( 502 ) 



notiilioii wliicli is iiuido use of and wliicli has been adopted i. a 

 in Pascal's Repeiiorinm dci- hlllicren Maflhunntil (Leipzig»', Tenl)iier, 

 1902). Ill llie follow iii.U' lines I iiijeiid to i^ive a more eoneise notation, 

 makinj;^' it possible lo write down the H (7/ — 1) relations l)etween the 

 \^i). Plückkk's (piantities in thi'ee foninilae w ilh an index, which ninst 



take the values 1.2 11 — J. sneeessively. In orik'r to make tlie 



dednelion eleai- to those, \vho are not so famibar wilh polydimen- 

 sional theories I sliaH beuiii by iiubeatiiiLi- them for the ease //=3 

 of our space. 



2. As is known the six rehitions lietween the nine Pi.ücker's 

 ((iianlilies of a skew ciirNC jire (UM-i\-ed in two triplets from the 

 consi<hM'atioii of \\\<) phiiie curves, the first of which is the central 

 projection of the ,L;i\en skew curve (J from any point () on any 

 plane «, whilst the second is the s(M'tion of any |»lane a with the 

 developable of the tan.uenls to the curve ('. Let ns indicate succes- 

 siveh' order, rank, class of the cnr\e ^ 'by //,/■,/// and let ns represent 

 as is ciistoinary by (r/, //), {(/,//), {,i\ //} the three pairs of dnalisti- 

 cidh related numbers, of \vhi(di /> is the number of stationary [)oiiits, 

 // the number of apparent nodes, ,/■ the order of the nodal cnr>e of 

 the (le\elopable ; then the se.\tnj)!es 



("i- '",, </,,t,J<\Jj^) , {"2, /"-r 'A' '.' ^■.' ^'J 



of the (piantities (order, (dass and numbers of nodes, double tangents, 

 cusps and inflexions) characteri/ing tlie two ]>lane curves are 

 ex|)ressed by the equations 



>', — ■>' 

 m^ m m. 



k^ = n 



ill the nine (diaracterizing \;dues of C -. so in connection with the 

 ^vell kllo^^ n Pi,f('Ki':j{'s formulae for a plane cur\'e the two triplets 

 of relations hold uood : 



?• = //(// — 1 ) — 2 A - H // 1 m = /■ ( /— 1 ) — 2 ,r— 3 n j 



n—vit—\) — -lv — -^rii , ?• =:?m(/// — 1) - 2v-'^" . (2) 



I . ' I 



/// — /' -:= o (r — n) I a — // m o (;//—/•) | 



If we substitute t\,. i\, /\^, j-^, /■, for the row of (piantities A, //. y, ///, ^/ 



(1) 



