1904 - 5 .] Instruments for Graphically Indicating Light Rays. 807 
a ray of light incident on the surface (plane or spherical) of a 
medium of refractive index = g, at the point A ; then A G will be 
the direction in the refracted ray, provided that the division in the 
scale A G corresponding to the value of the refractive index g be 
brought to the edge of the link C D. The proof is as follows. 
The divisions on A G are equally spaced, and are numbered from 
0 50 to 2*00, and the length from the centre A to the division 
1 *00 is equal to the length of the links A D and B C. Accordingly, 
if H be the division on the scale corresponding to a refractive 
index g, then we have the equation 
AH = |x, AD . . . (1) 
Further, the links AB and DC are of equal length, so that 
the perpendicular distances of the points D and H from the link 
A B are always equal. Accordingly we have, using equation (1), 
So 
sin i = 
ED E D _ ED 
aiF^Th ~~ ^'Ih ' 
sin i — g sin r. 
To use the linkage, the point A is brought to the point of 
intersection of the incident ray with the trace on the paper of the 
refracting surface. The edge of A L is laid along the trace if the 
latter be a straight line ; if it be the arc of a circle, then A L is 
made the tangent to that arc at the point A by arranging A B to 
pass through the centre of the circle (say at M). A F is then 
turned about A till it coincides with the incident ray, and the 
division on A G corresponding to g is brought to the edge of C D 
by turning A G about A. The edge of A G then gives the direction 
of the ray after refraction. If the medium above the boundary 
surface have a refractive index different from 1, then g must 
be taken as the ratio of the refractive indices of the two media, 
and so may be 
> 
< 
1, but as the scale on AG ranges from '500 to 
2 , 00, the procedure is exactly the same whatever the value of g. 
Should the incident ray lie on the other side of the line B N from 
that shown, the linkage is simply rotated through an angle of 180° 
about BN as axis. To avoid using values of g < 1, F may be 
moved to the other side of L, and the link A G then rotated till it 
