BREWSTER : COLLINEATIONS OF SPACE. 303 



Type VI. 



(7) (; Gi(H'mm'«F), Two generators of each system, a 



or pair of reciprocal polar lines, 



6 Gi(APpsmF). and all points on one of those 



lines. (VI. E c = i) 



(8) fi Gr2(H'mF). Two generators of one system, 



and one of other system. (V. C c= i) 



(9) 6 G3(lmF). One generator of each system. (IV. D c = i) 



(10) 6 G-2(APpsF). A point on the surface, tangent 



plane at that point ; a point 

 without surface and its polar 

 plane. (V. D) 



(11) 6 G 3 (PsF). Point and polar plane. (IV. E) 



Type III. 

 A. — Groups of first class. 



(12) 3 G'2(H'mF). Two generators of one system, 



one generator of other system. (V. F) 



(13) 3 Gs(lmF). One generator of each system. (IV. B) 



(14) 3 G4(1F). One generator of one system. (III. A) 



B. — Orovps of second class. 



(15) 3 Gi(ll'mF) a . Same as 3 G 2 (ll'mF) and con- 



stants. (VI. 0) 



(16) 3 G 2 (lmF) ;i . Same as 3 G 3 (lmF) and constants. (V. B) 



Type I. 

 A. — Groups of first class. 



(17) ^(H'mtii'F). Two generators of each system. (V. G) 



(18) 1 G3(ll'mF). Two generators of one system, and 



one of the other system. (IV. C) 



(19) 1 G-4(H'JF). Two generators of one system. (III. B) 



(20) Kr^lmF). One generator of each system. (III. C) 



(21) ^(lF). One generator of one system. (II) 



(22) : G 6 (F) None. (I) 



B. — Groups of second class. 



(23) KxiOl'mm'FJr. Same as ^(ll'mm'F) and con- 



stant r. (VI. E) 



(24) 1 G 2 (ll'mF) 1 , Same as ^(ll'mF) and con- 



stant r. (V. C) 



(25) ^(lmF),-. Same as ^(lmF) and constant r. (IV. D) 



(26) Identical transformation. (VII) 



