556 



NATURE 



{April II, I ; 



the reference to this subject in the preface there appears 

 to be an oversight. The effect of a certain cycle of 

 operations to be performed with the apparatus is described 

 and then we read : — 



" A connected series of vessels of this kind will enable 

 the experimenter to apply a measured pressure of an 

 amount depending on the number of vessels." 



Instead of a connected series of vessels, it is only 

 necessary to repeat, time after time, with the one vessel, 

 the cycle of operations which has been described ; and 

 this we understood to be Dr. Andrews's intention. The 

 apparatus was not brought into actual use, nor even con- 

 structed ; preliminary trials having shown that screw 

 plungers working in mercury (which were an essential 

 part of the design) could not be prevented from leaking. 



The various papers in this volume, and especially the 

 Presidential Address, show Dr. Andrews to have been not 

 only an accurate and original worker, but a man of wide 

 culture and refined literary taste. The editors have done 

 their work carefully and well. J. D. E. 



MACH'S ''HISTORY OF MECHANICS." 

 Die Mechanik m ihrer Entwickelung historisch-critisch 

 dargestellt. (An Historical and Critical Sketch of the 

 Development of the Principles of Mechanics.) By Dr. 

 E. Mach, Professor of Physics in the University of 

 Prague. Second Edition. (Leipzig : F. A. Brockhaus, 

 1889.) 



THE first edition of this work, which forms Vol. LIX. 

 of the "International Scientific Series," appeared in 

 1883. With the exception of a few short appendices and 

 the correction of misprints, it is identical with the original 

 edition ; but we are glad to take the present opportunity 

 of calling attention to a book which, while unpretentious 

 in form, is one of exceptional value to students, and 

 especially to teachers, of the subject with which it deals. 

 The book has not been translated into English, and 

 we understand that the English publishers did not con- 

 sider it sufficiently popular in form to be included in 

 the English series. This is much to be regretted. 

 The work is one which certainly ought to be translated, 

 as it would be most helpful to a large class of students 

 and teachers who are unable to read it in German. 



In the course of rather fewer than 500 pages the author 

 gives his readers a well-constructed outline of the develop- 

 ment of the science of mechanics from Archimedes down 

 to the present time, accompanied by well- reasoned cri- 

 ticisms and discussions of the significance and relative 

 importance of the various steps which he chronicles. 

 The first chapter is devoted to the development of the 

 principles of statics, and we would specially direct 

 attention to the masterly manner in which the author 

 shows the fallacies underlying the attempts of some of 

 the early philosophers to derive the principle of the 

 parallelogram of forces, or an equivalent one, from a priori 

 notions, without appeal to experiment. The proposi- 

 tion commonly known as the parallelogram of forces may 

 either be proved by direct experiment or by deduction 

 from some such experimental principle as Newton's 

 second law of motion. The advantage of the latter 

 method consists, as the author points out, in the fact that 

 he nature and extent of the experimental evidence for 



Newton's second law, or its equivalent, cause it to carry 

 with it a greater certainty of its accuracy than is possible 

 for a direct experimental demonstration of the proposi- 

 tion. This is a point to which it is most important to 

 call attention, for, although Thomson and Tait have long 

 since cleared away from the better class of text-books, and 

 from the minds of the higher class of students, the fog 

 which had accumulated around this essentially simple pro- 

 position, much of our school teaching is still enshrouded 

 by it. 



The second chapter treats of the growth of the prin- 

 ciples of dynamics, understanding this in the more re- 

 stricted sense of what Thomson and Tait called kinetics. 

 This is of great interest and value throughout, but there 

 are one or two points to which we would direct special 

 attention. 



The deduction of the approximate time of swing of a 

 simple pendulum vibrating in a small arc, from a recti- 

 linear simple harmonic motion, is, or at any rate should 

 be, well known to students who have had the advantage 

 of instruction from a Professor at one of our Universities ; 

 but it is quite time that this very simple method of obtain- 

 ing an important relation should take the place of the arti- 

 ficial and cumbrous methods which still disfigure some of 

 the elementary text-books in common use. The criti- 

 cism of Newton's exposition of the ideas of time, space, 

 motion, and mass, is also worthy of careful study. These 

 two chapters are of quite an elementary character, and 

 may be read with advantage even by students whose 

 mathematical acquirements are of the slenderest. 



The third chapter treats of the further application of 

 principles, and the deductive development of mechanics. 

 It does not, like the first two chapters, appeal to the 

 beginner, but will be most helpful to a student who has 

 already made some progress in the subject. 



The fifth chapter bears the heading, " The Formal 

 Development of Mechanics." It contains an interesting 

 discussion of isoperimetric problems, and a brief account 

 of the analytical method of treatment introduced by 

 Lagrange. It also contains a section mainly devoted to 

 an account of the theological vagaries of some of the great 

 mathematicians and natural philosophers. This section 

 is not of very great interest or value, and may have been 

 inserted merely to give a popular flavour to what is 

 essentially a scientific book. 



The volume concludes with a very brief chapter on the 

 relations of mechanics to other branches of knowledge. 



G. W. DE T. 



OUR BOOK SHELF. 



Das Klima des ausser-tropischen Sildafrika, mit Beriick- 



sichtigung der geographischen unci wirtschaftlichen 



Beziehungefi nach 'klimatischen Provinzen dargestellt. 



Von Dr. Karl Dove. 160 pp. and 3 charts. (Gottingen; 



Vandenhoeck and Ruprecht, 1888.) 



Meteorologists must welcome the reappearance ot 



the name of Dove among the contributors to climato- 



logical knowledge, and the present work does no discredit 



to the name. It is an endeavour to give a conspectus of 



the climate of South Africa as a whole ; and the author 



ekes out the actual meteorological results, which are 



somewhat scanty in parts, by evidence derived chiefly 



from the indigenous flora of the several districts, which 



