FOR FACILITATING GREAT-CIRCLE SAILING. 281 



Then proceeding along the horizontal line towards the highest latitude, measure the breadths 

 of the successive light and shaded spaces and the following series of courses and distances will 

 be obtained : 



S 5^ points E 45 miles. 



S 5^ ... E 253 ... 



S 5| ... E 235 ... 



S 6 ... E 220 ... 



S 6^ ... E 208 ... 



S 6^ ... E 197 ... 



S 6§ ... E 188 ... 



S 7 ... E 181 ... 



S 7i ... E 176 ... 



S 7| ... E 173 ... 



S 7f ... E 171 ... 



East 83 ... 



The highest latitude being now reached, the ship will have to go through the same courses 

 and distances in an inverse order ; but, as is evident from the chart, the courses will now run 

 between the North and East, and the series will be, 



East 83 miles. 



N 7| points E 171 ... 



N 7^ ... E 173 ... 



N 7i ... E 176 ... 



N 7 ... E 181 ... 



N 6| ... E 188 ... 



&c 



until the latitude of Perth 32" is reached, which, as the diagram shews, will be at 2465 miles from 

 the highest latitude. The total distance is therefore 4595 miles, which is 204 miles less than by 

 M creator, and the first course by Mercator would be N. 87° 59' E., differing nearly 3 points 

 from that by great circle. 



I have given all the courses and distances from Cape Agulhas up to and even from beyond 

 the liighest latitude, but in actual practice the first two or three alone would be required. 



Ex. 2. A ship in lat. 30° S., long. 18" W. is bound to Melbourne. 



The great-circle track will here be found to reach 77^° South, and is consequently imprac- 

 ticable. Suppose 55* to be the highest latitude decided on. 



Since the highest latitude is known, the courses and distances can at once be found by the 

 diagram. 



The intersection of the horizontal line through 55° with the parallel of the ship 30" falls on 

 the course 3f points at a distance 3140 miles. 



Hence the first course is S. sf E. or S.E. ^ S. 



And by examining the distances at which the changes of course take place, we find that the 

 ship must run 305 miles on this course, then 330 miles on the course S. 4 points E. &c.; but to 

 see whether these courses are practicable or not, we mugt refer to the chart. 



36—2 



