1904-5.] Instruments for Graphically Indicating Light Rays. 811 
teaching purposes, it simplifies the demonstration to apply the 
square as shown in fig. 4b. In this case the second step is 
taken with the right angle corner below the line 0 B. The lines 
0 A, A B, B C, and C 0 are all drawn in ; and the line 0 D is then 
drawn at right angles to CO by means of the square. In this 
case A 0 and 0 D are as before the rays, while A B and 0 C are 
the traces in the two media of the plane wave fronts, of which 
the relative velocities are represented by A O and B C. 
An alternative way of using this instrument, which is preferable 
when the angle of incidence is small, is to employ not the surface 
but the normal to it, as shown in fig. 4c. Here sin P 0 A = 
AF/PO = /x. PC/PO = /x. sin P'OD. 
Of these four instruments, each seems to have its particular 
advantages. The linkage is the most useful for class demonstra- 
tion, because it shows simultaneously both of the rays and 
also the surface. The jointed strip arrangement is extremely 
portable, while the celluloid device gives directly the actual sines 
of the angles involved. The set square instrument is found to 
be the most convenient form for private use in the graphical 
solution of optical problems. In dealing with spherical surfaces, 
too, it is an advantage that with this instrument the normal to 
the surface may be used instead of the tangent, because the former 
can be obtained very easily by drawing a line through the centre 
of the circle. 
