S. L. Penf eld— /Stereographic Projection. 137 



bearing, as one meridian after another is passed. The rhumb- 

 course, which intersects all meridians at the same angle, hence 

 maintains the same compass bearing (41° 20' West of South) 

 throughout, is y y. It would be somewhat difficult to estimate 

 the distance traveled in following the rhumb-course, but, 

 judging from the figure, it would not be very much longer 

 than that of the great circle. In regions near the equator the 

 discrepancies between great-circle sailing and rhumb-sailing, 

 both as regards distance and direction, would not be very 

 great. As the polar regions are approached, however, discrepan- 

 cies become greater. The rhumb-line from Cape Flattery to 

 Bass Strait, figure 30, if continued toward the polar regions, as 

 indicated by the dotted lines y y, deviates more and more 

 from the great circle x x, and terminates eventually in two 

 spirals, circling around the respective north and south poles, 

 constantly nearing, yet, theoretically, never reaching them. 



The problems presented by navigation are naturally compli- 

 cated, and such factors as ocean currents and the probabilities 

 of encountering favorable winds and weather during certain 

 seasons of the year must be taken into consideration. Hence 

 the route along which the shortest and safest passage may be 

 ■made must be selected, rather than the shortest course. The 

 main factor, however, in determining the shortest passage must 

 be the shortest distance from point to point, which may be 

 determined by a stereographic protractor giving great circles, 

 figure 14. The direction of ocean currents and prevailing 

 winds may be represented on a stereographic chart as well as 

 on any other, and it must be a matter of judgment on the 

 part of a navigator to shape his course so as to take advantage, 

 as far as possible, of favorable and avoid unfavorable conditions. 



Instruments needed for plotting Stereographic Projections. — 

 For the most part, ordinary drafting instruments may be 

 used. Pencils should be very hard and sharpened to a chisel- 

 like edge, rather than to a point. For locating points very 

 exactly, a fine needle, fastened in a suitable handle, is very 

 useful. Although a puncture made by the needle point may 

 be quite a fraction of a degree in diameter, its center may be 

 regarded as indicating the exact location of any point; and in 

 reading scales and protractors with reference to the puncture, 

 the reading may be easily made from its center. An instru- 

 ment which is not very generally used and is almost indispen- 

 sable where great accuracy is required is a beam-compass. 

 Ordinary dividers are not very satisfactory, and when used 

 with an extension bar for constructing large circles the utmost 

 pains must be taken in order to get good results. 



For drawing very flat arcs the instrument shown one fourth 

 natural size in figure 31, and designated as the curved ruler y 



