98 



NA TURE 



[May 31, 1894 



tion and the kinetic analogue when a helical wire is 

 pushed into a helical tube, of a different curve? 



A search through Clebsch's article in Crelle, t. 57, would 

 reveal the clue to the construction of pseudo-elliptic cases 

 of the general tortuous elastica, and thus also of its kinetic 

 analogue in the general motion of a Top. The spherical 

 catenary forms another analogue, and the special pseudo- 

 elliptic case, devised by Clebsch, has been constructed 

 in the series of models of Brill of Darmstadt, so that a 

 string of beads can be placed on a plaster sphere in the 

 appropriate curve. 



Mr. Love has devoted careful attention to the examina- 

 tion of different cases of elastic stability, familiar instances 

 of which are to be seen around us, in the waving of the 

 cornstalks in the field, the vibration of a fishing-rod or 

 of the mast of a steamer, or the whirling vibrations of a 

 rapidly rotating shaft ; an examination of the period of 

 vibration at once assigns the limits of stability, as the 

 place where the period of vibration becomes infinite, and ! 

 afterwards imaginary. Thus the farmer can tell by the 

 speed of the waves seen over the cornfield the appro- 

 priate time for the harvest. | 



The treatment of the wire generally, in chapters xiii.- 

 xviii., is complete, and the graphical method of Fig. 30 

 is very elegant ; but the period equation for lateral vibra- 

 tions, 



cos III cosh III = ±1, 



is improved by being thrown into the equivalent form, 



lank \m — ± tan \m, or ± cot \m, 

 of which the solution by a geometrical construction is 

 readily effected. 



We miss the theorems of the elasticity of cylindrical 

 bodies required nowadays in the construction of built-up 

 ordnance and in the wire gun ; the practical results can 

 be exhibited very simply by geometrical constructions, 

 merely requiring the drawing of a few straight lines. 



Prof Williamson's treatise of 130 pages will serve as a 

 very good introduction to the study of Mr. Love's work. 

 Great attention has been paid to the notation and nomen- 

 clature, and a suggestion of Prof. Townsend has been ' 

 adopted which seems clear and simple ; however, we 

 must not wander far from the system laid down in Prof. 

 Karl Pearson's history. 



The work concludes with a description of the models, 

 devised by Profs. Alexander and Thomson, for illustrating 

 Rankine's ellipse of stress. This model was e5(hibited at ' 

 the Munich Mathematical Exhibition, where it attracted 1 

 great interest. 



Prof. Bovey's theory of structures will provide for j 

 Canadian and American engineers the information and \ 

 exercises which our engineers derive from Rankine's 

 treatises; but Rankine's very condensed method of reason- j 

 ing has been expanded for the benefit of the average stu- 

 dent, so that the present work runs to over 800 pages. 



It would be impossible to give a complete account of 

 all the subjects discussed in the treatise within reason- 

 able limits ; but many elegant and novel theorems in the 

 treatment of the theory of the beam and cantilever are to 

 be found, illustrated numerically by an appeal to exist- 

 ing structures of the largest scale ; in this respect the 

 American engineer is at an advantage, as more bridge 

 work of great dimensions comes under his notice. 



Incidentally, Prof. Hovey provides his engineering stu- 

 NO. 1283, VOL 50] 



dents with a complete treatment of statics and dynamics, I 

 treated episodically as required for a problem in hand ; 

 and each chapter concludes with a large collection of 

 examples, by which the student can test the soundness of 

 his knowledge : these examples are based in general 

 upon existing realities, and form a great contrast to the 

 old-fashioned Cambridge mechanical problems, which 

 were generally geometrical or trigonometrical theorems, 

 with only a slight flavour of mechanics. One or two of 

 these problems, for instance, 47, on p. 220, and 60, on 

 p. 221, will doubtless receive revision in a future edition ; 

 and Mr. Macfarlane Gray's elegant constructions for the 

 points of maximum piston velocity may then well find a 

 place in p. 205. As the author writes for engineers, the 

 gravitation unit of force is used throughout, and expres- 



sions such as - and ■ abound in consequence. 



w 



The confusion introduced by writing M for — has 



been carefully avoided, with all its attempted a posteriori 

 explanations ; and for this mercy the engineering student 

 owes a great debt of gratitude to Prof. Bovey. 



A. G. Greexhii.l. 



LAW AND THEORY IN CHEMISTRY. 

 Law and Theory in Chemistry : a Companion Book / 

 Students. By Douglas Carnegie, M.A. Pp. vi. 2: 

 (London : Longmans, Green, and Co., 1894.) 



THE object of this book is to help fairly advanced 

 students " to recapitulate and co-ordinate the more 

 important principles of chemistry before proceeding to 

 more detailed and advanced works." The book make- 

 no claim to be regarded as a text-book ; it is intended to 

 be read along with the text-book, which it is meant to 

 supplement, especially in those parts of the subject that an 

 sometimes overlooked, but are needed, in the opinion m 

 the author, for "a liberal understanding of the science," 

 and in some of those parts that are thought to present 

 especial difficulties. In his preface, the author says that 

 "the seven chapters are really short and independent 

 essays on the subjects of which they severally treat"; he 

 also adds that " the attempt has been made to indicate, 

 with due appreciation of perspective, the trend of modern 

 research in its relation to the science as a whole." 



The first chapter, on ". Alchemy and the birth of scien- 

 tific chemistry," is evidently to be looked on as intro- 

 ductory to the study of law and theory in chemistry. The 

 second chapter introduces the student to chemical la.. 

 and chemical theories by sketching the " Phlogisi 

 period and the beginnings of chemical theory." Tli' 

 other parts of the science chosen for the display of lli< 

 workings of law and theory are chemical classification, 

 the atomic theory, isomerism, and chemical equilibrium. 



The first and second chapters are chielly historical ; 

 they present in a clear and interesting style the chief 

 features in the development of the general conceptions 

 regarding elements, and changes of properties, from the 

 early days to the overthrow of the phlogistic theory by 

 Lavoisier. 



The distinguishing marks of this book are, in my 

 opinion, clearness and suggestiveness. There are plenty 

 of facts, and these are lucidly stated ; but when the book 



