698 SCIENCE PROGRESS 



by Carson and Smith's example to devote a period at least early in their course 

 in geometry to reading and working out the Gold Bug, the greatest of all short 

 stories of treasure-trove. I am confident that a term, or even a year, spent 

 over the problems proposed in the introduction will redeem the subject from 

 the charge of dullness. Even teachers of geometry have to remember Herbart's 

 maxim Seien sie niemals absolut langweilig ! 



The various ways in which the book differs from the classical treatment of 

 Euclid are interesting. The first variation we note is the use of hypothetical 

 constructions. This seems to be sanctioned by modern usage, but we confess that 

 it is a shock to find a construction employed in the proof of Prop. iv. which has 

 to wait for its demonstration until Prop. xxv. A second innovation consists of 

 the statement of a largely increased number of postulates. Thus there are three 

 postulates of perpendicular and three of parallels ; proofs are given in small type 

 of five of these postulates. It is not easy to divine the gain in extending over 

 these five the aegis of the postulate. The same result would probably have been 

 attained by stating them as propositions and distinguishing their proof by 

 asterisks or other device. Elementary geometry can be simplified by assuming 

 the principle of symmetry ; this assumption is made tacitly by Euclid, and its 

 open employment would get over some of the difficulties which modern authors 

 surmount only by the use of hypothetical construction and new postulates. A 

 third difference from the classical method is created by the abandonment of the 

 reductio ad absurdutn proof. It is doubtful whether this represents a gain ; this 

 method of proof is of great value in analysis, and to the beginner it presents 

 a welcome variety, however boring it may become to a teacher who hears it for 

 the thousandth time. One outstanding feature of the book is the historical sketch 

 with which the volume concludes : it is excellent in every way, and will lighten the 

 labours of many a youthful traveller in his geometrical journeys. 



The book is a valuable stage in the evolution of a sound system of instruction 

 in geometry. The success of the authors has been achieved by their adherence 

 to the spirit of Euclid, for, whatever variations maybe introduced into geometry, it 

 is Euclid who will probably always supply geometrical writers with the theme. It 

 is books like the present one that will render it possible for schoolmasters to take 

 their better senior students through the Elements at the close of their school 

 course. In this way Euclid's masterpiece may return into school work in its 

 proper place, and be studied as a classic deserves to be by minds which are able 

 to appreciate its greatness. 



C. 



PHYSICS 



A Textbook of Physics. By J. H. Poynting, Sc.D., F.R.S., etc., and Sir J. J- 

 THOMSON, O.M., M.A., F.R.S., etc. : Vol. iv. Electricity and Magnetism. 

 Parts I. and II. Static Electricity and Magnetism. [Pp. xiv + 345, with 

 Illustrations.] (London : Charles Griffin & Co., 1914. Price 10.?. 6d.) 



The volume before us is, like its three predecessors, a model of good writing and 

 clear exposition. No attempt is made to overload its pages with experimental 

 details — a procedure which renders the reading of many " Handbooks" a weari- 

 ness to the flesh — yet the account of experimental work is adequate to the purpose 

 which the authors have in view, the establishment of fundamental principles, and 

 the attainment by the student of a physical as well as a mathematical grasp of the 

 main concepts. Considerable space is devoted to the development of the ideas 



