NA TURE 



[March 24, 1892 



During the second period (1813-1841) the chief names . 

 are Cauchy, Schweins, Jacobi, and Sylvester ; to these \ 

 may be added Desnanot and Scherk, to whom fresh j 

 departures, of less extent, are due. Schweins himself 

 may be said to have been discovered by Mr. Muir. .: 

 This author (1825) deals with the subject under the title 

 " Theorie der Producte mit Versetzungen." He made a 

 notable generalization described as the transformation of ; 

 an aggregate of products of pairs of determinants into 

 another aggregate of similar kind. He further discussed i 

 special forms, and, it is clear, possessed a firm grasp of ; 

 his subject. 



The work of Jacobi and Sylvester, and the further 

 work of Cauchy will be more or less familiar to mathe- 

 maticians. Germany has passed to the first place ; and 

 the occurrence of Sylvester's name in the history marks ' 

 a revival of learning in pure mathematics in England. ■ 



The volume is remarkable for the study it presents in 

 nomenclature and notation. There is an extraordinary 

 variety in the symbolism. It is easy to observe the dis- 

 tinctive characters of French and German notation that 

 are so marked at the present day. It is well known that 

 much lies in an appropriate notation. Every young 

 mathematician with a predilection for original work 

 should read this book, to note the power of suitable 

 symbols, to grasp the reason of their power, and, above 

 all, to see what to avoid. 



The book also points a moral which is not far to seek. 

 It would be easy to pick out many such phrases as, " was ! 

 acquainted with the writings of very few of his prede- 1 

 cessors " ; " was unaware apparently of the existence of I 

 a theory of determinants " ; " hasty, if not contemptuous, ' 

 disregard of historical research." To this tendency to 

 work on without proper attention to previous work is 

 doubtless due in some measure the unfortunate multipli- 

 cation of names and symbolisms which is so perplexing 

 and irritating to a reader. This failure to collaborate 

 with others can only retard the progress of the science. 

 It is perfectly true that great original thinkers, like 

 Gauss, Cauchy, Jacobi, and Sylvester, may take liberties | 

 of this kind ; and the fact of their doing so may even I 

 be beneficial to the subject, as resulting in memoirs of 

 more unfettered originality. But this is not so in the 

 case of lesser men. In taking leave of this fascinating ! 

 history one can look forward to Part II. with sincere j 

 pleasure, which is not diminished by the knowledge that \ 

 the later developments have been largely due to our 

 countrymen. We have yet to see Sylvester's most 

 powerful investigations, and all Cayley's researches; 

 and, finally, the successive steps by which the lofty 

 heights of the theory of matrices and the theory of 

 multiple algebra (involving the generalization of quater- 

 nions) have been attained. P. A. M. 



THE EVOLUTION OF MAN. 

 Anthropogenie, oder Entwickehingsgeschtchte des Men- \ 

 ■ scJmt. By Prof. Ernst Haeckel. Fourth Edition, re- | 

 vised and enlarged. Pp. i.-xxvi. and 1-906. (Leipzig : i 

 W. Engelmann, 1891.) ! 



nPHE importance of the subject-matter of the book, : 

 -L the length of time that has elapsed since the 

 appearance of the former editions, and the pro;ninent 1 

 NO. I 169. VOL. 45] 



position held by the author, seem to call for more 

 detailed notice of this work than is usually accorded to 

 a new edition. 



The " Anthropogenie," which was first published in 

 1874, is the third of the series of books in which Prof. 

 Haeckel has attempted to determine the laws governing 

 the form, structure, and mutual relations of living things, 

 and to establish the general principles of biological 

 science. The first of these, under the title " Generelle 

 Morphologie," appeared in 1866, almost simultaneously 

 with the completion of Herbert Spencer's " Principles of 

 Biology." It is a comprehensive and ambitious work, 

 which, in its author's words, 



" constituted the first attempt to apply the general doc- 

 trine of development to the whole range of organic 

 morphology, . . . and to introduce the Darwinian 

 theory of descent into the systematic classification of 

 animals and plants, and to found a 'natural system' on 

 the basis of genealogy ; that is, to construct hypothetical 

 pedigrees for the various species of organisms." 



It contains also the first systematic attempt to deal in 

 detail with the ancestry of man, as regards the groups of 

 animals lower than mammals. This is, perhaps, the 

 most solid piece of work Prof. Haeckel has done ; it 

 contains much matter of great value, and discussions 

 and speculations of extreme ingenuity and interest. 

 Later discoveries have rendered much of it obsolete, but 

 it still remains the most important work of its kind ; and 

 but for its somewhat cumbersome terminology, would be 

 widely read even now. The " Natural History of Crea- 

 tion/' first published in 1868, goes over a good deal 

 of the same ground as the earlier work, but is written in 

 a much more popular style, and aims at presenting in a 

 form suited to the general reader the main arguments on 

 which the Darwinian theory is based, together with a 

 detailed application of the theory to the principal groups 

 of animals, and an attempt to determine their mutual re- 

 lations and lines of descent. The "Anthropogenie," the 

 book now before us, is a more elaborate application of 

 the same principles to the special problem of the evolution 

 of man. 



In the new edition the general arrangement 'remains 

 much the same as before ; but, in order to include the 

 results of more recent investigations, a great part of the 

 book has been re-written, and new chapters have been 

 added on subjects that have attracted especial attention of 

 late years, such as the Gastraea theory, the Ccelom theory, 

 and the nature and origin of segmentation. A large 

 number of new figures have been inserted, and the genea- 

 logical tables, for which Prof. Haeckel has a special 

 fondness, have been greatly increased in number, and in 

 elaboration of detail. 



The book, which is adapted rather for the genera] 

 reader than the scientific student, is written in an attrac- 

 tive and popular style, and presents the main facts of 

 vertebrate embryology in an intelligible and well illus- 

 trated form. As might be expected from his former 

 writings, the main feature of Prof Haeckel's work is a 

 detailed exposition and vigorous defence of what he has 

 named " the fundamental law of biogenesis," better known 

 in this country as the recapitulation theory, according to 

 which the actual or ontogenetic development of an 

 animal is a repetition of the ancestral or phylogenetic 



