,dut*1 ab\t #cej1 came #ahgh into ,hav5 t[n%ip2 ,russians are settl$ 9 ,salt ,creek & ,m$=d t[n%ips4 ,all h *ur* s]vice & s*ools 9 _! native tongue4 ,!re are also a few ,fr5* & ,danes 9 ! c\nty4 ,,republic4--,no report4 ,,rice4--,!re is a consid]able settlem5t ( ,g]mans 9 ,valley t[n%ip1 also ,p5nsylvania ,g]mans 9 ! we/ "p ( ,/]l+ t[n%ip1 ) ,g]man *ur*es 9 bo?4 ,!re are also "s ,g]mans 9 ! t[n ( ,lyons1 ) a ,g]man *ur*4 ,,riley4--,sw$es1 ab\t #bejj1 occupy ,jackson1 ,sw$e ,creek & adjac5t portions ( ,mayday1 ,c5t]1 ,fancy ,creek & ,%]man t[n%ips4 ,!y h *ur* s]vices & summ] s*ools 9 _! own tongue4 ,bohemians & ,g]mans1 ab\t #ejj toge!r1 occupy ! nor? ea/ "p ( ,sw$e ,creek t[n%ip4 ,,rooks4--,g]mans1 #aj families1 settl$ #ahhj 9 nor? "p ( ,nor?hampton t[n%ip4 ,bohemians1 #aj families1 locat$ 9 nor? "p ( ,logan t[n%ip 9 #ahgi4 ,fr5*1 ab\t #cj families1 s\? we/ corn] ( ,logan1 & same numb] 9 ,tw9 ,m\nd t[n%ip1 settl$ 9 #ahgh1 speak ,fr5* & h prea*+ 9 t tongue4 ,! ,g]mans h *ur* s]vice 9 ,g]man4 ,,ru%4--,g]mans 7,russian ,m5nonites7 are locat$ z foll[s3 9 ,big ,timb] t[n%ip #ge families1 9 ,ill9ois t[n%ip #be families1 9 ,pione] t[n%ip #ej families1 9 ,lone ,/> t[n%ip #ej families1 9 ,bann] t[n%ip #be families1 9 ,g>field t[n%ip #be families1 9 ,belle ,prairie t[n%ip #cj families4 ,9 ea* t[n%ip !re is "o *ur* or m1 b no ,g]man s*ools 7874 ,bohemians are f\nd 9 ,bann] & ,g>field t[n%ips1 ab\t #be families 9 ea*4 ,,russell4--,no report4 ,,sal9e4--,g]mans1 7,bav>ians & ,swabians7 ab\t #bjj1 9 ,gypsum & s\? "p ( ,ohio t[n%ips2 ,sw$es1 #cjjj to #djjj1 9 ,wa%+ton1 ,smolan1 ,falun1 ,lib]ty & ,smoky ,view1 & adjac5t p>ts ( ,spr+ ,creek1 ,summit & ,walnut t[n%ips1 also 9 ,sal9a4 ,! ,sw$es came 9 #ahfh4 ,bo? ,g]mans & ,sw$es h prea*+ & ! latt] h s*ools 9 _! tongue4 ,,scott4--,no report4 ,,s$gwick4--,g]mans1 #cjjj to #djjj1 settl$ f #ahgd-hb 9 ,%]man1 ,gr& ,riv]1 ,g>d5 ,pla91 ,attica & ,union t[n%ips4 ,also ab\t #bjjj ,g]mans 9 ! city ( ,wi*ita4 ,9 bo? places s*ools & *ur*es 9 ,g]man4 ,russians1 ,italians1 ,fr5* & ,sc&9avians are repres5t$1 a few hundr$ ea*1 9 ,wi*ita4 ,9 ! c\ntry t[n%ips a few ,dut* & ,sw$es4 ,,sew>d4--,reports no =eign]s4 ,,%awnee4--,g]mans 7,moravians7 9 ,rossville t[n%ip1 speak _! native tongue almo/ exclusively1 b h nei!r s*ool nor prea*+ 9 ,g]man4 ,,%]idan4--,no reports4 ,,%]man4--,g]mans1 #bj families ab\t ! c5t] ( ! c\nty4 ,sw$es1 #aj families 9 nor? ea/ corn] & #be families 9 s\? we/ corn]4 ,bo? ,g]mans & ,sw$es h s*ools & prea*+ 9 _! native tongue4 ,,smi?4--,g]mans 9 we/ "p ( ,swan & ,c$> t[n%ips1 & on bord] ( ,h>vey & ,bann] t[n%ips1 9 bo? *ur*es1 & 9 ! fir/ s*ools1 9 ,g]man4 ,dut*1 9 ! s\? half ( ,l9coln t[n%ip1 h *ur* b no s*ools4 ,,/af=d4--,g]mans 9 ,hayes & ,coop] t[n%ips1 ?ree hundr$ 9 numb]1 ) two *ur*es hav+ s]vice 9 ,g]man4 ,,/anton4--,a few scatt]$ ,g]mans4 ,,/ev5s4--,no report4 ,,sumn]4--,no report4 ,,?omas4--,a few =eign]s scatt]$ ab\t ! c\ntry2 all anglicis$4 ,,trego4--,no report4 ,,wabaunsee4--,g]mans & "s ,sw$es 9 ,kaw1 ,newbury1 ,mill1 ,f>m]1 ,alma & ,wa%+ton t[n%ips1 ) bo? prea*+ & s*ools 9 ! "m tongue4 ,,wallace4--,sw$es1 to ! numb] ( #cjj1 h settl$ s9ce #ahhh 9 ! s\? we/ corn] ( ! c\nty4 ,!y h *ur* & s*ools 9 ,sw$i%4 ,,wa%+ton4--,g]mans 9 ,frankl91 ,*>le/on1 ,hanov] & nor? "p ( ,%]man t[n%ips1 h bo? *ur* & s*ools 7#f7 conduct$ 9 ,g]man4 ,bohemians are num]\s 9 ,little ,blue t[n%ip2 ,fr5* ab\t midway 9 ,%]man t[n%ip2 ,iri% 9 ,b>nes1 s\? "p ( ,%]man & ,koloko t[n%ips4 ,,wi*ita4--,no report4 ,,wilson4--,sw$es h settl$ s9ce #ahgj 9 ,colfax t[n%ip4 ,!y h prea*+ b no s*ools 9 ,sw$i%4 ,,woodson4--,no report4 ,,wy&otte4--,g]mans1 #aej1 9 nor? we/ corn] ( ,prairie t[n%ip2 ,sw$es1 #cej1 9 ,kansas ,city1 ,kas42 bo? h *ur* s]vice 9 ! native language4 ,wel%1 #bjj1 9 ,ros$ale1 & ,iri% ab\t midway 9 ,wy&otte t[n%ip4 ,,summ>ies4 ,!re are ,g]man settlem5ts ( ?irty or m p]sons 9 ! foll[+ c\nties3 ,all51 ,&]son1 ,butl]1 ,*ase1 ,*autauqua1 ,*]okee1 ,*ey5ne1 ,c(fey1 ,coman*e1 ,c[ley1 ,craw=d1 ,decatur1 ,dick9son1 ,doniphan1 ,d\glas1 ,edw>ds1 ,elk1 ,ellis1 ,ellswor?1 ,=d1 ,g>field1 ,ge>y1 ,gre5wood1 ,h>p]1 ,h>vey1 ,hodgeman1 ,jeff]son1 ,k+man1 ,leav5wor?1 ,l9coln1 ,m>ion1 ,m>%all1 ,miami1 ,mit*ell1 ,montgom]y1 ,mc,pherson1 ,nemaha1 ,neo%o1 ,norton1 ,osage1 ,osborne1 ,phillips1 ,pottawatomie1 ,rawl9s1 ,r5o1 ,rice1 ,riley1 ,rooks1 ,ru%1 ,sal9e1 ,s$gwick1 ,%awnee1 ,%]man1 ,smi?1 ,/af=d1 ,/anton1 ,?omas1 ,wabaunsee1 ,wa%+ton1 ,wy&otte4 ,total1 #fj4 ,sc&9avians 9 settlem5ts ( ?irty or ov] are f\nd 93 ,all51 ,*autauqua1 ,*]okee1 ,*ey5ne1 ,cl\d1 ,c[ley1 ,craw=d1 ,decatur1 ,dick9son1 ,doniphan1 ,edw>ds1 ,elk1 ,gove1 ,greeley1 ,gre5wood1 ,hodgeman1 ,jackson1 ,jewell1 ,labette1 ,l9coln1 ,logan1 ,lyon1 ,m>%all1 ,morris1 ,mc,pherson1 ,neo%o1 ,osage1 ,ottawa1 ,pawnee1 ,phillips1 ,pottawatomie1 ,rawl9s1 ,riley1 ,sal9e1 ,s$gwick1 ,%]man1 ,wabaunsee1 ,wallace1 ,wilson1 ,wy&otte4 ,total1 #dj4 ,settlem5ts ( ,slavonic peoples1 ,bohemians1 ,poles1 ,russians1 or ,hung>ians1 93 ,decatur1 ,ellswor?1 ,h>p]1 ,l9coln1 ,m>%all1 ,ottawa1 ,phillips1 ,rawl9s1 ,r5o1 ,riley1 ,rooks1 ,ru%1 ,s$gwick1 ,wa%+ton4 ,total1 #ad4 ,settlem5ts ( ,iri% h be5 made 93 ,&]son1 ,cl\d1 ,craw=d1 ,dick9son1 ,doniphan1 ,elk1 ,ge>y1 ,jackson1 ,k+man1 ,m>%all1 ,miami1 ,nemaha1 ,osage1 ,ottawa1 ,pottawatomie1 ,wa%+ton1 ,wy&otte4 ,total1 #ag4 ,fr5* are f\nd 9 settlem5ts ( ?irty or m 93 ,*]okee1 ,cl\d1 ,craw=d1 ,doniphan1 ,graham1 ,h>p]1 ,h>vey1 ,nemaha1 ,osage1 ,pottawatomie1 ,rooks1 ,s$gwick1 ,wa%+ton4 ,total1 #ac4 ,italians are 9 ,*]okee1 ,craw=d1 ,s$gwick4 ,total1 #c4 ,wel% 9 ,lyon1 ,osage & ,wy&otte4 ,total1 #c4 ,dut* 9 ,phillips1 ,r5o1 ,s$gwick4 ,total1 #c4 ,scot* are report$ f ,*]okee & ,osage4 ,total1 #b4 ,engli% 9 ,ge>y & ,doniphan4 ,total1 #b4 ,! foll[+ c\nties report t !re are no settlem5ts ( p ( =eign bir? )9 _! bord]s3 ,at*ison1 ,b>b]1 ,b\rbon1 ,cl>ke1 ,f9ney1 ,grant1 ,gray1 ,hamilton1 ,haskell1 ,lane1 ,l9n1 ,morton1 ,pratt1 ,sew>d4 ,total1 #ad4 ,no reports h be5 secur$ f ! foll[+ c\nties3 ,b>ton1 ,br[n1 ,clay1 ,frankl91 ,johnson1 ,ke>ney1 ,ki[a1 ,meade1 ,ness1 ,republic1 ,russell1 ,scott1 ,%]idan1 ,/ev5s1 ,sumn]1 ,trego1 ,wi*ita1 ,woodson4 ,total1 #ah4 ,sev5ty-f\r ( our ,kansas c\nties report settlem5ts ( citiz5s ( =eign bir? 9 numb]s above #cj4 ,9 s _m cases !re is no report or e/imate ( numb]s t x is n wor? :ile to give summ>ies4 ,probably !re are n actually t5 c\nties t h n su* settlem5ts4 ,*ur* s]vices 9 a =eign tongue are held z foll[s3 ,all5 ,s41#d ,&]son ,g41 ,butl] ,g41 ,*ase ,g41 ,*ey5ne ,g41 ,*]okee ,g41 ,cl\d ,f4 ,s41 ,c(fey ,g41 ,decatur ,g41 ,dick9son ,g4 ,s41 ,doniphan ,g41 ,d\glas ,g41 ,edw>ds ,g4 ,s41 ,ellis ,g41 ,ellswor? ,g41 ,=d ,g41 ,ge>y ,g41 ,graham ,f41 ,greeley ,s41 ,gre5wood ,g4 ,s41 ,h>p] ,g4 ,hung41 ,h>vey ,g41 ,hodgeman ,g41 ,jeff]son ,g41 ,leav5wor? ,g41 ,l9coln ,g4 ,du41 ,logan ,s41 ,lyon ,w4 ,g41 ,m>ion ,g4 ,boh41 ,m>%all ,g41 ,miami ,g41 ,mit*ell ,g41 ,montgom]y ,g41 ,morris ,s41 ,mc,pherson ,s4 ,g41 ,nemaha ,g41 ,neo%o ,g4 ,s41 ,norton ,g41 ,osage ,s4 ,wel%1 ,osborne ,g41 ,pawnee ,s41 ,phillips ,g4 ,du41 ,pottawatomie ,g4 ,s41 ,rawl9s ,g41 ,r5o ,g4 ,du4 ,rus41 ,rice ,g41 ,riley ,s41 ,rooks ,f4 ,g41 ,ru% ,g41 ,sal9e ,g4 ,s41 ,s$gwick ,g41 ,%]man ,g4 ,s41 ,smi? ,g4 ,du41 ,/af=d ,g41 ,wabaunsee ,g41 ,wallace ,s41 ,wa%+ton ,g4 ,wilson ,s41 ,wy&otte ,g4 ,s4 ,total1 #eh4 ,?is total ( fifty-eight c\nties 9 :i* *ur* s]vice is held 9 a =eign tongue does n at all indicate ! numb] ( su* *ur*es4 ,9 _m ( ! reports receiv$ ! numb] is n giv51 or m]ely 9 ! plural4 ,^! v incomplete reports indicate "o hundr$ ?irty-eight su* *ur*es2 x is safe to say t ! numb] is ne>ly d\ble ?is4 ,m int]e/+ is ! numb] ( s*ools conduct$ 9 a =eign tongue4 ,! c\nties hav+ !m are3 ,all5 ,s41 ,&]son ,g41 ,*ase ,g41 ,*ey5ne ,g41 ,*]okee1 ,g41 ,cl\d ,f41 ,dick9son ,g4 ,s41 ,d\glas ,g41 ,ellis ,g41 ,ellswor? ,g41 ,=d ,g41 ,ge>y ,g41 ,greeley ,s41 ,h>vey ,g41 ,leav5wor? ,g41 ,l9coln ,g4 ,s41 ,logan ,s41 ,m>ion ,g41 ,m>%all ,g41 ,mit*ell ,g41 ,morris ,s41 ,mc,pherson ,s4 ,g41 ,nemaha ,g41 ,osborne ,g41 ,phillips ,g41 ,pottawatomie ,g4 ,s41 ,rawl9s ,g41 ,r5o ,g4 ,du4 ,rus41 ,riley ,s41 ,ru% ,g41 ,sal9e ,s41 ,s$gwick ,g41 ,%]man ,g4 ,s41 ,smi? ,g4 ,du41 ,wabaunsee ,g41 ,wallace ,s41 ,wa%+ton ,g4 ,total1 #cg4 ,! numb] ( sep>ate s*ools 9 a =eign language s f> z report$ is sev5ty-f\r1 & "h1 too1 x is safe to say t ! actual numb] is mu* l>g]4 ,,explanation4 ,! spaces indicat+ settlem5ts are 9 _m cases too small to admit a complete description ( ! inhabitants1 & accord+ly !y h be5 m>k$ by races r ?an by nationalities & tribes4 8,g]man0 is made to d duty = all inhabitants ( ,g]many :e!r ,l[ or ,high1 z well z = ,au/rians1 ,g]man ,swiss1 & ,russo-,g]man ,m5nonites4 ,! la/ are report$ simply z ,m5nonites1 b are1 ,i believe1 9 all cases ( ,g]man orig94 8,sc&9avian0 is us$ in/ead ( ,sw$e1 ,norwegian & ,dane1 because 9 "s cases ! di/9ction 0 n made 9 ! reports1 & 9 ord] to limit ! numb] ( colors on ! map :i* is to come4 ,9 ! case ( ,scot* ,i h be5 unable to secure in=mation :e!r !y are ,highl&]s or ,l[l&]s1 & 9 case ( ,iri%1 to :at ext5t1 if at all1 !y speak ! old ,iri% language4 ,w4 ,h4 ,,c>ru?4 ,illu/ration3 ,a ,,prelim9>y ,,map ,,( ,,=eign ,,settlem5ts ,,9 ,,kansas4 ,b - ,bohemians 79 a few cases o!r ,slavs7 ,g - ,g]mans 7includ+ ,dut* & ,russian ,m5nonites7 ,s - ,sc&9avians 7,danes1 ,sw$es & ,norwegians7 ,i - ,iri% ,w - ,wel% ,x - ,italians ,f - ,fr5* ,h - ,hung>ians ,footnote3 #d ,g ,g]man1 ,s ,sc&9avian1 ,f ,fr5*1 ,w ,wel%1 ,du ,dut*4 ,! ,great ,_s ,spr+ ,m\nd4 ,,by ,e4 ,h4 ,s4 ,,bailey4 ,! 