NATURE 



[March 6. 1913 



book develops the fundamental ideas of tri- 

 gonometry, vector geometry, mechanics, and the 

 calculus. Considerations of space have made this 

 section somewhat brief, but it should prove useful 

 to those who regard it as an introduction to more 

 advanced text-books. 



(3) The distinguishing feature of this work is 

 the early introduction of the equations of curves of 

 the second and higher degrees. It is an undoubted 

 fact that if a student is compelled to make himself 

 thoroughly familiar with the analytical geometry 

 of the straight line and circle before proceeding to 

 other loci, he finds it hard to appreciate the purpose 

 and the value of the work in which he is engaged. 

 The boy who intends to specialise in mathematics 

 will not derive any harm from pursuing this course ; 

 in fact, there is much to be said for giving him 

 a sound grounding in the elementary principles at 

 the outset ; but those who are taking scientific or 

 engineering courses, and therefore require less 

 manipulative skill, secure what they need from a 

 course which is less detailed and more general in 

 character. Their requirements are met admirably 

 by such a treatment as is given in the work before 

 us. This will be made clear by a brief enumera- 

 tion of the subjects and the order in which they 

 are taken: (1) standard equations of the straight 

 line, circle, ellipse, parabola, hyperbola; (2) 

 gradient of curves; (3) locus problems; (4) polar 

 coordinates with applications to the limacon, car- 

 dioid, cycloid, etc. ;■ (5) the conic based on the 

 focus-directrix definition; (6) the solid geometry 

 of the plane, straight line, and simple curved 

 surfaces. 



There is an excellent collection of examples, 

 answers to which are given at the end of the book. 

 We would suggest that an index should be added 

 in future editions. 



(4) During the last ten vears a number of valu- 

 able reports on the teaching of elementary mathe- 

 matics have been issued by the Mathematical Asso- 

 ciation, and they have exercised a very consider- 

 able influence on the curriculum and the methods 

 employed. As evidence of this it is necessary only 

 to refer to the changes which examining bodies 

 have made in their regulations and to the altera- 

 tion in character of modern text-books. The 

 present work is based on the report dealing with 

 the teaching of arithmetic in preparatory schools. 

 Concrete and abstract questions are taken side by 

 side, those parts of the subject which are of small 

 intrinsic importance are omitted, and the artificial 

 divisions of the subject-matter into a number of 

 standardised types of problems are avoided. We 

 have no hesitation in recommending this book for 

 use with junior students. 



(5) This pamphlet describes a means of 

 NO. 2262, VOL. 91] 



exhibiting three-dimensional figures, examples 

 of which were shown at the International 

 Congress at Cambridge last August. Two 

 perspective figures are drawn close together 

 on the paper in the complementary colours green 

 and red, and they are viewed through red 

 and green transparent screens. A highly striking 

 effect is obtained. It is clear that the simplicity 

 of the method will contribute largely to its prac- 

 tical utility. For purposes of demonstration, in 

 the teaching of solid geometry, it should be in- 

 valuable. About thirty examples are given; the 

 diagram which represents a cube with one diagonal 

 vertical with its plan and elevation is particularly 

 good. The figures of the cylinder seen from one 

 end and the section of a tetrahedron by parallel 

 planes appear to be a trifle out of drawing. 



OUR BOOKSHELF. 

 TeUgraphie sans Fil: Reception des Signaux 



horaires et des Tclcgrammes mitiorologiqy.es. 



By Dr. Pierre Corret. Pp. 93. (Paris : Maison 



de la Bonne Presse, n.d.) Price 1 franc. 

 This little volume gives simply-worded directions 

 for the construction of apparatus that will enable 

 persons interested to make use of the time signals 

 dispatched regularly from the wireless telegraph 

 station at the Eiffel Tower. The author begins with 

 a description of the very simple apparatus re- 

 quired by a Parisian amateur, and gives a clear 

 account, with fully detailed examples, of the time 

 signals and the meteorological messages from the 

 tower. From his story of a day's programme 

 of the tower, including as it does telegraphic 

 exercises with other French stations as well as 

 regular service messages, it would appear that 

 the amateur in the French capital has excellent 

 opportunities of learning Morse with a very small 

 outlay on apparatus. 



The next two sections of the book give instruc- 

 tions for erecting a receiving station of sufficient 

 sensitiveness to pick up the messages at distances 

 of two or three hundred miles from the tower. 

 These directions are plain and sufficient. With 

 the apparatus described, a French amateur may 

 listen to a great variety of Spanish, Italian, 

 German, and English messages ; and an enter- 

 taining programme is made out for him in the 

 book. Here the information conveyed is just such 

 as will help those amateurs who are in a state of 

 mental fog as regards the origin of the signals 

 they listen to, and the information will be almost 

 as useful to English as to French amateurs. 

 The book closes with an account of the system 

 of signalling time adopted by the international 

 conference of October last. 



It is intended that different stations shall trans- 

 mit certain signs at different hours. Those 

 normally audible in England are Paris at mid- 

 night and 10 a.m., Norddeich at midday and 

 10 p.m. At present, it may be remarked, the 

 Paris signals indicate 10.45 a - m - and IJ -45 P- m - 



