Chemistry and Physics. 127 



9. Principles of Electrical Measurements ; by Arthur Whit- 

 more Smith. Pp. xiv, 243, with 99 figures. New York, 1914 

 (McGraw-Hill Book Co.). — " This book is written for the instruc- 

 tion of those who are beginning their course in Electrical Engi- 

 neering, or who desire a more complete understanding of this 

 branch of Physics than is afforded in most elementary manuals, 



" Hence the material is so presented as to meet the 



requirements both of the class room and of the laboratory. In 

 addition to covering a good deal of ground the book has several 

 other admirable features. For example, the practical and theo- 

 retical definitions of electric and magnetic units are clearly stated 

 and emphasized by italics. The subject is developed progres- 

 sively not only as regards the successive chapters but also with 

 respect to the material in each chapter. Thus it is shown in the 

 first chapter how to measure current, electromotive force, resist- 

 ance, and power, by ammeter and voltmeter methods. In the 

 seventh chapter considerable use is made of Kirchhoff's second 

 law. The sections dealing with B and H are unusually clear 

 and thorough. A few problems are distributed through the text, 

 the diagrams and typography are excellent, and the volume 

 closes with a subject index, therefore, as implied, the book is 

 very well adapted to meet the needs for which it was written. 



h. s. u. 



10. Geometry of Four Dimensions • by Henry Parker 

 Manning. Pp. ix, 348, with 3 plates. New York, 1914 (The 

 Macmillan Co.). — The chief object of this book is to meet the 

 difficulties of the subject as far as possible. In order to accom- 

 plish this purpose the author has used synthetic processes exclu- 

 sively. One advantage of the synthetic method is that it 

 concentrates our attention on the figures themselves and thus 

 takes us directly to the heart of the difficulty and keeps it before 

 us until the difficulty has been thoroughly mastered. Taken as 

 a whole, the text is an extension of ordinary Euclidean geometry 

 to four dimensions. It follows, therefore, that no knowledge of 

 higher mathematics is necessary for a full understanding of the 

 contents of the volume. The author has wisely given the pages 

 a familiar appearance by following the elementary text-books and 

 by building up a structure which rests on the foundations laid in 

 the schools. The theorems in the first five chapters are rigorously 

 demonstrated without the introduction of the axiom of parallels. 

 In other words, these chapters pertain to " Pangeometry™ 

 (Lobachevsky). The three remaining chapters relate to figures 

 with parallel elements, to measurement of volume and hyper- 

 volume in hyperspace, and to the regular polyhedroids. " In the 

 chapter on the hypersphere, its geometry, being elliptic, is stated 

 as such, and a group of theorems is given from the non-Euclidean 

 geometry; and in the last chapter the non-Euclidean properties 

 of the hypersphere are used quite freely." " Although these 

 portions of the book may be omitted, the student will find it an 

 advantage to make himself familiar with the Hyperbolic and 



