of Edinhurgli, Session 1883-84. 
295 
is longer than the circumference of the wheel. Now, if we write i 
for the angle GAB, and regard AB as the unit of linear measure, 
we easily find 
AG + G H = cos ^ + ( Jtt + i) sin i = l^ 
AG - GK = cos i - (Jtt - i) sin i = V. 
Since ^ can be found from the difference of diameters, or that 
difference from i, the two branches of our problem come eventually 
to be “ to find I and V from if and “ to find i when I or V is given.” 
The first question is solved by help of the canon of sines; the 
second presents greater difficulty, we can get the value of i from 
that of I only by a series of trials. Yet, in truth, there is no 
essential difference between the two processes, both consist of 
trials ; but the existence of the canon of sines, renders the trials in 
the former case so easy, that we come to regard the operation as 
direct. If we had a table of the values of I corresponding to all 
values of i from zero to the right angle, we would be able to resolve 
both problems with like facility. 
