138 Dr. Roget*s explanation of 
form the series of points w, w, p and q, in the curved spec- 
trum m D. 
That the attention may the more easily follow the wheel 
in its progression, it is necessary that its circumference be 
distinctly seen, and its real situation correctly estimated. 
Hence, although it be true, that by a sufficient exertion of 
attention the phenomenon may be exhibited by means of a 
single aperture, it is much more readily perceived, when the 
number of apertures is such as to allow the wheel to be seen 
in its whole progress. For this reason the phenomenon is 
very distinct in the case of a palisade. Each aperture pro- 
duces its own system of spectra ; and hence, when the aper- 
tures occur at short intervals, the number of the spokes is 
considerably multiplied ; but if the intervals be so adjusted 
as to correspond with the distances between the spokes 
at the circumference of the wheel, the images produced by 
each aperture will coalesce, and the effect will be much 
heightened. 
A mathematical investigation of the curves resulting from 
the motion of the points of intersection of a line moving 
parallel to itself, with another line revolving round its axis, 
will show them to belong to the class of Quadratrices, of 
which the one which touches the circumference of the inner 
generating circle is that which is known by the name of the 
Quadratrix of Dinostrates. Such a system of curves is 
represented in fig. 3, where MC, CN are the generating radii, 
A the outer, and B the inner generating circles, and PQ the 
common axis of the curves. 
All these curves have the same general equation, namely. 
