( 761 ) 
i== A-«*(<?+ «) + „*+ *-(,.) s = a8 + F(r) 
T =/.(*) /,(<?) «=<+■ /(*) 
*=r*«n(i9|/i + <0 
* = - 0- + 2i(r) 
«*) =aO+/ { r) 
0=arcc<,,*4 f(z). 
II. Let us discuss one of the above mentioned classes more 
closely, viz. 
2 = r fx (0).+/* (0) 1 ).(2) 
It is the general equation of the scrolls with the 2-axis as directrix. 
Of these scrolls we can find the striction line in the following way. 
Bianchi (l.c. p.223) deduces that the curvature K— —, for which 
mr—jy' 
in another place was found K — —— ——, is larger in the central point 
Eir — F * 
than in all other points of a generatrix. If we make up K for (2) 
we find 
K _ -(/,? _ 
mi + Jay +(77m* *aa+(ayy' 
Along a generatrix 6 is constant; there only the denominator of 
the expression for K changes. If we determine the value of r for 
which K becomes maximal we find 
///; 
(3) 
i + (AY + (AT 
So this is the (r,6) projection of the striction-line. 
This equation can be found in an other way, too. We have the 
property that the tangential plane in the central point of a generatrix 
is normal to the tangential plane in the point at infinity of that 
generatrix. We now determine for /= - 
V'V 
d# r dtf ’ 
infinity on the same generatrix. If then p is to be central point the 
sum of the products QQ * 
again the equation (3). 
values of 
r/m+fm the 
p and in the point ; 
This gives 
l ) In future we shall write f x and f % for f x { S> and f r (S). 
51 * 
