1904—5.] Instruments for Graphically Indicating Light Bays. 809 
A B at their unit graduations. The point B is now to be marked, 
and the instrument placed as shown by the dotted lines, so 
that the points of intersection at 0 and B each lie at the 
division corresponding to y. Then OD is the refracted ray ; for 
sin P O A = cos AOC = OC/OA = /i. OC/OA' = /x. cos A'O C = 
sin D 0 P'. 
It is to be observed that in proceeding from a more to a less 
optically dense medium, the above procedure must be reversed, 
and the g graduations used for the first step, and the unit 
graduations for the final one. 
II. The instrument consists of a piece of transparent celluloid 
shaped as shown in fig. 3a. Its straight edge E being set along 
Fig. 3a. Fig. 3b. 
the incident ray AO (fig. 3b), the intersection B of the inner 
semicircular edge (if the second medium be more dense than the 
first), or the outer semicircular edge (if the second medium be less 
dense than the first), with the surface BO is marked on the 
latter line. If the diameter of the semicircle 0 C be taken as 
unit length, then, because angle A 0 P = angle 0 C B, OB is the 
value of sin A 0 P. The instrument is now to be so placed that 
the semicircle whose diameter is equal to g takes the place of the 
semicircular edge with respect to the points 0 and B. We 
thus have, as before, sin P'O D = OB/OD = OB//q and therefore 
sin P'O D = sin A 0 P / g. Hence the straight edge of the in- 
strument which now lies along 0 D gives the direction of the 
