416 A Map of the World on Flamsteed's Projection. 



regions, as the distortion which would otherwise have been 

 produced would have been inconvenient to an astronomer. 



The Preface points out the advantages of the method as 

 follows : — u So will you have the picture of the Constellation 

 projected upon it, in which the parallels of declination will be 

 straight lines and their distances exactly equal, the same as 

 they are on the globe, as will also the distances and differences 

 of the right ascensions of any two stars that are equally dis- 

 tant from the pole." The advantage in Geography of a map 

 in which the parallels of latitude are equidistant straight lines 

 parallel to the equator is obvious, as the position with regard 

 to latitude is seen at a glance. There is, moreover, a property 

 of this projection which is evident at once from the way in 

 which the projection is constructed, viz. that the area of every 

 part is preserved unaltered. The imaginary threads have 

 simply slipped over one another, like the cards in a pack, 

 without altering their distances, so that only a distortion of 

 form has occurred. This property is not referred to by Flam- 

 steed, either because he did not notice it, or because it was of 

 no importance in Astronomy. I venture to submit, however, 

 that in Physical Geography it is a property of considerable 

 importance, and that it would be advisable in many physical 

 maps to use this projection. For instance, in maps showing 

 rainfall, depth of the sea, height of the land, ocean currents, 

 prevailing winds, distribution of plants and animals, &c, it is 

 essential to take account of the area occupied, and maps in 

 which this is correctly shown could not fail to be of use. 

 In Plate V. is shown a map of the World on Flamsteed's 

 projection, the small square at the side representing 1,000,000 

 square miles on the same scale. 



The formulae for constructing the map are readily obtained. 

 Take the equator as the axis of x, and the central meridian 

 (say the meridian of Greenwich) for the axis of y. Let x, y 

 be the coordinates of a point m° of longitude from the central 

 meridian, and n° of latitude from the equator. Then if a is 

 the length of a degree of latitude in the scale adopted, 



y/cc = n, x I a. = m cos n°. 

 an m de 



Hence the equation to a meridian m degrees from the central 

 meridian is 



x 



~ = m cos 



a 



