March i8, 1920] 



NATURE 



Ss 



explamed why he has rejected certain characters 

 made use of with great success by Chapuis in his 

 grouping- of the genera of Hispinae ; and it is to 

 be noticed also that he has not stated why there 

 is so very rarely any reference to sexual differ- 

 'jnces in his descriptions, either of genera or of 

 species, which otherwise appear to show close 

 observation. 



About ninety of the species described are the 

 author's own, and to many of these he has given 

 names which, derived from the ancient language 

 of his country, form a novel and interesting 

 feature of the book. In a short introduction to 

 each sub-family an account is given of the few 

 larvae and life-histories known, and a list of useful 

 references to other works in which information 

 about them may be found. Mimicry in the His- 

 pmae is touched upon, and Gahan's observations 

 on the interesting stridulatory structures met with 

 -in the same sub-family are quoted almost in full, 

 but without reference to the value they were 

 expected to have for systematic purposes. 



The volume is well illustrated, and the figures, 

 all greatly enlarged, appear to be carefully drawn, 

 with the exception of one on p. 86, which is not 

 what it is said to be — the " mentum " of a genus 

 which is unique amongst the Chrysomelidae in 

 having no labial palpi. Were it not for defects 

 of the kind pointed out, and frequent signs of 

 carelessness in the text, the volume, on the whole, 

 would deserve much praise, due regard being 

 «^iven to the fact that it is the author's first essay 

 in systematic work on more than a small scale. 



C. J. G. 



Mathematics: Pure and Applied. 



(i) The Fundamental Equations of Dynamics and 

 its Main Co-ordinate Systems Vectorially 

 Treated and Illustrated from Rigid Dynamics. 

 By Frederick Slate. (Semi-centennial Publica- 

 tions of the University of California.) Pp. ix + 

 233. (Berkeley : University of California 

 Press, 1918.) 



(2) Projective Vector Algebra: An Algebra of 

 Vectors Independent of the Axioms of Congru- 

 ence and of Parallels. By Dr. L. Silberstein. 

 F'p. vii + 78. (London: 0. Bell and Sons, Ltd., 

 1919.) Price 75. 6d. net. 



(3) Elements of Graphic Dynamics: An Element- 

 ary Text-book for Students of Mechanics and 

 Engineering. By Ewart S. Andrews. Pp. 

 viii+192. (London: Chapman and Hall, Ltd., 

 1919.) Price 10s. 6d. net. 



(4) Differential Calculus for Colleges and Second- 

 ary Schools. By Dr. Charles Davison. 



NO. 2629, VOL. 105] 



(Cambridge Mathematical Series.) Pp. viii + 

 309. (London: G. Bell and Sons, Ltd., 1919.) 

 Price 6s. • -.,. 



(5) The Analytical Geometry of the Straight Line 

 and the Circle. By John Milne. (Bell's Mathe- 

 matical Series.) Pp. xii + 243. (London,: G^ 

 Bell and Sons, Ltd., 1919.) Price 55. 

 (ij li /fANIFOLD adaptations ojf dynamicaf 

 iVl reasoning have given rise to special- 

 ised treatises of undoubted excellence. Prof. 

 Slate sets himself the task of surveying the com- 

 mon foundation and the common stock of re- 

 sources of these adaptations, as well as the trend 

 of modern development in dynamics. Six quan- 

 tities enter into the formulation of fundamental 

 dynamical principles : force, power, and force- 

 moment on one hand, momentum, kinetic 

 energy and moment of momentum on the other. 

 Each triad can be, and has been, used in the 

 enunciations of dynamics. But the enunciations 

 involve the use of reference-frames, leading to the 

 question of the relativity of such frames and the 

 transformation from one frame to another — bdth 

 when the transformation is that of a mere trans- 

 lation, and when it partakes of the more general 

 form of a shift and a rotation. The author cbh- 

 siders these transformations and the chief kinds 

 of co-ordinate systems. Euler's and Lagrange's 

 equations, and their use in the study of the 

 dynamics of a rigid body, conclude a presentation 

 possessing considerable interest and originality. 

 A number of notes are added containing refer- 

 ences and further elucidations. 



An objectionable feature of the book, and one 

 that destroys much of its value, is the difficult 

 English in which it is written. The most intel- 

 ligible portions are those consisting of mathe- 

 matical symbolism — the accompanying letterpress 

 is often a puzzle. What is one, e.g., to make of 

 the following? — 



" In consequence it has not been displaced as 

 a tenet of orthodox dynamical doctrine that 

 standards by which to judge of the energy, 

 momentum and force that ought to appear in its 

 accounts will not stand on a par if adopted at 

 random, • however interchangeable they have 

 proved in passing upon rest, velocity and ac- 

 celeration by the mathematical criteria in the more 

 indifferent domain of kinematics." 



The impression one has in reading the book is 

 that of a laborious progress over a succession of 

 obstacles. Not every reader can be expected to 

 persevere when so many of the obstacles are due 

 to the guide whose function it should be to remove 

 such difficulties as are inherent in the subject. 



(2) In Dr. Silberstein's book on "Projective 



