1892 - 93 .] Professor Schoute on a Certain Locus. 211 
4. AVhen the two augiilar velocities are incommensurable (??^ and 
n infinite), the surface is transcendental. 
For the common point we find 
or 
and therefore 
21 cos 0 + O' sin 0 = 0 ] 
21 sin 0 + (7 cos 0 = - 2« ) ’ 
2a sin 0 2a cos 0 
^ cos 20 ’ ^ cos 20 
x = a, 7 / = atan20, s = atan20. 
This proves that the locus of this point is the line ^ ^ | . Really the equa- 
tion {x^ + y-){y - = {ay - shows that this line is a double line of the 
surface. 
Now the surface can easily be constructed by means of the circle and the 
double line. To that end we only have to join every point P of the double 
line with each of the two points common to the circle and the plane OPZ. 
