Construction for Steering Course of a Ship. 563 



the value o£ K depending on the direction chosen in the first 

 belt but remaining constant throughout that path. 



Fig. 6. 



v 



4. It is easy to represent the function v+ geometric- 

 ally, fig. 6. Describe a semicircle centre A and radius u. 

 Draw a radius AB at angle « with Ax. Draw a tangent at 

 B cutting Ay at T. Take TV, measuring up, equal v. 



Then 



AT= 



u 



u 



sm a. 



and AV = v+- =K. 



sm a 



Also take AS, measuring down, equal v. 



Join SB, and draw AC parallel to SB. AC will be true 

 path where AB is steering direction. The dashed letters 

 give the construction for a negative value of K. AC being 

 true path for steering direction AB'. 



5. To apply this construction let there be a number of 

 parallel belts, as in fig. 7 (p. 564), the velocities in the belts 

 being 1, 2, 3, and 2 units, that of the ship u being 5. 



Describe semicircles with centres A 1? A 2 , A 3 , and A 4 , and 

 radius 5. 



2Q2 



