810 Proceedings of Royal Society of Edinburgh. [sess. 
refracted ray. For greater convenience, each semicircle drawn on 
the celluloid hears two numbers, one giving the ratio of its 
diameter to the diameter of the semicircle formed by the inner 
edge, and the other the ratio of its diameter to the diameter of 
the semicircle formed by the outer edge. 
III. The instrument consists merely of an ordinary “ 45° set 
square, 5 ’ graduated in identical fashion along each of the two 
equal sides. The number attached to any graduation line gives 
the distance of the latter from the right angle corner in terms of 
an arbitrary unit, and the scale ranges from 1 up to 2. It is 
best to provide several such scales, each beginning where the 
preceding one ends. In use, one of the equal sides is laid along 
Fig. 4a. Fig. 4b. 
the incident ray A 0, fig. 4a, so that the surface B 0 intersects 
it at 0 at the graduation on one of the scales marked with a 
number equal to the value of g. The intersection B of the other 
equal side with the line B 0 is then marked on the latter. If the 
square be now placed so that the equal sides still pass through 
0 and B, but with 0 at the graduation 1 of the scale, 0 D gives 
the direction of the refracted ray. Sin P 0 A = sin 0 B A = 
AO/OB = /x. CO/OB = /i. sin D 0 P'. When the ray passes 
to a less dense medium the procedure is reversed, the unit 
graduation being used for the first step and the g graduation for 
the second. 
When a large size square is being used on a blackboard for 
