(181 ) 
Qr2zt 
z—=rs—l ps 
fe(r) u (s) = =" e = M (rs) (zu (rij = 1) ; 
y— 
a— 
as in this case zr + sy assumes all positive integral values prime 
to and minor to them. So we have but to determine the value of 
ée(s) for an argument which is a prime number power (p“). For 
a = 1 we have 
Qari 
z—p—I p 
ft (p) =e =— 1 ’ 
rl 
whilst for a>1, we get 
Uri Quart Qari 
=p“ —l pe ap NSy pe rp —1 pe 
’ a 
(9?) = Se + 2"e +...+ 2’ 
dk = i app Ee 
rs 2u xi 2m i Ami 2(p—1) xi 
en dE (ler +ep +,...t¢e P 
A 
SS 0 . 
The application of the just-named definition of (x) is to be 
recommended for lecturing purposes. 
Mathematics. — “The number of conics intersecting eight given 
right lines”. By Prof. JAN DE VRIES. 
1. The number of conics resting on eight right lines given arbi- 
trarily can be defined by the direct application of the principle of 
the conservation of the number. 
For this we begin by searching for the number of conics through 
the points P, and P, intersecting four given right lines 4, lg. ls, bs. 
If we suppose lj, lo. ls to lie in a plane g, then the conic dege- 
nerated into the right line P, Py and the right line connecting its 
point of intersection on q with that of /,, satisfies the condition. 
Proper conics answering the question are obtained in the planes con- 
