806 
Proceedings of Royal Society of Edinburgh. [sess. 
Certain Mathematical Instruments for Graphically In- 
dicating the Direction of Refracted and Reflected 
Light Rays. By J. R. Milne, B.Sc., Carnegie Scholar in 
Physics. 
(MS. received March 10, 1905. Read June 19, 1905.) 
The refraction equation sin i = /jl sin r, though simple in itself, 
is apt to give rise, in problems connected with refraction, to 
formulae too involved for arithmetical computation. In such cases 
it may be necessary to trace the course through the optical system 
in question of a certain number of arbitrarily chosen rays, and 
thence to find the course of the other rays by interpolation. The 
Fig. 1 . — The divisions on the edge of the arm A G are not 
shown in the above figure. 
linkage about to be described affords a rapid and accurate means of 
determining the paths of the rays through any optical system. 
This linkage consists (see fig. 1) of five strips of metal, freely 
jointed at the points ABCD. If PA be the directionjof 