8,waconda0 or ,great ,_s ,spr+1 :i* is situat$ 9 ,mit*ell ,c\nty1 ,kansas1 ab\t two miles ea/ ( ,cawk] ,city1 has be5 describ$ 9 detail by ,g4 ,e4 ,patrick 9 vol4 vii1 p4 #bb1 ,transactions ( ! ,kansas ,academy ( ,sci5ce4 ,an analysis ( ! wat]1 & ( ! rock =m+ ! m\nd on :i* ! spr+ is locat$1 is also giv54 ,! spr+ is ^u a conical1 lime/one m\nd #db feet 9 height1 & #aej feet 9 diamet] at ! top4 ,! pool itself is a ne>ly circul> lake ab\t #ej feet 9 diamet]1 #ce feet deep1 & ! wat] rises to )9 a few in*es ( ! top ( ! bas94 ,!re is a level space on all sides ( ! spr+ s wide t a c>riage c be readily driv5 ar\nd x4 ,!re is b little indication ( organic matt] 9 ! wat] ( ! l>ge spr+1 ?\gh !re is a slimy :ite deposit adh]+ to ! bottom & sides1 b ! wat] is colorless1 cle>1 & transp>5t4 ,! excess ( wat]1 in/ead ( ov]fl[+ ! bank1 escapes by num]\s small fissures1 f #aj to #bj feet d[n on ! sides1 especially on ! side away f ! bluff4 ,9 ^! lat]al spr+s !re is an abundance ( gre5 alg1 & a :iti% scum1 :i* seems to be deta*$ f ! bottom & to float to ! surface4 ,?is has a slimy1 granul> feel+ sugge/+ 9 a v m>k$ mann] hydrat$ silica4 ,! m\nd is situat$ )9 ab\t #bjj feet ( a lime/one bluff1 :i* rises p]haps #bj feet above ! level ( ! spr+4 ,! natural inf]5ce w\ld be t ! h>d] mat]ial ( ! m\nd protect$ x f ! erosion :i* c>ri$ away ! rock 9 ! valley ( ! ,solomon on ! s\?1 & ! rock betwe5 ! spr+ & ! bluff4 ,is x n possible h[ev] t ! m\nd has be5 really made by ! successive deposits f ! spr+8 ,al?\gh ! m\nd is pla9ly /ratifi$1 ?is ne$ n int]f]e ) ! !ory1 = ! wat] may h be5 int]mitt5t 9 its fl[4 ,! rock is v por\s1 & on be+ gr\nd to a ?9 section is %[n to be concretion>y 9 /ructure4 ,an analysis ( ! wat] ( ! spr+ 7loc4 cit47 %[$ t x conta9$ ov] #aabj gra9s ( m9]al matt] p] gallon1 ( :i* #gge gra9s 7 sodium *loride & #bjf gra9s sodium sulphate1 ) #ff gra9s ( magnesium sulphate1 #da gra9s ( magnesium c>bonate1 & #ca gra9s ( calcium c>bonate4 ,an analysis by ! au?or %[s t !re are #j4hgd gra9s ( silica4 ,samples ( ! rock compos+ ! m\nd1 & ( ! adjo9+ bluff 7 secur$1 & comp>ative analyses made1 ) ! foll[+ results3 ,,great ,,c\ntry ,,_s ,,rock4 ,,m\nd4 ,silica & insoluble residue #b4ad #d4aj ,oxides ( ,iron & ,alum9a #c4bb #eb4ff ,sulphuric ,anhydride 4#jj #j4cd ,c>bon ,dioxide #dj4ij #ci4aj ,calcium ,oxide #ea4ij #di4bh ,magnesium ,oxide #j4fc #a4ae ,wat] & organic matt]1 undet]m9$ #a4ba #fc4cg ------------ ------------ #ajj4jj #ajj4jj ,specific gravity #b4eb #b4gi ,! rocks are entirely diff]5t 9 appe>ance & /ructure1 t ( ! m\nd be+ twice z h>d z t ( ! bluff4 ,! =m] conta9s mu* organic matt] z is %[n by black5+ :5 x is heat$ 9 a tube & giv+ (f ! *>act]i/ic odor4 ,! iron is practically ( ! f]r\s v>iety1 probably comb9$ ) c>bonic acid1 & ! rock conta9s traces ( *lorides4 ,! p>ticul> sample tak5 0 at "s di/ance f ! spr+1 & _h be5 ?or\ghly expos$ to ! wea!r4 ,! rock ( ! m\nd is ( j su* a "* z might h be5 built up by deposition f ! wat]1 z x conta9s ! lea/ soluble con/itu5ts ( ! wat]4 ,! process ( solidification w\ld h be5 assi/$ by ! silica 9 ! wat]1 =m+ insoluble cem5t+ silicates1 z notic$ by ,pr(4 ,patrick4 ,! analysis giv5 above %[s t !re is abundant silica 9 ! wat] = ?is purpose4 ,m5tion has be5 made ( ! organic gr[? 