278 Mr godfray, on a chart and diagram 



discretion whether he will continue on the parallel so attained, which would then be the 

 shortest track, or return to that first fixed upon. 



Construction of the Chart. 



The Pole is made the centre of projection, and a series of concentric circles will represent 

 the parallels of latitude, the radius of any parallel being r cot (lat-), where r is any convenient 

 linear magnitude and equals the radius of the parallel of 45°. The meridians are straight 

 lines drawn from the centre dividing each circumference into 360 equal parts. Any one of 

 these being selected for the meridian of Greenwich, the coast-lines of the different countries 

 may be then traced in the usual manner by means of the latitude and longitude of the 

 different points. 



The magnitude of the circles increases so rapidly in low latitudes, — becoming infinite at the 

 equator, — that it is impossible to bring in the equatoreal regions when the Pole is made the 

 centre of the chart, and even the 10th parallel of latitude cannot be introduced into any mode- 

 rate sized sheet without making the higher latitudes indistinct from their reduced dimensions. 



But there are two reasons which render it perfectly unnecessary to introduce any portion 

 of the inter-tropical regions. The first is that the difference between the track by great-circle 

 and by Mercator is so small both as to length and as to position when a ship has to cross or 

 to approach the Equator, that the one sailing has no practical advantage over the other. But 

 the circumstance which more especially renders the rules of great-circle sailing unimportant 

 in low latitudes is the presence of the trade-winds, which extend to from 20" to 25° on eacii 

 side of the Equator. Every method must be subservient to these well-known currents of our 

 atmosphere, and any chart which gives the correct outline of the continents and allows the 

 sailor to mark down the ship's position day by day, will answer his purpose, whether it be a 

 Great-circle, a Mercator, or even a Plane chart. There will be no sensible difference between 

 his courses whether determined by Mercator, great-circle, middle latitude, or Plane sailing; 

 for he will have to shape his course for comparatively short distances at a time, in order to 

 reach certain positions which experience has proved will enable him to derive the greatest 

 advantage or the least injury from the trade-winds and from those calms, the Doldrums, which 

 prevail near the Equator. 



Therefore since numerous charts for these regions have been published on Mercator's 

 projection, there is no necessity for introducing others which have no advantage to offer. As 

 I have already stated, Great-circle sailing must not be considered as a substitute for Mercator's, 

 but as an auxiliary to be employed when the judgment of the seaman tells him it would 

 shorten his voyage to do so. 



If however great-circle charts were desired which woiild include the Equatoreal regions, 

 we should merely have to take for our centre some point in the Equator. In such a chart the 

 meridians would be parallel straight lines, and the parallels of latitude would be represented by 

 hyperbolas. 



If a point not in the equator were taken for centre, the meridians would be converging 

 straight lines and the parallels would be hyperbolas and ellipses. There is no need to enter 

 upon any investigation of them here. 



