268 



NATURE 



[July 21, 1898 



are likely to be very useful is in giving practical illus- 

 trations of Lie's methods. Lie's colossal work on trans- 

 formation-groups is so very abstract and, at the same 

 time, so exhaustive that it must, we fear, repel the great 

 majority of readers ; still it is hardly rash to predict 

 that his ideas, as time goes on and they become more 

 familiar, will prove to be of extreme value and fertility, 

 and profoundly affect, not only the theory of differen- 

 tial equations, but almost every branch of analysis. It 

 should be added that M. Goursat points out that Ampere 

 employed contact transformations of a general character 

 more than seventy years ago ; and it is, in fact, one of the 

 author's objects to recall attention to Ampere's remark- 

 able memoirs in cahh. 17, 18 of the Journal de PEcole 

 Polytechnique. G. B. M. 



OUR BOOK SHELF. 



Our Weights and Measures : a Practical Treatise on the 



Standard Weights and Measures in use in the British 



Empire^ with some Account of the Metric System. By 



H. J. Chaney. Pp. viii -I- 164. (London : Eyre and 



Spottiswoode, 1897.) 



The Superintendent of Weights and Measures gives m 



this book an authoritative account of the present practice 



in regard to the various weights and measures used in 



trade or for the purposes of manufacture. The origin 



and history of ancient systems are briefly traced so far 



as to show how our present system comes to be what it 



is, and references are carefully given to other treatises 



and to Acts of Parliament on all points of importance. 



The book is well illustrated. Some of the views are 

 of antiquarian interest : e.g. the beautiful pictures show- 

 ing the interior of the Pyx Chapel at Westminster Abbey, 

 a depository for standards since the Norman period ; but 

 most of the illustrations have reference to weights and 

 measures in actual use, and to the arrangements for 

 their inspection and verification. Local inspectors of 

 weights and measures will no doubt look on this book 

 as a very useful and, indeed, indispensable compendium. 

 Teachers and writers of books on arithmetic would do 

 well to take to heart the remarks on pp. 1 12-1 14. Thus 

 not only is a list given of those weights and measures 

 which alone need be taught to the exclusion of various 

 customary and local designations which, from a national 

 point of view, are now obsolete, but it is well pointed out 

 that a few hours' actual weighing and measuring would 

 make the children in schools more at home with standard 

 weights and measures than many hours of bare learning 

 of the tables. 



The last section of the work is on weights and measures 

 used for special purposes ; it includes, for instance, an 

 account of engineers' gauges and standards, and gives 

 tables of particulars of the Birmingham wire gauge, 

 Whitworth's and Seller's screw threads, the B.A. small 

 screw gauge, and several other standard gauges. 



Practicuin der Wissenschaftlichen Photographic. By 

 Dr. Carl Kaiserling. Pp. xii -f- 404. (Berlin : Gustav 

 Schmidt, 1898.) 

 In this volume of about 400 pages we have a work 

 which will be read by most photographers, whether 

 amateur or professional, who are familiar with the 

 German language, for, besides covering a great deal of 

 ground, the subject is treated of in much detail. 

 Although portraiture and landscape photography are 

 included in the text, the author presents the subject 

 more especially for those who employ photography as a 

 means of aiding them in their scientific investigations. 

 Thus, for instance, the medical man is enlightened as to 



NO. 1499, VOL. 58] 



the best means of illuminating portions of the human 

 body to get the best effects from his point of view, and 

 to photograph with success anatomical sections for de- 

 monstrations or collections. Microphotography is also 

 treated at some length, and is well illustrated by some 

 fine autotypes. 



It must not be assumed that the optics and manipula- 

 tions are here somewhat ignored at the expense of the 

 new lines on which the book has been written. Both of 

 these come in for their full share, and are well discussed 

 and described, besides being copiously illustrated. Most 

 of the new lenses are referred to at some length, and are 

 accompanied by numerous tables for determining the 

 lengths of exposures under different conditions. Methods 

 of obtaining positives and enlargements, stereoscopic 

 photography, Rontgen photography, and photography in 

 natural colours, besides processes for reproduction, are 

 all in their turn dealt with individually ; and the reader 

 who wishes to specialise in any one or more of these 

 branches will find ample information in these chapters. 



Enough, perhaps, has been written to show that this 

 book is not only a useful vade-mecum for the student of 

 science who wishes to obtain the best results in his 

 special line of work, but is a valuable addition to our 

 photographic literature. The illustrations are numerous, 

 and there is, what is often absent from a great many 

 German books, a good index. 



Principles of Mechanism : a Treatise on the Modification 

 of Motion by means of the Elementary Combinations 

 of Mechanism, or the Parts of Machines, for use in 

 College Classes, by Mechanical Engi?teers, Qr'c. By 

 S. W. Robinson, C.E., D.Sc, till recently Professor of 

 Mechanical Engineering in the Ohio State University. 

 Pp. XV -t- 309. (New York : John Wiley and Sons. 

 London : Chapman and Hall, Ltd., 1896.) 

 The main value of this work may not unfairly be said to 

 consist in its 350 illustrations of elementary combinations 

 of mechanism (in many cases more curious than useful), 

 and in the descriptions appended thereto. In regard to 

 the scope of the book, and, it may be added, the degree 

 of clumsiness of expression of which the author is cap- 

 able, we may quote the second sentence of the introduc- 

 tion : " In Principles of Mechanism we find the application 

 to machines, of the principles of kinematics, or cinematics, 

 the elementary combinations of mechanism of which 

 machines, being studied separately." 



A good many rules, useful in the drawing office, are 

 exemplified ; but the fundamental principles on which 

 they are based are for the most part left unnoticed. 

 Thus in Fig. 297 we have a complicated drawing of the 

 fixed and moving centrodes of certain mechanisms, but 

 we search the book in vain for any demonstration of the 

 method of instantaneous centres on which the construction 

 depends. 



In Fig. 301 the curves of velocity-ratio of crank and 

 connecting-rod are shown : the accompanying descrip- 

 tion identifies them with the fixed and moving centrodes 

 of the motion. There is no appeal to the fundamental 

 principles involved. In fact the book before us, however 

 suitable for reference by an inventor, seems to us quite 

 unfit for a student's text-book. 



By Dr. E. Riccr. 



Introduzione alio Studio dei Silicati. 



(Milan : Ulrico Hoepli, 1898.) 

 In this pamphlet the author seeks to classify the complex 

 group of the mineral silicates, and he claims for his 

 arrangement the merit of simplicity. The distinction 

 between the hydrous and anhydrous silicates is aban- 

 doned, and all mineral silicates are grouped in the two 

 primary divisions of orthosilicates and metasilicates. 

 As simple orthosilicates he includes zircon, phenacite, 

 and willemite with the Peridot family (olivine, sepioHte 

 and calamine) ; and with the double orthosilicates he 



