102 
PHYSICS: A. G. WEBSTER 
Proc. N. a. S. 
The question now arises, how nearly does the curve actually described 
correspond with the above description? We may take as the simplest 
assumption that when the driver gets ready to turn he puts the steering 
wheel over with a constant velocity until he is half-way around, and then 
FIG. 1 
turns it back with the same velocity. This is to be sure not exactly true, 
but as the wheel is dominated rather by friction than by inertia it will do 
for an approximation, and is besides about what observation shows. 
If the effect of this is to make the curvature of the path proportional to 
the time or to the distance travelled since turning (which will be shown 
below to be nearly the case), we have 
K — dB/ds — as 
as the differential equation of the curve, where a is a constant. But a 
curve whose curvature is proportional to the length of the arc is the well- 
known spiral of Cornu, used in the theory of diffraction in optics. The 
curve may be constructed graphically from the differential equation, but 
more accurately by the use of tables of Fresnel's integrals. If we put 
