808 
Proceedings of Royal Society of Edinburgh. [sess. 
lies on the other side of AD. In this case 1/yu, takes the place 
of g, and a somewhat more accurate setting can he made. 
The case of reflection is obtained by having A G- and A F both 
on the same side of AL, and by setting g to l'OO. The linkage 
is to be applied to the trace on the paper of the reflecting surface 
(whether plane or spherical) exactly as before described for the 
case of refraction. 
It is convenient to have the ends of the links shaped as shown 
in the figure, that the eye may see at a glance which is the 
“ working edge ” of the link. A small hole through the rivet 
at the joint A is necessary to enable its centre to be set as above 
described. 
Since writing the above the author has continued to investigate 
the matter, and he has found three other graphical methods of 
which he thinks it may be worth while to give a brief account. 
Each of these new methods proceeds by two steps or stages. 
I. The instrument consists simply of two straight strips of 
suitable material jointed together at one end, and having the 
distances from the joint marked along each of them so as to form 
a scale (or, better, a succession of scales) ranging from 1 to 2. 
If AO, fig. 2, be a light ray incident on the surface 0 B of a 
medium of refractive index g, let one leg of the instrument be 
laid along 0 A in such a way that 0 B intersects the legs O A and 
