566 Graphical Construction for Steering Course of Ship. 



belt. Stated generally, i£ all the belts are to be crossed, K 

 must not be less than u plus the greatest positive velocity. 



Suppose the velocity in second belt so great as to bring 

 the point T 2 down below the circle as at T/, the drawing of 

 a tangent would be again possible. Then S 2 ' would be as 

 in figure, and S 2 'B 3 / produced would cut the circle again at 

 B 2 ". That is A 2 B 2 ' is steering direction for path parallel to 

 S 2 'B 2 '. But it was pointed out in paragraph 1 that this is 

 not a minimum time path at all. Hence T 2 cannot come 

 below the circle. (2) Similarly, if K is negative K must 

 not be less than u plus the greatest negative velocity. 



Fi 



o\ 9. 



7. Fig. 9 shows four minimum time paths, Ai«, Aj/3, 

 Ajy, and AjS. The construction has been modified in a way 

 which simplifies somewhat the drawing. The S points are 



