iuul it' wc jiiil ''/p /"i aiul (/.y L, tnr //, // and .r. </ tlic (Mjiialioiis (1) 

 pass iJilo 



nil -ziz r/i I 



; • i-'-i) (1') 



and ideiililies, ^^■llilsl the 1\\<> ti'i[)l('js of e((nali(^iis (2) ai'(> luiihMi to 

 'ï+i = ''i{''i —1) — - ^/, — :i 77 1 \ 

 r; =,.-^i(;v+, -1)- 2^,--3r/+2 .(/ = 1.2) . . (2') 



Ajid now these e(inatioiis pass ijito those for the geiiei'al case as 

 soon as the addition (/z=\,'2) is exchanged for (/'= '1, 2, ..., ;/—lj. 



'A, We shall ]iO\v pass to the ueneral case of a cnr\'e T',, of ordei- 



n', lying in an /S„ but not in an >Si— i ajid wc i-cnuiKt the readers 



how here we dcternniie the ofy/— 1) relations between the .'^//charac- 



terizing (pianlities. If we take in tSn two noji-intersccting spaces ;S^ , 



-S,_^,_i, and if we jjrojeet C'; out of N, _^,_i (ni .S^,, the pj-ojectiofi 



is a eui've C^,. If we imagine this process to be {jerfornied for 



p =: 2, 3, . . . , H — 1, we arrive at — tlie curve ('n included — a 



ip) 

 series of n — 'J curx'es C2, C3, . . . , CV-i, C],. U fartlierinore 62 — once 



more for p = 2,'S, . , . , n — 1 — is the section of the locus of the 



spaces 'S._i through p snceessi\'e p(.)inls of the curve '' ).-(-i \\itliany 



plane lyijig in the space 'S'^-fi <»f that curve, we a,rri\'c at, - iftiie 



plane curve C-> already found above is re|)resented Iw ('■, - -, n — 1 



(1) (2) (n-'\) 



plane curves Co , 6 j , . . . (o and these fnrjiish 11 \ tri[)lels of 



relations. If the septuples (y/,/, /y//, </;. /,. Ic;^ /?,), (/' = 1,2,..., 11 — 1) 

 represent tlie ciiai-acIeri/JiiL' nninbcr.-, of tlic^c phuic ciir\"es the 3(// — 1) 

 e(piations li(.)ld good : 



in, :=::: Uj, ( n, — \) — '1(1 ^ — 8/-, 



Hi — w, (w,/— 1) - 2 ti—Mn ' , (/■ = 1, 2, . . . , // — 1). 



hi — hi = 3 (/Ai/— ///) ) 



V)\ representing the series of //, -f- 2 quantities 



munber of ^ , number of 



, ,. / , c numhers , ^ . 



statu)nar\ . or(U'i', n — I ,. , class, stationary 



(»t raJik, ,,*' 



[Hjuits ' spaces 0,1—1 



