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LVIII. Graphical Construction for Steering Course of a Ship. 

 By John Wylie, B.A., Demonstrator of Physics, Queen s 

 University, Belfast *. 



GIVEN a number o£ parallel belts of water, along any 

 one belt the water flowing with constant velocity but 

 the velocity varying from belt to belt, to find the minimum 

 time path and the course a ship should steer going from a 

 point in one belt to a point in some other belt. 



1. For a single belt the true motion of the ship is the 

 resultant of the two velocities, v that of the current, and u 

 that of the ship in still water. 



Fijr 1. 



In fig. 1 let A be starting point. Draw AC to represent 

 v, and on same scale describe a circle with centre C and 

 radius u. Then if B be any point on this circle, the ship will 

 go from A to B along line AB by steering in a direction 

 parallel to OB. Since AB is a straight line, AB will be the 

 minimum time path between A and B, and so long as A is 

 inside the circle, that is v less than u, this holds from A to 

 any point of the circle. 



But if v be greater than u, then, as in fig. 2, AB, steering 

 parallel to CB, will be a minimum time path ; but AB', 

 steering parallel to CB', will not be a minimum time path. 

 AB X will be the minimum time path for steering course CB' 

 where CB' is parallel to CB. 



It is easily seen that if v is less than u it is possible for 

 the ship to reach any point in plane space, but if v is greater 

 than u she cannot get outside of the angle bounded by the 

 tangents AT and AT'. 



* Communicated by the Author. 



