593 
while 4, and A, are functions of the second degree in 2 and only 
A, contains the tind degree of A (the latter on the supposition that 
neither § nor 7 is equal to zero). 
Hence x, y and z become only infinite for 2 = oo and that in such 
a way that 
AE 
ìzo 2 
lim 
A=n 
The locus of the points of inflexion is in general We. unless 5 or 
r is equal to zero) a twisted parabola, which is osculated by the plane 
at mfinity at the point at infinity of the screw-awis. 
In case r is equal to zero, the motion at the moment in cunside- 
ration is a pure translation; vr and wv, are in this case equal to 
zero; if P(«, y, z) is to describe a point of inflexion, it is necessary 
and sufficient that also Jr and J, are equal to zero. 
If the motion at the moment considered is a pure translation, the 
locus of the points describing a point of inflexion is a straight line: 
AE, 
ITR et | 
e|s 
dr d dr 
sg VM \ 
dt dt --dt 
If at the moment considered ¢=—0O, the motion is at that moment 
a pure rotation. The equations of the locus in question are in this 
case 
dq dp d§ 
dt dt dt 
d d d 
r?(a*® + ye bk en peen 
If the motion at the considered moment is a pure rotation, the 
locus in question is a parabola in a plane parallel to the axis of 
rotation; finally the following cases are excepted to this: 
dp dg de o,% a Seed 
Sidi ant de de 
of revolution through the axis. 
dp dq d& dy_ a 
Made dt dt dt 
axis of rotation no points which describe a point of inflexion in their 
paths. 
Z 0; the locus in question is a cylinder 
b = 0; there are besides the instantaneous 
§ 5. Let in the second place be required: 
the locus of the points the paths of which have at the moment 
considered a stationary plane of osculation. 
