THE 

 LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FOURTH SERIES.] 



DECEMBER 1861. 



LIII. Explanation of a Projection by Balance of Errors for 

 Maps applying to a very large extent of the Earth's Surface ; 

 and Comparison of this projection with other projections. By 

 G. B. Airy, Esq., Astronomer Royal*. 



1. TN the projection for maps, whose principles I am about 

 X to explain, any point of the earth's surface (as Green- 

 wich, Paris, &c.) may be adopted as the Centre of Reference, to 

 be represented by the Central Point of the Map. But the pro- 

 jection which I propose, and those with which I shall compare 

 it, are all subjected to the following conditions : that the azimuth 

 of any other point on the earth, as viewed from the Centre of 

 Reference, shall be the same as the azimuth of the corresponding 

 point of the map as viewed from the central point of the map ; 

 and that equal great-circle distances of other points on the earth 

 from the Centre of Reference, in all directions, shall be represented 

 by equal radial distances from the central point of the map. 

 These conditions include the Stereographic Projection, Sir H. 

 James's Projection, and others; but they exclude Mercator's 

 Projection, and the projections proposed by Sir John Herschel. 



2. In projections like these, in which the relation of the sur- 

 face represented to the surface representing it is the same in all 

 directions from the central point, it is unnecessary for us to em- 

 barrass ourselves with considerations of the place of the pole and 

 the forms of the curves representing arcs of meridian and paral- 

 lels. It will be sufficient to consider what will be the radii of 

 circles on the map which shall represent circles on the earth, of 

 different radii (as measured by arcs of great circle), but having 

 the centre of reference as their common centre ; and when values 

 are found for the radii of these circles on the map, means will 



* Communicated by the Author. 

 Phil Mag, S. 4. Vol. 22. No, 149. Dec. 1801 . 2 E 



