E. H. Moore, jr.— Theorems of Clifford and Cayley. 13 
Setting y=ty, and y,=uUyn, this becomes 
ae 6 Gi . D4 ak. . 
OP OS ee De ts ars rel : D.C : Nee eel er be pos 
iter at ee Pea ciara gue ML BER ys: Ue Shi 
whence the plexus of equations 
x FOG, DO Ge C1 ORC Dae 5) p. Gre Dra ’ Dee ’ ». ean Gp OO OOS Cas, a0 
oa a 7s — 
X, oe ae Gott 0) As a, HD. eid VG irs gt tae a Cer erergam. rem 
(db) m odd =2m" +1. Gis Vis Yor r=; 0, 1: 
In accordance with the simplified abbildung-system, set 
DRT NA Ep ted, (1a) PIAS SORACE RITA DRIP O NGS ate eta 
). Gwe Ni uae EFS oF etd Vet, el leh 0) a Foe ol tel e (D.C Nig: 
m+1 m+2 
Syn Yn SY RY ta, sha, ai 0! 0. gio! « ATES Us a Yen 
= 3 —9 O45 A 1 — 1 On, mI 
BG yey yy ye: F. . nt ye hytye'), 
or, setting Yo=ty, and y;=uy,, 
Re Kgs Ks? SD: ee. Gear Mee. ome pre 
Uohet ts te: Has Or eA (eae es fidgerskee ae pl 
whence the see of equations 
2 7a 
xe xs xe 0) et Ore Dare 5) Dre ’ Xe aietd 5) Da ae Oe Pe ea DG —0 
Ss Dae eevee ts a. re 9 Cae, 9 Gee ger tose lees Xe 9 Dts 
In each case the canonical form exhibits the S, 7,4: a8 the locus 
of the line of intersection of corresponding m-flats R,, of m projective 
pencils of R,,; X,—tX,=0, X,—¢X,=0, &e. 
In fact, these right lines on and ruling the 8, 4, m4 correspond to the 
right lines on the plane %, through the multiple point ©; y,.—ty,=0 
is met by a C”* or Ct! (which corresponds to an R,,-section of 
So, m,m4i) In only one point. 
a! 
A full skew curve O of order tS) an » corresponds to the point @. 
@ is (0, 0,1); or w= w,¢indeterminate ; and, therefore, @ corresponds 
>. Cra) 6) pie pose eee Dah 
ees eye) dy ele ie ON 9 Bah 
2S 9 2. Ce San ». Care = 
2 eer 7 Jhb) MS Tiel OC) Gee Ao See 
(a) DOG No, >. ora) =) 
(OC). S =>. eran oe. Corin!) 
| Date Meal ral ot erat BP 
or the (unicursal) curve (B) m" in an flat. Cf. Clifford, p. 310. 
(a) A line A corresponds to the point A. For Q is (1, 0, 0); or 
u indeterminate, ¢==0; and, therefore, A corresponds to 
Ne eel g = 0 Os ei oe —). Che 
m n-fats R,, in R,,4, intersect in R,, a right line. 
