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FOR FACILITATING GREAT-CIRCLE SAILING. 279 



Description of the Course and Distance Diagram. 



The object of this diagram is, as its name implies, to determine the course or rather the 

 succession of courses which the ship must follow to keep on the great-circle track and the 

 distance from any one point on the chart to any other. 



It must, in the first place, be noted that the course on a great circle, i.e. the aqgle made 

 with the meridian, changes continually from point to point. Now, it would be impossible for 

 a ship, with the compass for its guide, to be put on this ever-varying course; — the helmsman 

 must be told on what course to steer, and may be instructed to alter it after running a certain 

 number of miles or a certain time ; but to alter it every instant according to a definite law 

 would be altogether impossible. The nearest quarter-point is the greatest amount of nicety 

 ever aimed at, and he is a good helmsman who can secure that under the most favourable 

 circumstances. 



I have constructed this diagram so as to give the quarter-point nearest to the true course, 

 and also the distance to be run on that quarter-point before the next one is substituted for it. 

 The course can therefore never be more than |-th of a point in error, and while running one of 

 these distances the error will be one way during the first half and the other way in the second, 

 vanishing altogether about the middle, so that the compensation will be nearly perfect, and 

 the route thus marked out will not perceptibly differ in length or in position from the real 

 great-circle track. 



The diagram consists of a series of concentric curves corresponding to the parallels of 

 latitude, bounded by a horizontal and a vertical line ; the degrees of latitude are marked on 

 the latter, and the distances from the highest latitude on the former at intervals of 100 

 nautical miles, or any other convenient number, according to the size of the diagram, and 

 through the various points of division are drawn horizontal and vertical straight lines over the 

 whole figure. 



All these are again intersected by 32 curve lines, the spaces between which are alternately 

 light and shaded, marked in points and quarter-points for the determination of the courses. 

 Before explaining the construction of these curves I shall proceed to shew how the diagram 

 is to be used in the solution of the great-circle problem. 



Use of the Chart and Diagram. 



Prob. Given the latitudes and longitudes of the ship and of her destination, to find the 

 courses and distances to be run in order to follow the great-circle. 



Find the ship's place on the Chart and join it by a straight line with the port or place 

 bound to [a thread stretched from the one place to the other will be the most convenient and 

 simplest way]. This will be the great-circle track. 



Note the direction of the track near the ship's place, i.e. whether from N. or S. towards 

 E. or W. 



Note also the highest latitude of the track, i.e. the latitude of the place where (produced 

 if necessary) it approaches nearest to the pole. 



Vol. X. Takt. II. 36 



