560 Mr. John Wylie on Graphical 



curved path, and by the above the time along the chord AB 

 is less than the time along the arc AFB. This can be ex- 

 tended in the ordinary way to any size of an arc, so that 

 finally we get the straight line law as above. 



Fig. 4. 



A-k 



2. In all that follows, as in fig. 4, A, the starting point, is 

 taken as origin of axes, and belts are all parallel to Ay. 



Positive direction of currents is upwards. 



Let AC : CB = v : u, fig. 4. 



Then CB will be steering direction for minimum time 

 path AB. Drop AD a perpendicular to CB produced, and 

 CM a perpendicular to edge of belt through B. Let breadth 

 of belt be a, and angle MCB be a. 



Then 



DA : MC = AC : CB, 



or 



DA 



a = v 



u, 



u 



a constant, 



CB touches a circle centre A and radius ~a. 



it 



So to go from A to any point B, the steering course is 

 found by drawing from B a tangent to this circle. As two 

 tanocnts can be drawn from B it is necessary to discriminate 



