November 23, 191 1] 



NATURE 



^05 



but they are incapable of competition in the outside 

 world, and require constant and sl<illed supervision. 

 There is a large amount of accommodation for these 

 patients, but, as already said, it is too small for the 

 numbers to be found in this country. Those in charge 

 of institutions for the feeble-minded will find a great 

 deal of help in their management and treatment in 

 the book by Dr. Lapage, and they will find consider- 

 able interest added to their work if they study these 

 patients in a scientific spirit on the lines laid down 

 by Dr. Sherlock. 



ELEMENTARY MATHEMATICS. 

 (i) A First Book of Geometry. By J. V. H. Coates. 

 Pp. xi+142. (London: Macmillan and Co., Ltd., 

 191 1.) Price IS. 6d. 



(2) A School Algebra. Part ii. By H. S. Hall. Pp. 

 vi + 30 1-450 + xxxix-l. (London: Macmillan and 

 Co., Ltd., 191 1.) Price i5. 6d. 



(3) Theoretical Geometry for Beginners. By C. H. 

 Allcock. Revised and rearranged. Part i., pp. xii + 

 125. Parts ii.-iv., pp. xii + 204. (London : Mac- 

 millan and Co., Ltd., 1911.) Price, part i., is. 6d.; 

 parts ii.-iv., 25, 6d. 



(4> A New Trigonometry for Schools and Colleges. 

 By the Rev. J. B. Lock and J. M. Child. Pp. xii + 

 488. (London : Macmillan and Co., Ltd., 191 1.) 

 Price 6s. 



(5) Solid Geometry. By C. Godfrey, M.V.O., and 

 A. W. Siddons. Pp. ix+109. (Cambridge L'nlver- 

 sity Press, 191 1.) Price is. 6d. 



(6) Engineering Descriptive Geometry: a Treatise on 

 Descriptive Geometry as the Basis of Mechanical 

 Drawing, explaining Geometrically the Operations 

 Customary in the Draughting Room. By Com- 

 mander F. W. Bartlett and Prof. T. W. Johnson. 

 Pp. vii+159. (New York: John Wiley and Sons; 

 London : Chapman and Hall, Ltd., 1910.) 



(7) Trigonometria Esfdrica. By Prof. C. Wargny. 

 Pp. 219. (Valparaiso: Talleres Tipograficos de la 

 Armada, 1909.) Price 6 dollars. 



(t) 'T^HE object of this small text-book is to give 

 J- the reader a sound appreciation of the funda- 

 mental ideas of geometry, rather than a systematic 

 knowledge of its theorems. Without doubt this is the 

 best way of approaching the subject. As soon as m 

 intelligent grasp is acquired of such concepts as angles, 

 itallelism, areas, &c., it is a simple matter to take 

 theoretical course; but without this preliminary 

 ige, not only is progress very slow, but the work is 

 itself of little educational value. Part i., which 

 ■upies one-quarter of the book, is entirely practical ; 

 It ii. contains a selection of the important theorems 

 Euclid, I., III., with a large quantity of numerical 

 Tcises; it is, in our opinion, unfortunate that few 

 I'Ts have been inserted. 



'2) The second part of this book carries the reader 



' to the binomial theorem. A change from the 



lustomary order has been made by taking a first 



' iurse of progressions immediately after quadratics. 



is to be expected of so well known an author, the 



, ality of the workmanship is excellent throughout. 



I lie explanations in the text are clear and concise, 



NO. 2195, VOL. 88] 



and the examples have evidently been selected with 

 great care. 



(3) In spite of the title of this book, which is a 

 revised form of an older edition, practically no work 

 on experimental geometry has been included. After 

 an introduction of twelve pages on definitions, axioms, 

 postulates, &c., the reader is at once immersed in the 

 theoretical work. The course of theorems given agrees 

 fairly closely with the Cambridge schedule, with a few 

 additions. Each proposition or group of propositions 

 is followed by a number of riders, of which only a few 

 are numerical. We are unable to find any very novel 

 or distinctive features in this text-book. 



(4) This volume is designed for the use of candi- 

 dates for scholarships at the universities, and is 

 intended to form an introduction to the more advanced 

 parts of Dr. Hobson's standard work on the subject. 

 Although it assumes no previous knowledge of trigono- 

 metry, the earlier portions are scarcely sufficiently full 

 for the novice in view of the modern idea of taking 

 the subject at a very early stage in the school course. 

 For introductory purposes, some such book as 

 Mercer's "Trigonometry for Beginners" is more use- 

 ful. But after this preliminary stage is covered, it 

 is well for the student to revise this work once more 

 in such a form as is provided by this text-book. 

 Practical applications are fully treated, and there is an 

 abundance of numerical and graphical work. One 

 important change has been made in the sequence of 

 subjects. The applications to the geometry of the 

 triangle and quadrilateral have been deferred to the 

 closing chapters, thus avoiding any break in the pre- 

 sentation of the purely analytical work. The sections 

 on geometry are far fuller than usual, and indeed 

 contain more than the ordinary boy is likely to require 

 or be able to digest. This is, however, a matter for 

 each individual teacher. We are glad to find a full 

 treatment of the geometrical interpretation of 

 imaginary quantities ; the interest which the student 

 takes in this kind of work and the stimulus it applies 

 to his mind more than justify the expenditure of time 

 involved. The general theory of infinite series and 

 products is regarded as beyond the scope of the book, 

 but sufficient is said to justify the validity of the use 

 of those particular series and products met with in 

 the course of the work. Hints for the solution of the 

 more difficult questions are included among the 

 answers. 



(5) In spite of recent geometrical reforms, the atten- 

 tion paid to three-dimensional geometry is still, to say 

 the least, inadequate. Time does not allow of a course 

 on the lines of Euclid XL, nor would this be par- 

 ticularly beneficial. What is required is an informal 

 study of the ideas and practical applications of solid 

 geometry; and this is supplied in an excellent and 

 brief form by the work before us. The authors have 

 had a great deal of experience in this direction, and 

 it is not therefore surprising that this small book 

 should seem so admirably adapted to the purpose for 

 which it is intended. It falls into three sections : (i) 

 a discussion of the main properties of lines and planes ; 

 (2) the properties and mensuration of the principal 

 solids ; (3) the elements of practical solid geometry. 

 The examples are chiefly numerical, l)ui a -unicient 



