io6 



NATURE 



[June 



2, i: 



circle arc to her destination. This is demonstrably 

 the shortest distance between the two places under the 

 given conditions. 



The labour of utilising great circle sailing by the 

 rigorous method has been much magnified. It is not 

 necessary to find the distance accurately (or even at 

 all) every day, and the first and last courses are easily 

 and quickly worked with the two co-latitudes and 

 difference of longitudes (two sides and the contained 

 angle to find the angles at the base) ; and for this pur- 

 pose it is near enough in practice to take out the logs to 

 three or four figures. This is the same formula as for 

 time azimuths, which explains why great circle courses 



A-aU^fUi. 



Exantpli 



Cot 9"S903o 



Cos 9-91336 

 Cos 9-74943 



Cos 9-66279 



AB 62° 37' 

 60 



; circle dist. B to equator 3757 miles. 



Last course N. 49° 46' W, 



-can be obtained from azimuth tables. Towson gets a 

 right angle at the vertex, and so obtains brevity of solu- 

 tion. Now I will introduce a short method of my own, 

 vi^hich I always use when the conditions are suitable. It 

 is a very general, practice to settle on the point to cross 

 the equator according to the season of the year. Pro- 

 ceeding from Cape Leeuwin to Cape Guardafui, for in- 

 stance, to be well to windward in the south-west monsoon, 

 it is advisable to cross the line in about 60° E. long. Now, 

 by working towards this point, the first course and distance 

 may be obtained by quadrantal spherics quicker than by 

 Mercator's sailing, because, though there are the same 

 number of figures, the logs can be taken out in pairs, 



NO. 1492, VOL. 58] 



or triplets if the last course is required, to see if the ship 

 is keeping on the same great circle. Unfortunately, it can 

 only be used approaching the equator or in calculating a 

 track thence to the next point of destination ; but I have 

 already shown how the courses alone can be quickly ob- 

 tained in other cases, independent of the innumerable 

 ways of getting them by inspection, and the graphic 

 methods of Airy and Fisher, besides which there are 

 various protractors and mechanical devices for those that 

 favour such methods. 



Now, whilst the foregoing methods are all sufficient to 

 enable the navigator to obtain the bearing and distance 

 of his port or destination, they are far from being irre- 

 proachable as a means of finding the 

 daily position of a ship at sea, though 

 they are always used for this purpose 

 in case no better position is obtain- 

 able, or if it is, to compare with it. 

 The cause of the deficiency is the un- 

 certainty of the elements used in the 

 calculation. When a ship on any 

 given day leaves a well-ascertained 

 point of departure, her position next 

 day is obtained by the course steered 

 and distance run. But neither can be 

 absolutely relied on. In the finest 

 vessels afloat with the most perfect 

 navigating appliances, the course 

 steered, even in fine weather, will 

 be uncertain to 1°, which is equivalent 

 to a deflection of i| miles in every 

 100. This may easily be trebled or 

 quadrupled in bad weather if com- 

 pass errors cannot be checked, which, 

 with every possible care, are liable to 

 sudden and unlooked-for changes. 

 In bad steering vessels, or with badly- 

 placed compasses, or where the errors 

 are not frequently checked, or from a 

 combination of these causes, tlie error 

 in the course may amount to 10^, 

 which is equivalent to a deflection of 

 \'j\ miles in every 100. The distance 

 run, under the most favourable cir- 

 cumstances, is liable to an error of 

 3 per cent., which head winds or 

 other causes may easily double or, 

 in exceptional circumstances, magnify 

 still further. Then, again, the cur- 

 rents of the sea are the most 

 uncertain element with which the 

 navigator has to deal. Half a knot 

 to a knot per hour is quite common, 

 whilst five knots, or over, is not un- 

 known. Except in a few localities, 

 the direction is almost as uncertain 

 as the strength. Even where currents 

 run pretty regularly, these ocean 

 rivers are not confined and held in 

 position by fixed limits like those 

 of the land, but are as flexible 

 as snakes, which is perhaps the origin of the symbol de- 

 noting them on current charts, which at best only give a 

 general idea what to expect : they are frequently deflected, 

 or even reversed, by distant winds, or other causes quite 

 beyond the ken of the navigator whose ship is being 

 affected by them. With all these elements of uncertainty 

 in the data used, it cannot be wondered at if the position 

 by dead reckoning be of doubtful accuracy ; and it would 

 probably be more uncertain still, but that the numerous 

 sources of error generally tend to compensate one 

 another. It is, none the less, of the highest importance 

 to the navigator to keep his log account with the greatest 

 care, in case he has nothing better to depend on. Luckily, 



Cot 10-15477 

 Sin 9-91772 



