appendix.] GBEAT CIRCLE SAILING. 169 



monly called ' Great Circle Sailing,' it is as well to re- 

 mark that, when sailing from Southampton to Madeira, the 

 rhumb line (or track cutting all meridians at the same 

 angle) approximates so closely to an arc of a great circle, 

 owing to the very trifling difference of longitude between the 

 positions as compared with the difference of latitude, that the 

 unsophisticated seaman, while shaping his course by either 

 Mercator's or middle latitude sailing, is, without knowing it, 

 sailing closely upon an arc of a great circle, and consequently 

 upon the most direct route. For example, the distance be- 

 tween the Lizard Point in England and Funchal is, by Mer- 

 cator's sailing, 1164 geographical miles, and by great circle 

 sailing 1163, only one mile shorter. 



" I add, for the benefit of the amateur sailor, this case 

 worked out both by the usual method (Mercator's sailing) and 

 by great circle sailing. 



" Let difference of latitudes = a, and meridional diff. of 

 lats. = >i ; diff. of longitude = A ; bearing, or course, = ; 

 distance required = x. 



"TO FIND THE COURSES. 



n = 1389 Log . . 3-145507 



Radius . 10-000000 



A = 703 Log . . 2-846955 



= S. 26-42' W. Tangent . 9-701448 



"to find the distance. 



Radius 10-000000 



a = 1040 Log .... 3-017033 

 0= 26-42' Secant . . . 10-048968 



* = 1164 Log 3066001 



I 



