354 Penfield — Use of the Stereographic Projection. for 



Calcu- 

 lated. Measured. Error. 



I. 



From 42° 



K, 



79° 



W. to 45 c 



>K, 



74 c 



W. 



325-2 



3253 



+ 0-1 



II. 



« 



43 



N., 



79 



W. " 43 



N., 



73 



W. 



303-4 



303-2 



— 0-2 



III. 



<( 



43 



N., 



79 



W. " 41 



N., 



72 



w. 



385-3 



385-3 



o-o 



IV. 



cc 



45 



N., 



74 



W. " 41 



N., 



74 



w. 



276-6 



.276-4 



— 0-2 



V. 



(( 



44 



N., 



76 



W « 41 



N., 



74 



w. 



231-1 



231-0 



—o-i 



VI. " 41 N., 80 W. " 41 N.,- 72 W. 417*4 417*5 +0*1 



It will be noticed that the maximum error given in the table 

 does not exceed 0*2 mile, and this is to be attributed largely 

 to the excellency of the method of projection. It should be 

 stated that on this map, as also on that of the United States, 

 previously cited, measurements of distances were in all cases 

 made with a millimeter scale, and were converted to miles by 

 simple proportion, using logarithms in making the calcula- 

 tions ; hence, in determining the results, there was absolutely 

 no personal bias, or possible unavoidable tendency to favor the 

 reading of the scale so as to make the errors small. The tables 

 show exactly what may be done on such maps, except that 

 even better results could be obtained by those having more 

 skill and experience in map drawing, and better appliances for 

 measuring. On a map of so small an area as that shown in 

 figure 23, the course of a great circle deviates but very little 

 from a straight line. Thus, the line AB, at the right, is 

 straight, and it may scarcely be told that it differs from the 

 seventy-second meridian, which is a portion of a circular arc, 

 drawn with a curved ruler. 



Applications of the Stereographic Projection to Navigation. 

 — The writer has been given to understand that no body of 

 men are so conservative as mariners, and that they are fully 

 committed to the use of charts based upon Mercator's projec- 

 tion, to which they have been long accustomed ; also that per- 

 haps the majority of seafaring men abominate nothing so much 

 as a chart with only curved lines on it. In spite of these 

 strong prejudices, however, it is believed that charts based 

 upon the stereographic projection possess so great merit, that 

 it would well repay any navigator to study into their possi- 

 bilities. 



Although the shortest distance between two places on a 

 sphere is along the arc of a great circle, it is not always best to 

 continue to sail along the course of one great circle, for it may 

 lead into too high latitudes, or into regions where unfavorable 

 winds or ocean currents may be anticipated. Aside from the 

 consideration of winds, ocean currents, and latitude, however, 

 which must be studied into and reckoned with for each par- 

 ticular problem in navigation, there must always be some sav- 

 ing of distance from following great circles, rather than 