9 ! adjac5t spr+s4 ,! mix$ scum on be+ heat$ *anges f a dull gre5 to a vivid grass-gre51 & if ignit$ x swells up & emits an ill-smell+ vapor1 :i* is evid5tly nitrog5\s 9 its "*4 ,a grayi% :ite a% is left1 :i* conta9s mu* c>bonate ( lime4 ,?is is evid5tly fre%ly deposit$1 z x is entangl$ 9 ! alg 9 granul> lumps4 ,a specim5 ( ! :ite scum1 notic$ above1 only slightly mix$ ) ! gre5 alg1 0 analyz$4 ,! acid solution ( ! a% conta9s #a4bf p] c5t ( soluble silica4 ,?is 0 ( c\rse a comb9$ silica1 probably calcium silicate1 :i* becomes ! cem5t+ mat]ial 9 ! rock4 ,9 ano!r sample ( a%1 aft] remov+ all ! sub/ances soluble 9 hot wat]1 ! residue 0 f\nd to conta9 #gf4df p] c5t ( silica4 ,! silice\s residue f ! scum 0 exam9$ by ,dr4 ,s4 ,w4 ,willi/on4 ,x consi/s mo/ly ( diatoms4 ,he recogniz$ ,navicula-- #b species ,nitzs*ia-- #b species ,a/]onella-- #a species4 ,all ?ree g5]a are f\nd bo? 9 fre% & salt or bracki% wat]4 ,! gre5 mat]ial consi/s ess5tially ( ,oscill>ia & ,conf]v4 ,if ! scum is all[$ to /& = a %ort "t a v /rong sulphurett$ odor is develop$1 /rangely sugge/ive ( salt wat] m>%es or mud flats2 & inde$ ! same odor is notic$ 9 ! vic9ity ( ! spr+4 ,no *>act]i/ic salt wat] organisms1 t %\ld occasion ?is peculi> odor h1 h[ev]1 yet be5 obs]v$ "h4 ,a m ext5d$ & special /udy ( ! organic life ( ^! int]ior salt wat] m>%es & spr+s w\ld be ( great int]e/4 ,footnotes3 #e ,mo/ly ,fe,o1 & s calculat$4 #f ,) alkalies4 ,on ,pascal's ,limaon & ! ,c>dioid4 ,,by ,h4 ,c4 ,,riggs4 ,! inv]se ( a conic ) respect to a focus is a curve call$ ,pascal's ,limaon4 ,f ! pol> equation ( a conic1 ! focus be+ ! pole1 x is evid5t t ! pol> equation ( ! limaon may be writt5 9 ! =m3 e #a r ------ cosx ------ 2 p p :]e e & p are con/ants1 be+ respectively ! ecc5tricity & semi-latus rectum ( ! conic4 ,f ! above equation x is readily se5 t ! curve may be trac$ by draw+ f a fix$ po9t ,o on a circle any numb] ( *ords & lay+ (f a con/ant l5g? on ea* ( ^! l9es1 measur$ f ! circumf]5ce ( ! circle4 ,! po9t ,o is ! node ( ! limaon2 & ! fix$ circle1 :i* ,i %all call ! base circle1 is ! inv]se ( ! directrix ( ! conic4 ,?is is readily %[n z foll[s3--! pol> equation ( ! directrix is r p_/7e cosx74 ,h5ce ! equation ( its inv]se is r 7e cosx7_/p1 :i* is ! equation ( ! base circle ( ! limaon4 ,if ! conic :i* we inv]t be an ellipse1 ! po9t ,o w be an acnode on ! ,limaon2 if ! conic be a hyp]bola1 ! po9t ,o is a crunode4 ,if ! conic be a p>abola1 ,o is !n a cusp & ! inv]se curve is call$ ! ,c>dioid4 ,! limaon may also be trac$ z a r\lette4 ,let ! circle ,a ,c h a diamet] j twice t ( ! circle ,a ,b4 ,!n a giv5 diamet] ( ,a ,c w always pass ?r\gh a fix$ po9t ,q on ! circle ,a ,b1 7,williamson's ,diff4 ,cal4 ,art4 #bhf7 & w h its middle po9t on ! circle ,a ,b4 ,n[ any po9t ,p on ! diamet] ( ,a ,c w always be at a fix$ di/ance f ,c & w !re=e describe a limaon ( :i* ,a ,b w be ! base circle4 ,! p$al ( a circle ) respect to any po9t is a limaon4 ,?is may be inf]r$ f ! g5]al !orem t ! p$al ( a curve is ! inv]se ( its pol> reciprocal1 7,salmon's ,h4 ,p4 ,c4 ,art4 #abb74 ,= ! pol> reciprocal ( a conic f its focus is a circle & h5ce its p$al is a limaon4 ,! base circle is ! locus ( ! in/antane\s c5tre = all po9ts on ! limaon4 ,let ,b ,o ,p be a l9e cutt+ a circle 9 ,b & ,q4 ,let ! l9e revolve ab\t ,b1 ,q foll[+ ! circle2 ! po9t ,p w trace a limaon4 ,n[1 = any in/ant1 ! in/antane\s c5t] w be ! same :e!r ,q be foll[+ ! circle or ! tang5t at ! po9t :]e ! l9e cuts ! circle4 ,!re=e ! in/antane\s c5t] = ! po9t ,p is f\nd by erect+ a p]p5dicul> to ! l9e ,p ,b1 ?r\gh ,b1 & a normal to ! circle at ,q4 7,williamson's ,diff4 ,cal4 ,art4 #bid74 ,! int]section 7,c7 ( ^! two l9es is ! in/antane\s c5t] = ! curve at ! po9t ,p4 ,b by elem5t>y geometry ,c is on ! circle4 ,n[ z ! l9e ,p ,b revolves ?r\gh #cfj ar\nd ,b1 ! l9e ,b ,c :i* is always p]p5dicul> to x also makes a complete revolution & ! in/antane\s c5t] ,c moves once r\nd ! base circle4 ,bel[ we give a li/ ( !orems obta9$ by inv]t+ ! correspond+ !orems respect+ a conic4 ,9 ^! !orems any circle ?r\gh ! pole is call$ a nodal circle1 any *ord ?r\gh ! pole is call$ a nodal *ord1 & ! l9e ?r\gh ! pole p]p5dicul> to ! axis ( ! curve is call$ ! latus rectum4 ,! lett]s e & p signify respectively ! ecc5tricity & half ! latus rectum ( ! inv]t$ conic4 ,! locus ( ! po9t ( int]section ( two tang5ts to a p>abola :i* cut "o ano!r at a con/ant angle is a hyp]bola hav+ ! same focus & directrix z ! orig9al p>abola4 ,! locus ( ! po9t ( int]section ( two nodal tang5t circles to a c>dioid :i* cut ea* o!r at a con/ant angle is a limaon hav+ ! same d\ble po9t & director circle4 ,! sum ( ! reciprocals ( two focal *ords ( a conic at "r angles to ea* o!r is con/ant4 ,! sum ( any two nodal *ords ( a limaon at "r angles to ea* o!r is con/ant4 ,p ,q is a *ord ( a conic :i* subt5ds a "r angle at ! focus4 ,! locus ( ! pole ( ,p ,q & ! locus envelop$ by ,p ,q are ea* conics ^: lat]a recta are to t ( ! orig9al conic z #b 3 #a & #a 3 #b respectively4 ,if ,p & ,q be two po9ts on a limaon su* t !y int]cept a "r angle at ! node1 !n ! locus ( ! po9t ( int]section ( ! two nodal circles tang5t at ,p & ,q respectively1 is a limaon ^: latus rectum is to t ( ! orig9al limaon z #b 3 #a4 ,& ! envelope ( ! circle describ$ on ,p ,q z a diamet] is a limaon1 ^: latus rectum is to t ( ! orig9al limaon z #a 3 #b4 ,if two conics h a common focus1 two ( _! common *ords w pass ?r\gh ! po9t ( int]section ( _! directrices4 ,if two limaons h a common node1 two nodal circles pass+ ea* ?r\gh two po9ts ( int]section ( ! limaons1 w pass ?r\gh ! po9t ( int]section ( _! base circles4 ,two conics h a common focus ab\t :i* "o ( !m is turn$2 two ( _! common *ords w t\* conics hav+ ! fix$ focus = focus4 ,two limaons h a common node ab\t :i* "o ( !m is turn$2 two ( ! nodal circles ?r\gh two ( _! po9ts ( int]section w envelope limaons hav+ fix$ node = node4 ,two conics are describ$ hav+ ! same focus1 & ! di/ance ( ?is focus f ! correspond+ directrix ( ea* is ! same2 if ! conics t\* "o ano!r1 !n twice ! s9e ( half ! angle betwe5 ! transv]se axes is equal to ! diff]5ce ( ! reciprocals ( ! ecc5tricities4 ,if two limaons are describ$ hav+ ! same node & base circles ( ! same diamet]1 & if ! limaons t\* ea* o!r1 !n twice ! s9e ( half ! angle betwe5 ! axes ( ! limaons is equal to ! diff]5ce ( ! ecc5tricities4 ,if a circle ( a giv5 radius pass ?r\gh ! focus 7,s7 ( a giv5 conic & cut ! conic 9 ! po9ts ,a1 ,b1 ,c1 & ,d2 !n ,,sa4 ,,sb4 ,,sc4 ,,sd is con/ant4 ,if a circle ( a giv5 radius pass ?r\gh ! node 7,s7 ( a giv5 limaon & cut x 9 ,a1 ,b1 ,c1 & ,d2 !n #a ------------------------------ is con/ant4 7,,sa4 ,,sb4 ,,sc4 ,,sd7 ,a circle passes ?r\gh ! focus ( a conic ^: latus rectum is #bl & meets ! conic 9 f\r po9ts ^: di/ance f ! focus are r1 r1 r1 r1 !n #a #a #a #a #b ------ ------ ------ ------ ------ 4 r r r r l ,a circle passes ?r\gh ! node ( a limaon ^: latus rectum is #bl1 meet+ ! curve 9 f\r po9ts ^: di/ances f ! node are r1 r1 r1 r1 !n r r r r #bl4 ,two po9ts ,p & ,q are tak51 "o on ea* ( two conics :i* h a common focus & _! axes 9 ! same direction1 su* t ,,ps & ,,qs are at "r angles1 ,s be+ ! common focus4 ,!n ! tang5ts at ,p & ,q meet on a conic ! squ>e ( ^: ecc5tricity is equal to ! sum ( ! squ>es ( ! ecc5tricities ( ! orig9al conics4 ,two po9ts ,p & ,q are tak5 "o on ea* ( two limaons :i* h a common node & _! axes 9 ! same direction1 su* t ,,ps & ,,qs are at "r angles1 ,s be+ ! common node4 ,!n ! nodal tang5t circles at ,p & ,q int]sect on a limaon ! squ>e ( ^: ecc5tricity is equal to ! sum ( ! squ>es ( ! ecc5tricities ( ! orig9al limaons4 ,a s]ies ( conics are describ$ ) a common latus rectum2 ! locus ( po9ts ^u !m at :i* ! p]p5dicul> f ! focus on ! tang5t is equal to ! semi-latus rectum is giv5 by ! equation p -r cos #bx ,if a s]ies ( limaons are describ$ ) ! same latus rectum1 ! locus ( po9ts ^u !m at :i* ! diamet] ( ! nodal tang5t circle is equal to ! semi-latus rectum1 is giv5 by ! equation pr -cos #bx ,if ,,pop be a *ord ( a conic ?r\gh a fix$ po9t ,o1 !n w tan ,p,,s tan ,,pso be a con/ant1 ,s be+ ! focus ( ! conic4 ,if ,,pop be a nodal circle ( a limaon pass+ ?r\gh a fix$ po9t ,o1 !n w tan ,p,,s tan ,,pso be a con/ant1 ,s be+ ! node4 ,conics are describ$ ) equal lat]a recta & a common focus4 ,also ! correspond+ directrices envelop a fix$ confocal conic4 ,!n ^! conics all t\* two fix$ conics1 ! reciprocals ( ^: lat]a recta are ! sum & diff]5ce respectively ( ^? ( ! v>iable conic & _! fix$ confocal1 & :i* h ! same directrix z ! fix$ confocal4 ,limaons are describ$ ) equal lat]a recta & a common node4 ,also ! director circles envelop a fix$ limaon hav+ a common node4 ,!n ^! limaons all t\* two fix$ limaons ^: lat]a recta are ! sum & diff]5ce respectively ( ! reciprocals ( ! v>iable limaon & ( ! fix$ limaon1 & :i* h ! same base circle z ! fix$ limaon4 ,e focal *ord ( a conic is cut h>monically by ! curve1 ! focus1 & ! directrix4 ,e nodal *ord ( a limaon is bisect$ by ! base circle4 ,! envelope ( circles on ! focal radii ( a conic z diamet]s is ! auxili>y circle4 ,! envelope ( ! p]p5dicul>s at ! extremities ( ! nodal radii ( a limaon is a circle hav+ = ! diamet] ! axis ( ! limaon4 ,bel[ we give a numb] ( !orems respect+ ! c>dioid obta9$ by inv]t+ ! correspond+ !orems conc]n+ ! p>abola4 ,! /raight l9e :i* bisects ! angle conta9$ by two l9es drawn f ! same po9t 9 a p>abola1 ! "o to ! focus1 ! o!r p]p5dicul> to ! directrix1 is a tang5t to ! p>abola at t po9t4 ,! nodal circle :i* bisects ! angle betwe5 ! l9e drawn f any po9t on a c>dioid to ! cusp & ! nodal circle ?r\gh ! po9t :i* cuts ! director circle or?ogonally1 is a tang5t circle at t po9t4 ,! latus rectum ( a p>abola is equal to f\r times ! di/ance f ! focus to ! v]tex4 ,! latus rectum ( a c>dioid is equal to its l5g? on ! axis4 ,if a tang5t to a p>abola cut ! axis produc$1 ! po9ts ( contact & ( int]section are equally di/ant f ! focus4 ,if a nodal tang5t circle cut ! axis ( a c>dioid1 ! po9ts ( int]section & ( tang5cy are equally di/ant f ! cusp4 ,if a p]p5dicul> be drawn f ! focus to any tang5t to a p>abola1 ! po9t ( int]section w be on ! v]tical tang5t4 ,if a nodal circle be drawn tang5t to a c>dioid1 ! diamet] ( su* circle pass+ ?r\gh ! cusp w be a common *ord ( ?is circle & ano!r describ$ on ! axis ( ! c>dioid z diamet]4 ,! directrix ( a p>abola is ! locus ( ! int]section ( tang5ts t cut at "r angles4 ,! base circle is ! locus ( ! int]section ( nodal circles tang5t to a c>dioid1 :i* cut or?ogonally4 ,! circle describ$ on any focal *ord ( a p>abola z diamet] w t\* ! directrix4 ,! circle describ$ an any nodal *ord ( a c>dioid z diamet] w be tang5t to ! base circle4 ,! locus ( a po9t f :i* two normals to a p>abola c be drawn mak+ complem5t>y angles ) ! axis1 is a p>abola4 ,! locus ( ! po9t ?r\gh :i* two nodal circles1 cutt+ a c>dioid or?ogonally1 & mak+ complem5t>y angles ) ! axis1 c be drawn is a c>dioid4 ,two tang5ts to a p>abola :i* make equal angles ) ! axis & directrix respectively1 b are n at "r angles1 meet on ! latus rectum4 ,two nodal circles tang5t to a c>dioid :i* make equal angles ) ! axis & latus rectum1 respectively b d n cut or?ogonally int]sect on ! latus rectum4 ,! circle :i* circumscribes ! triangle =m$ by ?ree tang5ts to a p>abola passes ?r\gh ! focus4 ,if ?ree nodal circles be drawn tang5t to a c>dioid1 ! ?ree po9ts ( int]section ( ^! ?ree circles are on a /raight l9e4 ,if ! two normals drawn to a p>abola f a po9t ,p make equal angles ) a /raight l9e1 ! focus ( ,p is a p>abola4 ,if ! two nodal circles cutt+ a c>dioid or?ogonally & pass ?r\gh ! po9t ,p1 make equal angles ) a fix$ nodal circle1 ! locus ( ,p is a c>dioid4 ,any two p>abolas :i* h a common focus & _! axes 9 opposite directions int]sect at "r angles4 ,any two c>dioids :i* h a common cusp & _! axes 9 opposite directions int]sect at "r angles4 ,a numb] ( o!r !orems on ! limaon & c>dioid are giv5 9 ,pr(essor ,newson's article 9 ?is numb] ( ! ,,qu>t]ly1 & ^! ne$ n be repeat$ "h4 ,dialect ,^w-,li/4 ,,by ,w4 ,h4 ,,c>ru?4 ,! foll[+ are "s ( ! dialect words t h come to "o obs]v]'s e>s )9 ! pa/ tri5nium4 ,!y are all f ,kansas1 unless o!rwise not$4 ,!y are pr9t$ "h to int]e/ o!rs1 & to secure a basis = obs]vation4 ,! writ] w be "u obligations to any "o :o w note 8 famili>ity ) any ( ^! words1 ins]t o!rs1 or o!r mean+s1 & s5d !m1 ) a /atem5t ( 8 place ( bir? & *ildhood1 to him at ,lawr5ce3 among3 all (1 z1 ,:]e are y go+ among y8 all3 all gone1 z1 ,! corn is all4 7,indiana1 ,p5n47 ,comp4 ,g]man4 bat3 a #8h>d case4' bid3 91 to bid ! 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,,kansas ,,univ]sity ,,qu>t]ly is ma9ta9$ by ! ,univ]sity ( ,kansas z a m$ium = ! publication ( ! results ( orig9al rese>* by memb]s ( ! ,univ]sity4 ,pap]s w be publi%$ only ^u recomm5dation by ! ,committee ( ,publication4 ,contribut$ articles %\ld be 9 ! h&s ( ! ,committee at lea/ "o mon? prior to ! date ( publication4 ,a limit$ numb] ( au?or's sep>ata w be furni%$ free to contributors4 ,! ,,qu>t]ly w be issu$ regul>ly1 z indicat$ by its title4 ,ea* numb] w conta9 fifty or m pages ( read+ matt]1 ) necess>y illu/rations4 ,! f\r numb]s ( ea* ye> w con/itute a volume4 ,! price ( subscription is two doll>s a volume1 s+le numb]s v>y+ 9 price ) co/ ( publication4 ,ex*anges are solicit$4 ,communications %\ld be address$ to ,v4 ,l4 ,,kellogg1 ,univ]sity ( ,kansas1 ,lawr5ce4