September i 6, 1922] 



NA TURE 



3/J 



connected with 400 k\v. high-frequency alternators 

 through two or three frequency doublers connected in 

 cascade. The smaller sections are connected to smaller 

 machines. Although the antennae are close they can 

 be operated quite independently of one another. 



Dr. Meissner, the engineer-in-chief, hopes to reduce 

 the earth-resistance of the antennae to a fraction of its 

 present value. How much this resistance lowers the 

 efficiency can readily be seen by the figures given in 

 this book. For example, in one case the effective 

 current in the antennae is given as 360 amperes and its 

 resistance is 2-7 ohms. We learn that radio-telephonic 

 systems are now established between Munich and 

 Frankfort and between Berlin and Hamburg. 



Phytopalaontologie und Geologic. Von Prof. Dr. W. 

 Deecke. Pp. iii + 97. (Berlin : Gebriider Born- 

 traeger, 1922). 6s. 3d. 



Prof. Deecke's essays on broad questions of geology 

 always provide interesting reading. The present work 

 is perhaps unduly sceptical ; but its stimulus to further 

 comparison and correlation is based on careful reasoning. 

 While mention is made of the importance of plants as 

 rock-formers, the main thesis is their value for geologists 

 as indicating topographic and climatic conditions in 

 the past. The author shows how vegetation growing 

 on cold uplands may become entombed in the down- 

 wash from mountain-sides, and he strongly opposes 

 the notion that the .flora of a sheltered Miocene marsh 

 at CEningen may be used as an illustration of the con- 

 temporaneous flora on the Swabian Alb. Even the 

 beautiful theory that the occurrence of rings of growth 

 in fossil trees indicates an orderly recurrence of seasons, 

 while their absence indicates a uniform climate, comes 

 in for useful criticism. Though the author states the 

 importance of calcareous alga: in forming Carboniferous 

 limestones and, aided by their magnesium, Triassic 

 dolomites, we miss a reference to the Cryptozoon 

 question. This is a mere petrographic detail in the 

 general discussion, which leaves us with the impression 

 that geology, including the determination of local 

 conditions of plant -growth, may be of more service to 

 palasophvlology than phvtopalaeontology can be to 

 geology." G. A. J. C. 



Practical Mathematics. By A. Dakin. Part 1. 

 (Mathematical Series for Schools and Colleges.) Pp. 

 viii + 362 + 12 + xxiv. (London: G. Bell and Sons, 

 Ltd., 192 1.) 5s. 



There should be a considerable demand for Mr. 

 Dakin's book, as it contains just the sort of mathe- 

 matics that is required by those who have to learn 

 some elementary mathematical processes for practical 

 use : decimals, mensuration and a few other topics 

 in arithmetic, algebraic formulae and equations, 

 graphical methods, the geometry of rectilinear figures, 

 similar figures, the circle and the sphere, with some 

 numerical trigonometry. The treatment is very 

 pleasant, and the student who uses the book will 

 certainly fail to experience the aridity that the popular 

 mind associates with mathematics. Mr. Dakin's 

 account of graphs is particularly good ; the intro- 

 ductory portion with the comparison and correlation 

 graphs cannot but grip the student's interest, and 



NO. 2759, VOL. I IO] 



make him feel that the method of graphs is worth 

 acquiring. Historical notes are incorporated in the 

 main text, and occasionally they are worked in very 

 skilfully. Presumably the tables are given the title 

 " logarithmic tables " from force of habit : they con- 

 tain only natural trigonometrical ratios. 



If the second part maintains the high standard of the 

 present volume, the author will have added a valuable 

 treatise to available books on the subject. It is to 

 be hoped it will not suffer the fate of so many 

 sequels. S. B. 



Cows complet de mathematiques speciales. Par Prof. 



J. Haag. Tome 2, Geometrie. Pp. viii + 661. 



(Paris : Gauthier-Villars et Cie, 1921.) 65 francs. 

 This is the second part of Prof. Haag's complete 

 treatise on pure mathematics as required by the 

 ordinary student specialising in mathematics. The 

 first part dealt with algebra and analysis : the present 

 volume is geometrical in the widest sense. We thus 

 have analytical and synthetic geometry in two and 

 in three dimensions, all treated simultaneously. A 

 correct description of the book is therefore to call it 

 a compendium of modern methods in geometry ; it 

 contains a vast amount of information of a funda- 

 mental character, and makes excellent reading. 



Contrary to usual practice, especially in this country, 

 the author does not devote very much space to conies as 

 such. Perhaps he is right in thinking that the general 

 practice of making a long and detailed study of the 

 curves of the second degree tends to endow them with 

 an importance that their practical usefulness does not 

 justify. On the other hand the methods of the calculus 

 are used freely. 



Exercises in illustration of the principles and methods 

 are conspicuously scarce, and no examples are given 

 for the student to work. One is led to wonder whether 

 a student can derive any considerable benefit from 

 reading mathematics like a novel. 



The Foundations of .Esthetics. By C. K. Ogden, I. A. 

 Richards, and James Wood. Pp. 95 + pi. I-XV. 

 (London : G. Allen and Unwin, Ltd., 1922.) -js. 6d. 

 net. 



The aim of the authors of this short treatise on 

 aesthetics, as stated by themselves, is to present in a 

 condensed form the greater part of accredited opinion 

 on the subject while relating it to the main positions 

 of the theory of art criticism. The various theories 

 are not brought into opposition, but are distinguished 

 to allow to each its separate sphere of validity. Beauty 

 is thus discussed as intrinsic, in relation to the medium, 

 to mysticism, and to its social effects and the like. 

 They themselves find the solution of the problem in 

 synaasthesis, a term covering a state of equilibrium 

 and harmony in which the percipient becomes more 

 fully himself and at the same time is in sympathetic 

 understanding with other personalities. Hence arises 

 the educative value of art. This theory is acceptable 

 so far as it goes, but, like much of the current theory of 

 aesthetics, in describing the " how " it fails to answer 

 the question " why," a matter in which the anthro- 

 pologist, censured by the authors, may be able to assist, 

 in view of the current vogue of non-European art. 



