Febbuary 27, 1920] 



SCIENCE 



213 



can be surmounted, it may ultimately be 

 possible to connect Australia with the East 

 Indies and so with Asia. 



H. L. Cooke, 

 Henry ISToeris Eussell 

 Princeton TTnivebsity 



TWO NEW BASE MAPS OF THE 

 UNITED STATES 



An outline base map of the United States 

 ou the Lambert Zenithal equal area projection, 

 scale 1-7,500,000, dimensions 19| inches by 

 25| inches, price 15 cents, has just been 

 issued by the Coast and Geodetic Survey. 



The map covers the whole of the United 

 States, including the northern part of Mexico. 

 Only state names and boundaries, principal 

 rivers, capitals, and largest cities are shown, 

 the chief object being to furnish a base map 

 for political, census, or statistical purposes on 

 a projection in which the property of equiv- 

 alence of area is one of the essential features. 

 It is the first publication of a projection of 

 this type by the Coast and Geodetic Survey. 



The two errors, to one or both of which all 

 map projections are liable, are change of area 

 and distortion, as applying to portions of the 

 earth's surface. Errors of distortion imply 

 deviation from right shape in the graticules 

 or network of meridians and parallels of the 

 map, involving deformation of angles, curva- 

 ture of meridians, changes of scale, and errors 

 of distance, bearings, or area. 



In the mercator projection as well as in 

 the Lambert Conformal Conic projection, the 

 changes in scale and area can not truly be 

 considered as distortion or as error. A mere 

 alteration of size in the same ratio in all 

 directions is not considered distortion or 

 error. These projections being conformal, 

 both scale and area are correct in any re- 

 stricted locality when referred to the scale of 

 that locality, but as the scale varies in lati- 

 tude from point to point large areas are not 

 correctly represented. 



In the Lambert Zenithal projection the 

 zenith of the central point of the surface to 

 be represented appears as pole in the center 

 of the map; the azimuth of any point within 



the surface, as seen from the central point, 

 is the same as that for the corresponding 

 points of the map; and from the same central 

 point, in all directions, equal great circle dis- 

 tances to jKiints on the earth are represented 

 by equal linear distances on the map. The 

 amount of scale error, as we depart from the 

 center of the map radially, increases (scale 

 becoming smaller), while in a direction at 

 right angles thereto the scale is by the same 

 amount too great. 



For a distance from the assumed center of 

 the map equal to 23 degrees of arc of a great 

 circle, an extent embracing the whole of the 

 United States, the maximum scale error is 

 but one and seven eighths per cent. The 

 amount of this error is less than one third of 

 the scale error in a polyconic projection of 

 the same area, while the direction errors 

 (errors of angles and azimuths) are likewise 

 considerably less than in the latter projection. 



An outline base map of the United States 

 on the Lambert Conformal Conic projection, 

 scale, 1-5,000,000, dimensions, 25 by 39 inches, 

 price, 25 cents, has also been issued by the 

 Coast and Geodetic Survey. This map is 

 similar to the one on the Zenithal Equal Area 

 projection in general treatment. It is larger 

 in scale, however, but embraces a lesser extent 

 of latitude, being limited to the area of the 

 United States, whereas the zenithal equal area 

 map includes the greater portion of Mexico. 



The map is of special interest from the fact 

 that it is based on the same system of pro- 

 jection as that which was employed by the 

 allied forces in the military operations in 

 France. 



The term conformal has been defined as 

 follows: If at any point the scale along the 

 meridian and the parallel is the same (not 

 correct, but the same in the two directions) 

 and the parallels and meridians of the map 

 are at right angles to one another, then the 

 shape of any very small area on the map is 

 the same as the shape of the corresponding 

 small area upon the earth. The projection is 

 then called orthomorphic (right shape). 



The value of this new outline map can best 

 be realized when it is stated that throughout 



