Geographical Mays and Sailing Charts. 255 



found to be 97° 50', while by calculation it is 97° 45'. To 

 measure from Luzon to Honolulu, and from Honolulu to San 

 Francisco, along the great circles drawn on the plate, it would 

 be necessary to turn the protractor about its center until its 0° 

 and 180° points corresponded with the intersections of the equa- 

 tor with the two great circles shown in the figure. The dis- 

 tances, as measured with the protractor shown in figure 12, 

 were 75° 5' and 34° 30', as against 75° V and 34° 40' by calcu- 

 lation. 



Even when it is desired to measure from the northern to 

 some point in the southern hemisphere, it may be accomplished 

 easily. Take, for example, from Luzon to the western 

 entrance of the Strait of Magellan : Keferring to an atlas sheet 

 of South America, the entrance to the Strait is found to be 

 75° W., 52° 30' S., hence the antipodal point, J/, figure 6, is 

 located in the northern hemisphere on the continuation of the 

 seventy-fifth meridian (105° E.) at 52° 30' K Measurement is 

 then made from Luzon to a, on the equator, and, taking up 

 the measurement from the opposite point, from a' to M, along 

 that portion of the great circle indicated by a full line. This 

 distance measured with a protractor was found to be 144° 10' 

 as against 144° 15' by calculation. Another way would be to 

 measure from Luzon to M, along that portion of the great 

 circle which is dashed, w T hen the supplement value gives the 

 desired distance from Luzon to the Strait. The track of the 

 great circle indicated by the diagram could not be sailed, as 

 it runs through Australia and other islands. Another and 

 simpler method of measuring from one hemisphere to another 

 will be indicated in a later paragraph. 



In addition to facility of construction, projections on the 

 plane of the equator are especially adapted to ready measure- 

 ment of angles, since a meridian through any point, which 

 gives a true north and south direction, is a straight line. 

 Methods of measuring spherical angles have already been 

 described by the writer,* and figure 7 is an illustration, taken 

 from crystallography, of a still simpler method of making such 

 measurements. It is recommended to use a special protractor 

 PP, having the lines of graduation continued to near the 

 center, and which could easily be engraved by means of a 

 dividing engine. From a, figure 7, to the nearest point 

 marked d is 45°, and three great circles running from a to d 

 intersect at the points lettered o ; the angles made by the 

 meeting of the great circles at o being exactly 60°. To measure 

 an angle, the protractor, printed on transparent celluloid, is 

 centered as at o, figure 7, its 0°-0° line is made to coincide 



*Loc. cit., pp. 18 and 19. 



