FOR FACILITATING GREAT-CIRCLE SAILING. 273 



It is true these tacks will not be persevered in; for both A and B know that a course 

 which does not lead direct to the destination must gradually become less and less favourable, 

 until at length it becomes desirable to adopt the other tack ; but B will know when to make 

 this change, and A, with the same object in view, will either start on the wrong tack, or 

 abandon the right one too soon, or else persevere in it too long after it has become the 



2. The difference of distance between two places as measured on a great-circle or on a 



Rhumb course may in some instances be very small, although the two tracks differ considerably 



in position. 



„ . „ ^ ^, . flat. Sl'se'Nl „ „ . flat. 46"40'N1 



For instance : from Cape Clear in ;, , ,,, \ to Cape Kace in <, , „,? > 



^ jlong. g^ap Wj ^ (long. 53° 8 Wj 



the distance by Mercator is 1738 miles, 



and by Great-circle ... 17H ... 



so that the difference is only 24 miles, but at starting 



the course by Mercator is S. 80° 32' W, 



and by Great-circle is N. 82* ll' W, 



which differ by 17* l', or rather more than 1^ points. 



Now 24 miles is a run of 2 or 3 hours, and this, with a fair wind or for a steamer, is the 

 advantage to be derived from the adoption of Great-circle sailing in this particular instance ; 

 but suppose a sailing vessel beating against a contrary wind, the advantages will be far 

 greater. The difference of l^ points between the courses at starting may allow a ship running 

 within 6^ points of the wind to steer 5 points from her course, if that course be the great- 

 circle and the wind blow from the Rhumb ; and therefore in a day's run of say 120 miles the 

 1714 miles will be reduced to about l647, a decrease of 67 miles. But a second ship also 

 running within 6^ points and selecting the other tack, which according to Mercator appears 

 equally favourable, will be steering at right angles to the great-circle course, and at the end of 

 the 24 hours this ship instead of having gained will actually be a little further from Cape 

 Race than at the commencement. On the next day this second ship will be put on the other 

 tack, which will now be the correct one, and at the end of this day will have gained some 67 

 miles, that is, be about the same distance from her destination as the other ship was at the end 

 of the first day. 



Here then we see that one day out of two is lost by not adopting Great-circle sailing. 

 The differences will not be so great when the vessels come near the place of destination ; but 

 on the whole there will be a gain of 4 or 5 days, and this merely from Cape Clear to Cape 

 Race. 



In this instance the two tracks are about 140 miles apart at their widest separation, and 

 the value of Great-circle sailing is shewn by that which is the proper way of estimating it, 

 viz. the gain in time, — the difference of 24 miles would otherwise be comparatively un- 

 important. In crossing the Pacific under similar circumstances of contrary winds the gain 

 might extend to from 30 to 40 days. 



