( 240 ) 
A 1 1 1 vie ; 
then as is known errs are given as roots of the equation 
a C 
di A 412 (113 
a9] agg — À A93 == 0, 
daj A3g C33 Bs À 
or 
HB POEME BY eet. 
so that the condition, which must be satisfied by the 3 roots 
Ay, dg, As, IS 
A, a A; = As : 
Now we have hy a hy a. hs —- a A; A, ho +- hy As ied hg ds == S B, 
Ay dos = —C, from which results after some deduction as a relation 
between the coefficients 
27 48 386 AB18C=0. 
Expressed in the coefficients of the general equation this becomes 
27 (aq) 4- aag + a33)° Sa 
2 
geeks 
— 36 (aj + age + ag) ( @11 Agg + Agg A33 + A33 U — As — 45,451) RE 
+ 8 (aj dog 433) = 0; 
so we see, that this is a relation where the coefficients appear in 
the third order. 
If there is a pencil of quadratie surfaces of the second order, we 
substitute aj, + 46); for aj, ; for & we obtain a cubic equation, which 
proves that there are three rectangular hyperboloids in the pencil, 
a result corresponding with that of the geometrical considerations. 
Up till now the treatment of the problem has borne a general 
character. For a complete insight the imaginary circle at infinity 
must be exchanged for the arbitrary conic K?; there are moreover 
many particular cases. This would however lead to too extensive 
discussions; so this communication must be concluded here. 
