and 
(w,— acosp)? + (a,—b sing cosp‚)° Har? + (a, —b sing sing, cosp‚) +... 
+ (tE+2 — bsing sing, sing, ... sinpp—s singz—1)? + a Fene Fn — 
= (¢cos p + o)° 
is the equation of the spherical space Sp,(E,ccosy+e). If we 
write this equation in the form. 
n 
Zur +b—?= 
gl 
= 2 far, cos p Hb sing [w, cosp, +a, sing, cosp‚ Haya sin Py- « sin Pier Ì 
and underneath the / equations formed out of it by differentiation 
according to 9, ,,...ge—1, then addition of the £ + 1 equations, after 
having squared them, furnishes us with 
“ k+2 
(Zi + 6? — 9%)? = 4[(aa, + co)? Hb (oe, + 2 m’)). . ( 
Jl Uik 
And this same equation is obtained in the form 
n 
n 
(= a? — b? — 0’)? = 4[(ex, + ag)? — 8? (#,? + = 2;7)], 
LS 
di 
if we consider the spherical space of system Sy, 
9. For a variable parameter @ equation (1) represents a system 
of parallel n-dimensional cyclids of Durin. Here we can then ask 
after the m numbers indicating successively how many of those eyelids 
pass through a point or touch a line, a plane, a space, ete. In this 
investigation the &£-+-(n—4—1)-, i.e. the n—1-fold congruence of 
the right lines is in prominence, connecting an arbitrary point Z of 
aya with an arbitrary point M of QS: the case of 7 = 3 has been 
treated before in a small paper (“Prace matematyczno-fizyczno”’, 
vol. 15, pages 83—85, 1904). And the more general case we do 
not touch here. 
Mathematics. — “On a special tetraedal complex.” By Prof. Jan 
DE VRIES. 
1. By the equation 
Ze re. | 
c 
DAG 
ar 
a system of similar ellipsoids is indicated. 
The normal in a point P, on the ellipsoid containing this point is 
determined by 
