910 
f— 6,448. In the absence of such an axis f =7 or f > 7. But this 
is still entirely uncertain. 
If the given relations are assumed to be perfectly correct, the 
reduced equation of state assumes the following form : 
Sb SD en Be 
pS io Ee: 
ry blim Ver by 3 bim 
h, 
e “9 ‘ 
For 6 constant, and so also — = 1 and 7‘= 3 we find back 
Aim 
the same form as occurs in Continuiteit p. 127. This form is found from : 
f- 1 1 26 ) ae 
T = rp ee 
et. Ter bg, 
If in this equation we put a, vp and 7'—= 1, we find: 
a relation, which had already been found before. 
Mathematics. — “On metric properties of biquadratic twisted curves”. 
By Prof. JAN DE Vriks. 
(Communicated in the meeting of December 28, 1912), 
§ 1. The quadratic surfaces #* of a pencil cut the imaginary 
circle y? 
„ common to all spheres in the groups of an involution of 
order four. The lines 7, joining two points of the same group enve- 
lop a curve of class three. Any of these lines /, is the axis of a 
pencil of parallel planes cutting a determinate surface ®° of the 
pencil according to circles. 
Such a plane cuts the base 9* of the pencil (@°) in four concyche 
points. So we find: the planes cutting a biquadratic twisted curve 
of the first species in four concyclic points envelop a curve of class 
three lying at infinity. 
§ 2. Let / be the axis of a pencil of planes. Any plane A cuts 
et in four points which will be denoted by 1, 2, 3, 4, whilst Mr 
will indicate the centre of the circle Zon. We consider the locus 
of the quadruples of centres Mand take first the particular case 
where 1, 2 are fixed points and line / is a bisecant of g*. 
As the centres M, and M, (of the circles 124, 123) lie in the 
