Graphical Construction for Steering Course of Ship)* 559 



Fig. 2. 



Should it not be thought self-evident that the straight line 

 joining two points is the minimum time path, consider fig. 3. 

 AB is the straight line path from A to B. Let AFB be any 



Fiar. 3. 



other path, AF and FB being straight lines. Take 



AC : CF = v : u. 



Then CF will be steering direction for AF. Let circle with 

 C centre and CF radius cut AB in E. Produce CE to meet 

 vertical through B in D. Describe circle with D centre and 

 DE radius. This circle cuts FB in G, G hying between F 

 and D. As in fig. 1 



time along AE = time along AF, 

 and time along EB = time along GB, 



therefore time along AB is less than time along AF and FB. 

 Now AFB may be taken as three consecutive points on a 



