138 KANSAS UNIVERSITY QUARTERLY. 
Re DY av ieal x Saye — oe 
a, DEvace Gl AbD. aC, ae 
[Eo sp yu GOOF aT) ie, oe 
Wes a Sait Sloat fie CEM De Led pea olan 2 
— —— +a. 
oe re ; 
Kaige Spe MS Vee a 
aly, DE Che alt lara) MG an 
; | | 
Deal cee ca a, beeice a 
Lae CPW Dpto tee Oi Slee SI 
The coordinates of the invariant point A are (a,b,c) while p and 
q determine the direction of the line Al; (a,,b,,c,) are the coordi- 
nates of some point on the line BC, every point of which is an 
invariant point, while p, and q, determine the direction of BC. k 
is the anharmonic ratio along each line of the pencil with vertex at 
A and lying in the plane ABC; a is the characteristic constant 
along the line Al. 
TV. Eee 
Ki ¥a 2, ¥ i 2 IK; Y, 2, 1 [X-men 
ia ly “@ a BE |). <@o ot ele ee ae. ‘Lie a. JD seme 
| | | 
a Pq 9 1ay Dis, yee a, be dene a, Dy seam 
pe ep el Woy eh P Py GO eee 
—k — 5 - —— — = K-—_ -—— 5 
Ramee ONT SDS AN ot Ka VaqokZa. Kare Zan 
a io) 6G itl 2 |) © i 21) Slo Gee it AV |) 1 
We | Ohm CP um ay Poa Ger ie OF ee ok me a, Dies r) 
Es *CnO E gD gly te Lips kane i p, 4,9 
x, an Be Ki | eee eel 
ay jo) (ei ae Gb! wiGaae eT 
LNs 2S ei SEN) LSP eh. ¥o 
to Pa Gao I P; qi ° 
ey ee zeae alll a ERY? eteign aL 
ele oye eC ae BY | le MOL 
an Degen Tia, Baresi 
19a, 20 i Sp. Gi6 
(a,b,c) are the coordinates of some point on the line AD, and 
(p,q) determine the direction of AD; (a,b,c) are the coordinates 
of some point on the line BC, while (p,q) determines the direction 
of BC. kis the anharmonic ratio along every line joining a point 
on AD with a point on BC. 
