172 tr. S. COAST AND GEODETIC SITRVET. 



PROJECTION FOR THE INTERNATIONAL MAP ON THE SCALE 

 OF 1 : 1 000 000. 



The projection adopted for this map is a modified 

 polycomc projection devised by M. Lallemand. The scale 

 IS slightly reduced along the central meridian, thus brining 

 the parallels closer together in such a way that the meridians 

 2° on each side of the center are made true to scale. Up 

 to 60° of latitude the separate sheets are to include 6° of 

 longitude and 4° of latitude. From latitude 60° to the 

 pole the sheets are to include 12° of longitude; that is, two 

 sheets are to be united into one. The top and bottom 

 parallel of each sheet are constructed m the usual way; 

 that is, they are circles constructed from centers lying on 

 the central meridian, but not concentric. These two par- 

 allels are then truly divided. The meridians are straight 

 lines joining the corresponding points of the top and 

 bottom parSlels. Any sheet will then join exactly along 

 its margins with its lour neighboring sheets. The cor- 

 rection to the length of the central meridian is very slight, 

 amounting to only 0.01 inch at the most, and the change 

 is almost too slight to be measured on the map. 



In the resolutions of the International Map Committee, 

 London, 1909, it is not stated how the meridians are to be 

 divided; but, no doubt, an equal division of the central 

 meridian was intended. Through these points circles 

 could be constructed with centers on the central meridian 

 and with radii equal to Pn cot <p. In practice, however, an 

 equal division of the straight-line meridians between the 

 top and bottom parallels could scarcely be distinguished 

 from the points of parallels actually constructed by means 

 of radii or by coordinates of their intersections with the 

 meridians. The provisions also fail to state whether, in 

 the sheets covermg 12° of longitude instead of 6°, the 

 meridians of true length shall be 4° instead of 2° on each 

 side of the central meridian; but such was, no doubt, the 

 intention. In any case, the sheets would not exactly join 

 together along the parallel of 60° of latitude. 



The appended tables give the corrected lengths of the 

 central meridian from 0° to 60° of latitude and the coordi- 

 nates for the construction of the 4° parallels within the 

 same limits. Each parallel has its own origin; i. e., where 

 the parallel in question intersects the central meridian. 

 The central meridian is the Y axis and a perpendicular to 

 it at the origin is the X axis; the first table, oi course, gives 

 the distance between the origins. The y values are smaU 

 in every instance. In terms of the parameters used 



