578 



NATURE 



[February 29, 191 



NiiiMu^ (ic 1.(1 ih.ii nferences and authorities are im- 

 prihcily K''»»'i. •"•'^' 'li^'t the work reads like a book 

 meant to be used in cramming men for examinations 

 and not like a real introduction to the subject. Dr. 

 Ernest Playfair has performed the diflicult task of 

 translation admirablv. 



nir.HEh' DYNAMICS FOR E^FGINEERS. 



A Treatise on Dynamics, xvith Examples and Exer- 

 cises. By Prof. A. Gray, F.R.S., and Dr. J. G. Gray. 

 Pp. xvi + 626. (London: Macmillan and Co., Ltd., 

 ic)ii.) Price I05. net. 



THE preface to this book states that it is inte.ided 

 "to provide a discussion of higher dynamics 

 suitable to students of engineering, physics, or astro- 

 nomy." It is doubtful whether it would be a good 

 book for intending students of astronomy, but it will 

 be useful both to physicists and to students of applied 

 mathematics as supplementing other treatises, and 

 is an excellent book for an engineer whose mathe- 

 matical equipment is sufficient to follow the reason- 

 ing. 



l'"\;miplcs of problems which occur in engineering 

 or are of special interest to engineers appear earlv, 

 and continue right through the book; in addition to 

 those included in the majority of treatises (including 

 trajectories in resisting media) may be mentioned 

 resistances of water to ships, steering of ships, brakes 

 of trains, motion of wheeled vehicles, and dynamics 

 of self-propelled vehicles. The conditions which con- 

 tributed to the Salisbury accident of 1906 are fuUv 

 dicussed, and although there is a misprint in the figure 

 used in this discussion, and a misprint of tan-* for 

 sin-\ the results, both algebraic and arithmetic, are 

 correct. The reasons why a blacksmith uses small 

 and large hammers for different purposes (p. 399) do 

 not appear in most treatises on dynamics ! 



Although elementary dynamical questions like the 

 above are clearly and fully discussed, elliptic integrals 

 are introduced where thought to be practicallv useful 

 (as in the pendulum), and there is a clear and full 

 discussion of three-dimensional rigid dynamical 

 problems, mainly of a practical nature. The change 

 in the ordinary figure (art. 9) by which the usual 

 right-handed screw notation is made consistent with 

 the traditional forms of Euler's- and kindred three- 

 dimensional equations will commend itself equally to 

 teachers and students of dynamics, though the figure 

 might with advantage have been repeated in the later 

 chapters. The principle of this article is claimed in 

 the preface to be comparatively new, but seems not 

 to differ from that practically used by the standard 

 treatise of Routh. The principle is, however, ex- 

 pressed clearly and made good use of in the chapter 

 on gyrostats, which should be specially useful to 

 engineering students as giving a clear and practical 

 explanation of a subject generally regarded as diffi- 

 cult. The discussions of gyrostatic control of the 

 rolling of a^ips, the monorail, the gyrostatic action 

 of turbine-driven steamers, and other questions are 

 very full, while examples, such as those on self-steer- 

 ing torpedoes and on the effect of the rotation of the 

 NO. 2209, VOL. 88] 



earth on the aiming of artillery, give practic.il 

 illustrations of the value of the higher parts of tli 

 subject. The gyrostats in Thomson and Tait § 34 

 X., are reproduced, and partially discussed; but tl 

 discussion is not quite full enough, and it may 1 

 remarked that the a/imuthal equilibrium in case 3 i 

 said to be made stable by rotation, which is contrar 

 to Thomson and Tait's result, and seems to be i: 

 correct. 



Lagrange's equations, though foreshadowed early in 

 the treatise (p. 112), are not introduced seriously until 

 chapter x. ; they might have been of assistance to ' 

 students in the two preceding chapters, in which toi>- 

 gyrostats, motion about a point under no forces, an 

 motion of hoops are discussed, but the authors cer- 

 tainly do very well without the aid of these equations. 

 Chapter x., which gives the transformations of Hamil- 

 ton and Appell of the general equations, will be mot 

 useful to students of physics than to engineers < 

 engineering students; but in all the rest of the book 

 except in chapter v., which deals with orbits, the needs ' 

 of engineering take a prominent place. Chapter v.. 

 which is presumably written for the astronomer, 

 scarcely differs sufficiently from the traditional tre.r 

 ment to be of much use to him, although some littl 

 known theorems by G. W. Hill and others are in- 

 cluded in it. 



A rather easy chapter on some quite simple statical 

 properties comes as a surprise at the end of the book, j 

 following the advanced chapters on rigid dynamics, \ 

 and is scarcely in keeping with the character of what 

 precedes. But the general arrangement and presenta- 

 tion of the subject is likely to be most useful to all 

 engineering students of sufficient mathematical capa- 

 city, and to many students of physics and of applied 

 mathematics. 



There are a few misprints, in addition to the- 

 noted above, but none which could not be readilv 

 corrected. A little revision of pp. 392 and 393, and 

 a re-wording of the second line of p. 137 might ! 

 use<^ul in subsequent editions. The results of ti 

 examples, so far as the reviewer has verified them, 

 seem to be correct. 



APPLIED MICROBIOLOGY. 

 Ei)ifiHirung in die Mykologie der Genussmittel tn 

 in die Gdriingsphysiologie. By Prof. Alex. Kossi 

 wicz. Pp. viii-f-211-1-2 plates. (Berlin: Gebriidtr 

 Borntraeger, 1911.) Price 6 marks. 



THIS work, a companion volume to the author'- 

 " Mycology of Foodstuffs," deals with thosi 

 adjuncts of the table the use of which, although noi 

 strictly necessary, and classed, and for the most part 

 taxed, as luxurious, has become so firmly established 

 that few of us are sufficiently Spartan entirely to 

 avoid it. Fermented beverages, both alcoholic and 

 (reputedly) non-alcoholic, vinegar, mustard (of th 

 French variety), vanilla, cocoa, coffee, tea, and tht 

 post-prandial cigar are all submitted to processes of 

 fermentation at one stage or other of their progres> 

 towards that culmination of perfection which delight- 

 the connoisseur. It is with the organisms concerned. 



