MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES. 529 
A 

Then CD=PD .:. =~ DCP = —DPC, and CP is perpendicular to OE, 
.'. <CPE=2 DCP+=_DEP. Takeaway — DCP=— DPC, and there remains 
DPE— DEP .-. PD = DE.: CE=2 PD. 
Therefore the curve ACH has a constant tangent equal to the diameter of the 
circle, therefore ACH is the orthogonal tractory of the straight line, which is the 
tractrix or equitangential curve. 
The operation of finding the fixed curve from the rolled curve is what Sir 
JoHN LESLIE calls “ divesting a curve of its radiated structure.” 
The method of finding the curve which must be rolled on a circle to trace a 
given curve is mentioned here because it generally leads to a double result, for 
the normal to the traced curve cuts the circle in two points, either of which may 
be a point in the rolled curve. 
Thus, if the traced curve be the involute of a circle concentric with the given 
circle, the rolled curve is one of two similar logarithmic spirals. 
If the line traced be a tangent to the circle, the rolled curve is either of the 
parts of the polar catenary. 
If the curve traced be the spiral of ARCHIMEDES, the rolled curve may be either 
the hyperbolic spiral or the straight line. 
In the next case, one curve rolls on another and traces a circle. 
Since the curve traced is a circle, the distance between the poles of the fixed 
curve and the rolled curve is always the same ; therefore, if we fix the rolled curve 
and roll the fixed curve, the curve traced will still be a circle, and, if we fix the 
poles of both the curves, we may roll them on each other without friction. 
Let a be the radius of the traced circle, then the sum or difference of the radii 
