XI.—On the Curves produced by Reflection from a Polished Revolving 
Straight Wire. By Epwarp Sane, Esq. (Plate XIX.) | 
(Read 5th February 1877.) 
If light, emanating from a fixed source, be reflected to the eye, also fixed, 
from the surface: of a polished cylinder, which cylinder changes its position in 
some definite manner, the point of reflection moves in some curve or locus 
whose nature may be made the subject of investigation. 
In the present paper I propose to examine that case in which an indefi- 
-nitely thin cylinder is restricted to pass through a fixed point. The locus of 
: the point of reflection is then a curved surface, For the present I shall still 
farther restrict the polished line to the plane passing through the vertex, the _ 
Source of light, and the eye ; the locus being then a plane ‘curve. 
| Let then a fine polished straight. line, extended indefinitely both ways, turn 
on the vertex O, while light emanating from the source A is reflected to the 
eye at B; it is required to investigate the locus of the point C at which the 
reflection takes place. . 
The reflection is only possible while the polished line passes outside of the 
jangle AOB. When the wire lies along AO, the point of reflection is at A; 
when along OB, at B; and when it is equally inclined, outwards, to OA and 
| OB, the reflection occurs at O, wherefore the curve must pass through the 
three points O, A, and B. 
When the direction of the wire is between OA and OB, the optical genesis 
jlines AP, BP drawn to a point in it must make equal angles OPA, OPB on 
opposite sides of the wire OP. 
| The shape of the curve would seem to depend on two arguments, namely, 
the angle AOB and the ratio of OA to OB. However, if we take two 
positions OC and OD of the wire, making equal angles AOC, BOD outwards, 
and find the points C and D belonging to these positions, we find that the 
angle CAO is equal to DAO and CBO to DBO. So that if C were taken as 
|the source of light and D as the position of the eye, A and B are points in the 
jcurve belonging to them ; and hence we conclude that the curve belonging to 
C and D is identic with that belonging to A and B. 
VOL. XXVIII. PART I. 4B 

of the curve falls to be supplemented by the geometrical one, that the two | 
