NEWSON: NORMAL FORMS OF PROJECTIVE TRANSFORMATIONS. Ey 
TYPE VII. 
I I 
X,—a x—a y,—b y—b 
ee —_—= = - — —-a. 
Zee BC Ag Oy ZG 6) ee ee awake 
1 1 IX Way 2a) ok Sot Ga Zv ok 
2 DieGe tl, sa. Dyer 
Hit SIR ONT Or eit.) Tmo 2-0 
|O elo © OFS prea © 
The coordinates of the point D are (a,b,c); mand n determine 
the position of the plane through D every point of which is inva- 
riant. ais the characteristic constant along each line of the bundle 
through D. 
TYPE VIII. 
4 | E : } oie 
X,Y, 4, 1 Be Wyahs Zee eT Shana hay a Noe ean 
lev < Soya Newnan 3 lo: te 1 a |) © i ates alli aC egal 
| | 
a, Se iy Ale etG gud cia On ayes 1 aaa ees 
fae Po gO} oa Decl O| Ie) SP ALG} Tl) py) iene 
—k = —]1-r 5 
Seng 72 ptt Kae V0, (ral 7 MM Gh ay he Kae Veep Nl 
ieebs..cH> ¥ Vie Oh ea Pecl PM Os Na iia Gln OM oeseeyy aac 
Bem Cant An YO py G nal 2 il Samos r Ase Daven. I 
71 Sail Oat ye Ee DawGow t Als Die ese a dere Der Coe T 
| fat - i i ~ | i a4 © ba has 
eee (teat eee 
Rn Vane eek i ma VCR Gana 
2ioGe Sree Coma | a, DaeGa a 
Ai Deeply |\ay, eDic ao asl 
Dat oleae Ree iE) ap O 
Bins Vie eal Ke WV yz eatl 
Ameen Cla: | bee a or 
AD y ECoetlciidia, (Deus Tt 
2 nieh Diag AO 11) Ne Waa] Om ena 
In these equations (a,b,c) are the coordinates of some one of the 
invariant points of the line AB, and p and q determine the direc- 
tion of this line; (a,,b,,c,) and (a,,b,,c,) are the coordinates of C 
D respectively. k is the anharmonic ratio along each of the inva- 
riant lines in the plane ABC; k!* is that along each invariant line 
in the plane ABD. 
TYPE IX. 
Sot A ep Ag isco, cere eva Za ee Vile Za di 
in Dees — oF falgit A ene. oe egies 5) Flamer oF tera 
| | | 
1 5] OK GRAN) let pumae @ ear CupsT Ah Deh Gage 
Tee eis! eae le Tyce 62.92 a; Dede 5O 
——— F - 4K =F 
ae pn inar : | 
Lek Ves Za I Sarpy) Zee Mave 2a ul Key ze T 
Are VOy oi eget) Cin al bei) ak Drs Cry ek 
zeal epee Cae | ALS Cal dep bere: Aten Dare aunl 
a ee Siig 2) 218 Si His ek MO ER ee Dard? 
