5 Ac Se 
$ 3. To fix our thoughts we suppose that A and £ have the 
same signs. 
A 
For k= + 1/5 to each ray p, of the regulus /è, wound to 
the right lying on O,? two rays p, and p', are conjugated of the regulus 
R, wound to,the right lying on 0, so that „POP == POR =z 
The complex @ is originated by revolution about Oz of the con- 
gruence J’ with the directrices p, and p, as well as of I with 
directrices p, and p,. 
A | 
For k= — ze to each ray p,* of the regulus A,“ wound to 
the left lying on O,* are conjugated two rays p,* and p’,* of the 
regulus #2,* wound to the left lying on Q,*, so that the points of 
intersection of p,* and p,* with «Oy as well as those of p,* and 
p* are seen from Q under an angle a“. The complex 2 originates 
by revolution of the congruence P* with directrices p,* and p,* as 
well as of T'* with directrices p,* and p’,*. 
Let the right: line. P,P,,be eut by. 0,2 still vin. Q, by, 0," mage 
Through Q, pass the rays q, and q,* of R, and R,*, through Q, 
pass the rays q, and q,* of AR, and &,*. We then find that @ ig 
built up in four ways out of systems of oo! congruences (1,1), which 
are originated in the following manner: 
1. by revolution of I” with directrices p, and p,, 2. by revolution 
of IF’ with directrices g, and q,, 3. by revolution of 1’* with q,* 
and p,*, 4. by revolution of P'* with p,* and q,*. 
If C=O, then from (10) follows that a* — a and as p,* and p,* 
are then the images of p, and p, with respect to «Oy, then 2 is 
proof against reflection to Oy, thus symmetric. 
§ 4. Let A, be a point of p,. The complex cone of A, consists 
of the planes (A,,p,) and (A,, p’,), the singular ray s starting from 
A, rests upon p, and p’,. If A, deseribes the right line p,, thenss 
describes the regulus e,, of which the system (p,, p,, p’,) is the 
conjugate one. As p,, p, and p', belong to reguli wound to the right 
on O,* and Q,? and these surfaces touch each other in B, and B, 
we find that p,, p, and p’, are cut by two isotropic lines 6,7 and 
B,J, at right angles to Oz so that / and J are the circlepoints of 
„Oy. If thus we bring through one ray s of @, the linear complex 
C, having Qz as axis, then ©, lies entirely inside C,, having s, Bl 
