NATURE 



[September io, 1914 



tang^ent properties of the circle and theorems 

 in proportion and similarity, to be taken at an 

 early stage. 



The course of solid geometry, which occupies 

 about one-third of the volume, and can also 

 be obtained separately, follows the usual lines. 

 There are three sections : (i) lines and planes 

 in space; (2) polyhedra, cylinders, cones; (3) the 

 sphere, the latter being treated more fully 

 than usual. The examples are less conventional 

 and more interesting than those in the ordinary 

 text-book. 



(2) The author holds very strongly that pure geo- 

 metry should not be separated from other branches 

 of mathematics. In a single volume he has in- 

 cluded quite a considerable amount of trigono- 

 metry, calculus, and analytical methods (solid 

 geometry is reserved for a second volume) ; and 

 he has attempted to show how all these subjects 

 should be combined together, each assisting the 

 development of the other. If proofs of geo- 

 metrical properties can be simplified by the use 

 either of trigonometry or analysis, he maintains 

 that not only is it legitimate to do so, but that 

 it is definitely wrong to ignore this opportunity. 

 Mr. Dobbs's book should exercise a refreshing 

 influence on educational methods. 



(3) Into the ordinary analytical course a certain 

 number of sections on pure algebra have been 

 introduced on the ground that their utility can 

 best be explained in this connection. This cer- 

 tainly justifies the inclusion of simultaneous 

 equations, theory of equations, complex numbers, 

 gradients, and determinants; the brief account, 

 however, of permutations and combinations in 

 connection with the latter seems somewhat irrele- 

 vant. The examples are of a numerical character, 

 and advanced geometry of the conic is left 

 aside. Special mention must be made of an in- 

 teresting section on higher plane curves and 

 empirical equations. The last four chapters cover 

 the usual course of solid geometry so far as 

 quadrics referred to principal axes. 



(4) Mr. Jackson's name is in itself a sufficient 

 guarantee that students will find all that they 

 can possibly require in this account of the use 

 of the slide-rule. After a brief introduction there 

 are successive chapters on proportion, evolution 

 and involution, the solution of quadratic and cubic 

 equations, the trigonometric and logologarithmic 

 scales, the plotting of curves and errors. The 

 reader must of course have a slide-rule in his 

 hand, but the clearness of the diagrams from 

 which all superfluous markings have been 

 omitted will make his task easy. 



(5) This book is designed for the junior forms 

 of secondary schools, in view of the fact that 



NO. 2.^41, VOL. 94] 



trigonometry is now given an early place in the 

 curriculum. The examples are therefore of a 

 simple character ; radian measure is postponed to 

 the last chapter, and identities and compound 

 angles are excluded. We think that an unneces- 

 sary amount of space has been devoted to 

 logarithms ; all modern text-books on arithmetic 

 and algebra contain chapters on this subject, and 

 its repetition here is a survival from the times 

 when only seven-figure tables were used. There 

 is a first-rate -set of test-papers at the end of the 

 book. 



(6) This is a book for the practical engineer, but 

 it contains many problems that might usefully be 

 set to the mathematical specialist. No previous 

 knowledge of mechanics and only the elements of 

 algebra are required. After a clear discussion of 

 resolution and composition, the triangle of forces 

 and Bow's notation, various problems of the crane 

 are considered. The graphical theory of moments, 

 bending moments, and shearing forces is then 'I 

 described, and applications are made to dead and ^ 

 rolling loads, symmetrical and unsymmetrical roof 

 loadings, wind pressure, walls withstanding 

 pressure, centre of gravity and moments of 

 inertia. The author has succeeded in compress- 

 ing into a comparatively small compass a great 

 deal of valuable matter. There is, of course, 

 naturally nothing that is original, but the contents 

 are just what the ordinary engineering student 

 most needs. 



(7) The purpose of this tract is to advocate the 

 introduction of some account of modern views 

 upon the foundations of mathematics into 

 elementary work. It is claimed that by a judicious 

 use of models an insight can be gained fairly 

 easily into the root ideas of mathematical philo- 

 sophy, and that by a method which involves only 

 an extension or rearrangement of the practical 

 work now being done at school. The ideas here 

 dealt with are correspondence, class, classifica- 

 tion, multiplexes, etc. We cannot think this is 

 suitable for the ordinary boy : however simple 

 the illustrations may be, he will almost certainly 

 fail to carry away with him anything he can 

 himself regard — and that is in itself of very great 

 importance — as real knowledge. 



(8) Every teacher should possess this book ; the 

 exercises cover the course of arithmetic, algebra, 

 geometry, and trigonometry taken by the non- 

 specialist, and may be used either for revision or 

 to supplement at a first reading the ordinary text- 

 book. Some of the sections are headed by a note 

 recommending their omission if not required for 

 examination purposes. Apart from these, the 

 questions are so chosen as to test the intelligence 

 of the student, to illustrate the utility of the 



