308 



(A,),, (A,),, (A,),, 



(^>)„ (A,),, (^)m 

 {Ai)i, (^2)22 (At),, 



= 0. 



Their number amonnts llierefore lo 3 (/« - — 2). 



There are coiisequeiilly 3 (/« — 2) iiull-rays with Iriide 11 nil- point; 

 they are evidently siaticmnri/ tdugents of the ciii've t enveloped by 

 the niill-rays t. 



Analogously the bitam/eut.s of that cnrve are intersected in their 

 points of contact by the pairs of double rays that occur in the 

 groups of the in\olution. Their nuuiber, as is known, amounts to 

 2 {m — 2) {ill — 3). 



For the order of r we find now in-, it has no cusps, but 

 ^{in — !)(/« — 2) nodes. It is, just as y2»i— 1^ rational. 



Tiie involution has 4 ("^ — l)("i — 2) neutral pairs. Kach pair 

 belongs to 00' groups and corre.sj)onds projectively to a plane pencil 

 of null-rays. In connection with this the null-curve of the centre 

 of that pencil consists in the coirespondijig neutral pair of rays and 

 a curve of order {m — 1), which has an {m — 2)-fold point in aS,,. 



The null-curve of a singular point S],- consists of the ray *Sa:«So ^Jid 

 a curve of order m with {m — J)-fold point \. 



