416 



NA TURE 



\_Angust 30, 1883 



as maps and charts showing the way in which the 

 foreshores, &c, are leased by Government to indi- 

 viduals and companies interested in oyster culture. 

 For further details concerning oyster culture in the 

 Netherlands, we may refer the reader to the conference 

 paper on this subject. On the whole oyster culture 

 appears to be very successful in this country. 



In the American department there is a large collection 

 of the most various oyster-shells, as well as the model of 

 a vessel occupied in dredging an oyster bed. "Culture" 

 of oysters appears to be very little practised in that 

 country up to the | resent day, the natural beds being as 

 yet of a nearly inexhaustible richness, especially in the 

 Southern States, where they are principally situated in 

 the lagoons along the coast-line, and the oysters very 

 often used as manure. Nor has the trade in these re- 

 gions been developed to any extent. More northward 

 Chesapeke Bay is the richest ground, and from thence 

 oysters are transplanted along the coasts of the different 

 Northern States, and at the same time brought into the 

 market in enormous numbers. Together with the scien- 

 tific investigations in the Netherlands, those in the 

 United States, conducted by Brooks and Ryder, and 

 those of Bouchou Beaudely in France, stand foremost as 

 commendable efforts to bring pure science to bear upon 

 fishery problems of great practical importance. 



UNITED STATES COAST AiXD GEODETIC 

 SURVEl ' 



THE author of this very important treatise states, in 

 *■ his preface, that he has attempted to give a suffi- 

 ciently comprehensive account of the theory of projections 

 to answer the requirements of the ordinary student of this 

 subject. The literature of projections being extensive — 

 the work of the most eminent mathematicians— the author 

 has contented himself with making such extracts from 

 the great mass of papers, memoirs, &c, which he deemed 

 requisite for his purpose, giving, for further information, 

 references to such original sources as are comparatively 

 easy of access. 



As the different conditions which projections for par- 

 ticular purposes have to satisfy are so wholly unlike, no 

 general theory underlying the whole subject of projections 

 can be given ; it is therefore conveniently divided into 

 several sections : and here the author mentions his obli- 

 gations to M. Germain's most important " Traite des 

 Projections " (Paris, 1865), which contains an account of 

 almost every projection that has been invented. At the 

 request of the Superintendent, Carlile P. Patterson, the 

 treatise has been divided into two parts. The first part 

 contains the mathematical theory of projections, while 

 the second part contains merely such a sufficient account 

 of the various projections as will enable the draughtsman 

 to construct them. 



The surface of the sphere being non-developable, the 

 exact representation of even a portion of it upon a plane 

 is impossible. Certain conditions can, however, be ful- 

 filled which will render it sufficiently exact for any par- 

 ticular purpose. The areas may be proportionately 

 preserved, in which case we have an equivalent projec- 

 tion ; or the angles of small portions may be preserved, 

 in which case we have an orthomorphic projection. The 

 exigencies of any particular use for which a projection is 

 designed give rise to a great number of other conditions 

 corresponding to which projections have from time to 

 time been invented : so that the history of projection has 

 been peculiarly that of the solution of more or less inde- 

 pendent problems : for a complete account of which the 

 reader is referred to M. D'Avezac's " Coup d'CEil histo- | 

 rique sur la Projection des Cartes de Geographic" (Paris, 

 1863). 



1 ''United States Coast and Geodetic Survey" (Carlile P. Patterson, 

 Superintendem) A Treatise un Projections. By Thomas Craig. (Wash- 

 ing! d: Government Piinting 1 Mfice, 1882.} 



The author has treated his subject under the following 

 heads : — 



I. Orthomorphic Projection. 



II. Equivalent Projection. 



III. Zenithal Projection. 



IV. Projection by Development. 



The first part of the volume treats of the mathematical 

 theory, and is subdivided into nine sections. The first 

 section contains a brief introductory account of the prin- 

 cipal properties of conic sections and perspective projec- 

 tion — the most natural and simple method of representa- 

 tion. Sections II. and III. treat of methods of ortho- 

 morphic projection. Section IV. treats of projections by 

 development ; Section V. gives an account of zenithal, 

 and Section VI. of equivalent projections. Students of 

 these sections are presumed to have a fair acquaintance 

 with the methods of ordinary analytic geometry and the 

 elements of the differential and integral calculus. The 

 next three sections are extremely general, and will require 

 rather more extensive mathematical knowledge. These 

 sectijns were designed to connect the particular problem 

 of the plane representation of a sphere with the much 

 more comprehensive methods of representation of one 

 surface upon another, and to induce in the student. 

 having a real interest in the general theory, a desire to 

 consult the original memoirs for fuller information. 



The second part of the volume, which treats of the con- 

 struction of projections, doei not appear to require any- 

 detailed description; but as much of it is merely reprinted 

 from the fir=t part, the propriety of thus separating the 

 ''construction" fro .11 "theory" seems rather doubtful. 

 The book ends with tlrrty-one tables, nearly all extracted 

 from the original memoirs of the writers on different parts 

 of the subject of projections. In some cases, however, 

 improved tables by other authors are given. Where the 

 ellipticity of the earth has been taken into account the 

 tables ate given unchanged, as the effect of small changes 

 of ellipticity « ould be almost inappreciable ; and, more- 

 over, we have in p. xiii. of the introduction the important 

 state. nent that "The United States Coast and Geodetic 

 Survey will undoubtedly soon be able to produce a 

 much better value of the ellipticity than has yet been 

 given." 



Such are the contents of this valuable book we have 

 endeavoured to describe. It presents, however, some 

 signs of hasty arrangement and want of strict attention 

 to the correction of the press, which will doubtless be 

 removed from the next edition. Indeed the copy under 

 notice would scarcely seem intended for publication in its 

 present form. For instance, " The accompan) ing plates 

 . . ."mentioned in p. 230 are wanting; and we notice 

 the following typographical errors, &c. : — 



Preface, p. x. Philosophical Magazine, 1865, should be 

 1 862. 



Preface, p. x., and Introduction, p. xiv. There are 

 obvious errors in the title of Gauss's Memoirs. 



Introduction, p. xiv. Phil. Trans, vol. 1. should be 

 vol. L. 



P. So, line 12 from bottom, for plotting read plotting. 



Pp. 80 and 210. The descriptions of Cassim's projec- 

 tion do not seem to be correct. 



Pp. 81, 82, and 210. The woodcuts defective. 



P. 83. Curious error in the numerator of the general 

 expression for p. 



Pp. 67 and 197. Woodcuts of Fig. 13 not good. 



Pp. 71 and 201. Fig. 15, woodcuts require correction. 



Pp. 76 and 206. Fig. 18, woodcuts not very good. 



P. 149. In the denominator of the value of in the 

 power 2 of (1 + € cos w) should be c In the first term of 



the denominator of the value of k, sin- ' should be 



sin- ---, and in the second term a>, should be 



2 



; 



