2 74 



NATURE 



[October 28, 1920 



examples and to formal riders. The fourth stage 

 knits all the theorems, previously considered, into 

 a logical chain with formal proof. A few riders 

 are interspersed, and there is a considerable 

 amount of general discussion in this part of the 

 text; the section closes with a collection of riders 

 arranged under headings corresponding to suit- 

 able groups of propositions. 



With the general changes of procedure adopted 

 by the authors we are in entire agreement. There 

 can be no question that boys are capable of 

 making simple appOcations of the fundamental 

 theorems of geometry long before they are able 

 to appreciate the formal proofs, and the stimulus 

 which work of this nature supplies is most bene- 

 ficial to their mental development. 



On its numerical side the exercises are very 

 good, being numerous, varied, and interesting ; on 

 the formal side we do not consider the work quite 

 so satisfactory; more riders of the "two-step" 

 nature are needed, particularly, for example, in 

 dealing with angle and tangent properties of the 

 circle. We think also that much of the dis- 

 cussion, which at present bulks so largely in the 

 text, might be omitted. We doubt whether any 

 boy reads it, and there is much that we find hard 

 to believe is really necessary for the instruction 

 of the teacher at the present time, when modern 

 methods are so much better understood than they 

 were, say, fifteen years ago. Some drastic prun- 

 ing of this kind would affect materially the size 

 of the book, and, we think, leave its utility un- 

 impaired, and at the same time appear to lighten 

 the student's burden. 



The printing is excellent, and the diagrams are 

 clear and numerous. A set of answers and sug- 

 gestions for class-work (which we have not seen) 

 is issued separately. We regard the new form 

 of this text-book as a definite advance in the right 

 direction, and commend it to teachers. 



The Evolution of Vertebrate Animals. 



Die Stamme der Wirbeltiere. By Prof. Othenio 



Abel. Pp. xviii-f9i4. (Berlin and Leipzig: 



Walter de Gruyter and Co., 1919.) Price 

 56 marks. 



PROF. ABEL, of- Vienna, is a most voluminous 

 writer on extinct animals, and even the diffi- 

 cult circumstances of the time do not impair his 

 energy and enthusiasm. He has now produced a 

 most interesting volume summarising our present 

 knowledge of the past history of the backboned 

 animals, and his technical descriptions are illus- 

 trated by numerous up-to-date figures which are 

 NO. 2661, VOL. 106] 



refreshing by their newness in a text-book. The 

 work is not merely a laborious compendium, but 

 is enlivened by many critical observations based 

 on Prof. Abel's own researches. 



Prof. Abel's classification will not in all re- 

 spects prove acceptable. He avoids too many 

 difficulties in the determination of affinities by an 

 undue multiplication of sub-classes and orders. 

 He also in some cases adopts the fantastic pro- 

 posals of certain dabblers in scientific literature 

 who discuss merely names without any acquaint- 

 ance with the fossils to which they refer. The 

 familiar generic name Ichthyosaurus, for example, 

 completely disappears, while the almost equally 

 well-known name Megalichthys is applied to the 

 wrong fish. The work, however, is intended for 

 advanced students who will be able to make allow- 

 ance for these idiosyncrasies without much 

 trouble. 



According to Prof. Abel, the Cyclostomes are 

 unknown among fossils, because the problematical 

 Devonian Palaospondylus, with its suctorial 

 mouth, is most likely the larval condition of 

 Coccosteus. The earliest fishes are the Upper 

 Silurian Anaspida. The earliest land-vertebrates, 

 the Stegocephala, are treated at great length on 

 account of the primitive character of the skeleton 

 and its morphological importance. Among rep- 

 tiles, the newly discovered Chelonia, from the 

 L'pper Trias of Germany, are especially striking. 

 Some of them retain traces of true teeth. The 

 Dicynodonts are described as "the Sirenians 

 among reptiles." The Triassic Parasuchia and 

 Pseudosuchia are separated from the Crocodilia. 

 The marine Thalattosauria, from the Trias of 

 California, are arranged with the Lacertilia. The 

 birds are treated in the usual manner. 



Among mammals, the Monotremata are re- 

 garded as unknown by fossils before the Pleisto- 

 cene; and the Triassic Tritylodon is referred to 

 the Marsupialia. The South American Tertiary 

 Sparassodonta are also retained among Marsupi- 

 alia. A few of the mammalian jaws of Jurassic 

 age (e.g. Amphitherium and Stylodon) are re- 

 garded as belonging to Placentalia. The Insect- 

 ivora follow, and the Primates, as usual, conclude 

 the series of orders. The various groups are 

 rather unequally treated, but students will be glad 

 to have the preponderating sections on Cetacea 

 and Sirenia as summarising Prof. Abel's own re- 

 searches. 



The volume is provided with two exhaustive 

 indexes, one to morphology, the other to tax- 

 onomy, and is a most valuable work of reference, 

 which should be added to every zoological library. 



A. S. W. 



