NEWSON: NORMAL FORMS OF PROJECTIVE TRANSFORMATIONS. 139 
TYPE XI. 
| ‘ | ; 3 | F | 
X,Y: 2, 1 AV heal 2 OR ie aR Be AYE Za E| 
abev st) ch) 1 Fane er. a), Wee lonely OTsh stale We Ge. ere 
re) Boh inte ly prey Bia a0) Palate quer cnl Olay Dian ct sg 
erOw ur. SF O° SOM MAT) Oia G Sph sbi: (ON. Gt =p. TE 
—k = 
Reve Zao 1 2 aie ay Ama Seewpnezie al KVM Vasey 
nib) Mes “i BM ole en str AV lo) Ce ia 2 lee a 
ele Moa oe I| Aner Drei) 3 i, Mile aes peel ely OL ROM be 
14 a OSUmMC [eae Ker Gh 5O EA pred, © th Pia Gy 0 
i} 
I I 
= —Q. 
[Xue YZ 1 au RG aR eae wid 
(atten bse 3 Coneat vere [ole (Ou ati 
lage Din eG) apa One Camel 
iz D2 Um Olly “pe Page 
The coordinates of the point A are (a,b,c); the direction of the 
line Al is determined by p and q. The coordinates of the point B 
are (a,,b,,c,); { determines the inclination of the plane z to the 
plane of AB]. kis the anharmonic ratio along each of the lines of 
the pencil in the plane ABI passing through B; a is the character- 
istic constant along each line of the pencil in the plane z passing 
through A. 
TYPE XII. 
| E : ne ie 2 
Peay Sat ek oY 2h od re ch are PS Bye ea 
De “Cat, Olay De char iat Ds Claas @lap wibarac eer 
Peppa Ol. wan), PGi. o Of) G) =p 6)" 108 dp = pare 
eet eet OL CO at § ek De Or Oh Utne Mo GhatOn Lk 
— fd . a {a 
F | E 5 - | 
aa ete Mia: Wises ot aT Veh me wath Ze gE 
eer SG aril. Way tp. e040 ae dD Ge AL 4 ice Cbae cr 
aaa, Cle ien Pei GevOl | 81t. Py SqalO) ir Datq: oO} 
fee On Oe lt lie OL Os), tf OC /Os abies Ono af 
I I 
i 
ES (ots 
P =e r 
Leama he YZ. Oe 
EVP AS] D) es 121 Pinu 2 oa Ooi Om 
HG pa O| Z pedo 
ip OMe TOMMEnrGe Ne. Or FOr | | 
(a,b,c) are the coordinates of some point on the line of invariant 
points and p and q determine the direction of this same line. 
