Febeuaey 2, 1900.] 



SCIENCE. 



181 



' Notes on regeneration and regulation in 

 Planarians,' by F. R. Lillie. 



J. 8. KiNGSLEY, 



Secretary. 



SCIENTIFIC BOOKS. 

 Leitfaden der Kartenentwurfslehre fur Studierende 

 der Erdkunde und deren Lehrer bearbeitet von 

 Prof. Db. Karl Zoppritz in zweiter neube- 

 arbeiteter und erweiterter Auflage herausge- 

 geben von Dr. Alois Bltjndau. Erster 

 Theil : Die Projectiouslehre. Mit 100 Fig- 

 uren und zahlreichen Tabellen. Leipzig, B. 

 Or. Teubner. 1899. 



The first edition of Zoppritz ' ' Leitfaden der 

 Kartenentwurfslehre,' a volume of 162 pages, 

 appeared in 1884, and treated of projections, 

 topographical drawing, plotting of itineraries 

 and other matter more remotely connected 

 with the construction of maps, such as the as- 

 tronomical determination of geographical posi- 

 tions, constructions of geometrical curves, etc. 

 The reputation of the author and the variety of 

 contents secured a favorable reception to the 

 volume, but it is a singular fact that its chief 

 merit, that of opening a warfare upon the 

 almost universal practice of misusing projec- 

 tions, should have been the least appreciated. 

 Zoppritz was the first one in Germany who 

 recognized the far-reaching importance of 

 Tissot's investigations concerning distortions of 

 projections and utilized them for his work, but 

 the innovation was coldly received by German 

 geographers. It was not until two years after 

 Zoppritz ' death, in 1887, that Hammer took 

 up the fight and by his masterly translation of 

 Tissot's m6moire succeeded in securing foothold 

 for Tissot's ideas in the German scientific mind, 

 and thus removed the last doubt about an ulti- 

 mate victory of the principle " that the proper 

 selection of a projection for a special pur- 

 pose is not, like fashion, a matter of custom 

 and taste, but dictated with analytical rigor," 

 and thus prepared the way for a new edi- 

 tion of Zoppritz' 'Leitfaden.' The first part 

 of this new edition, now in our hands, treats 

 of projections exclusively and will be fol- 

 lowed by a second volume, devoted to topo- 

 graphical drawing. No disparagement of the 



memory of Zoppritz is implied, but a tribute 

 is paid to the sound judgment and industry 

 of his successor, Blundau, for the proper as- 

 similation of the new information and experi- 

 ence accumulated since Zoppritz ' death, if I 

 make the statement that the present edition 

 is superior to the first one by a more exhaus- 

 tive and systematic treatment of the subject in 

 hand, by a general application of Tissot's tests 

 and by the subordination of mere geometrical 

 construction to computation. 



The ' Leitfaden ' was designed primarily as a 

 guide to students and professors of German uni- 

 versities ; and it is a significant indication of the 

 conditions prevailing in these institutions, that 

 Zoppritz should have deemed it necessary to 

 apologize for the introduction of two or three 

 formulas of spherical trigonometry, and that 

 Blundau should make it a rule to avoid 

 calculus ; and in several instances, such as in 

 giving the formula for equatorial distances in 

 Mercator's projection, to rather omit the proof. 



In passing over the contents of this volume in 

 cursory review, I propose to pause only when 

 meeting meritorious projections, which appear 

 to have been neglected in this country, or such 

 as recommend themselves to cartographers for 

 special purposes. 



Azimuthal projections. — This class of projec- 

 tions, although of considerable antiquity, has 

 of late years become almost totally neglected. 

 Many of them possess peculiar properties not 

 found in any other projections which make 

 them well suited for special purposes. Blundau 

 introduces a very salutary departure from the 

 usual practice of treating these projections 

 separately by stating their common properties 

 and the distinguishing featui-es of each kind. 

 It is a common property of all azimuthal pro- 

 jections that every point on the surface to be 

 represented is shown in its true azimuth from a 

 central point, and the distinguishing feature of 

 each kind is the particular function of the 

 spherical zenith distance of the point from the 

 center of the map which is adopted as a measure 

 of its distance, orm^ / ('')i where m represents 

 the radius or distance from the center of the 

 map, and (5 the zenith distance. The first pro- 

 jection coming under consideration is PosteVs, 

 in which the distances are given by the arcs 



