Kebeuaky 2, 1900.] 



SCIENCE. 



185 



der may also be made tangent to a meridian 

 instead of the equator by which the square pro- 

 jection is changed into Cassini's, which, for mod- 

 erate distances from the central meridian, great- 

 ly resembles the polyconic. Cylindric projections 

 may also be made equivalent (3/= sin o), when 

 we obtain Lambert's equivalent cylinder projec- 

 tion, but it is only when it assumes that shape 

 (called conformal by Gauss and autogonal by 

 Tissot), in which there is no angular distortion, 

 or in which the elementary arcs of longitude and 

 latitude preserve their relative dimensions, when 

 y =log nat. tang (45°+ J*), that this projec- 

 tion, as the Mercator, has attained an impor- 

 tance which puts all others into the shade. The 

 vexatious question of nearly fifty years stand- 

 ing whether the Mercator or polyconic pro- 

 jection offers greater advantages for hydro- 

 graphic charts, does not appear to have been 

 finally settled yet. Granting that sailing by 

 the orthodrome is preferable to sailing by the 

 loxodrome, and that the polyconic gives the 

 orthodrome in a more nearly straight line than 

 the Mercator, this departure from a straight 

 line may assume sufficient proportions to render 

 the polyconic chart unreliable while, with the 

 positive knowledge that, with the exception of 

 Meridians and the equator, all great circles are 

 curves on the Mercator chart, no sailor will 

 meet with any difficulty in laying down ortho- 

 dromes on a Mercator chart without calculations 

 with the assistance of a gnomonic chart ; but 

 the chief argument in favor of Mercator charts 

 will always remain the facility of laying down 

 positions and courses. For hydrographic charts 

 which are not intended to be used as sailing 

 charts, or which are on such large scales that 

 the sea area occupies but a narrow margin, the 

 employment of theMercator projection should be 

 avoided for the reason that the differences with- 

 in the narrow limits between the two contend- 

 ing classes of projections are sufficiently small 

 to allow the use of a polyconic for the same 

 purpose as the Mercator chart, but they are 

 great enough to render a Mercator chart unfit 

 for most of the uses a map may be put to, such 

 as the measurement of distances and areas. 

 Another very extensive use to which the Mer- 

 cator projection has been put is for planispheres 

 in atlases, especially for the purpose of dis- 



seminating and illustrating information of a 

 statistical or physical nature, and here Blundau 

 is slightly mistaken if he assumes that in this 

 capacity it could very properly be superseded 

 by projections of less objectionable features. 

 For many purposes, for meteorological charts 

 for instance, it is of greater importance to have 

 the cardinal directions, north and south, east 

 and west always point the same way and re- 

 main parallel to the borders of the chart, than 

 to have correct areas and to have these lines 

 run in every possible way. The objection so 

 frequently raised against the Mercator projec- 

 tion that it does not furnish any indications for 

 the courses of great circles, may readily be over- 

 come by constructing on transparent paper a ■ 

 system of great circles which intersect the 

 equator in two opposite points. If, however, 

 the Mercator chart is used to illustrate condi- 

 tions in which correctness of area is more im- 

 portant than parallelism in identical bearings, 

 like those showing density of population, or the 

 distribution of animals and plants, it may very 

 properly be superseded by others of an equiva- 

 lent nature; if no other, by Mollweide's which 

 is very easily constructed, and always available. 



The closing chapter about projections treats 

 of the selection of one with least distortion and 

 gives a resume of the results of Tissot' s inves- 

 tigations with tables giving the relative values 

 of the elements of ' deformation ' for the prin- 

 cipal projections in use, reducing the formerly 

 often troublesome question about the relation 

 of a projection for a special purpose to one of 

 easy solution. But this applies only to maps 

 embracing large areas, as those of continents ; 

 the question about the projection with least 

 distortion for areas of restricted size, such as 

 European countries, does not admit of a general 

 solution, but has to be solved for each country 

 separately and this solution is definite. In no 

 such case would the projection be one admitting 

 geometrical construction ; it would be one en- 

 tirely dependent upon analysis. 



Having carefully perused the volume from 

 beginning to end, I conclude that it is an emi- 

 nently practical book and gives to the cartog- 

 rapher all the information he may possibly 

 need regarding the nature of projections and 

 their constructions ; but it is because of this 



