668 



MATURE 



[February i8, 19 15 



163 + 338. (London: Mills and Boon, Ltd., 

 1914.) Price 15. 3d. 



(6) Elementary Mathematical Analysis: a Text- 

 book for First Year College Students. By 

 Prof. C. S. Slichter. Pp. xiv + 490. (New 

 York and London: McGraw-Hill Book Co., 

 Inc., 1914.) Price 105. 6d. net. 



(7) Stability and Equilibrium of Floating Bodies. 

 By B. C. Laws. Pp. ix + 251. (London: Con- 

 stable and Co., Ltd., 1914.) Price 105. 6d. net. 



(i) " I "* HIS set of books on arithmetic consists 



T 



chiefly of examples, carefully graded in 

 difficulty. No answers are given ; teachers who 

 use these books will look for an edition in which 

 they are supplied. The course includes mensura- 

 tion, percentage, and interest. 



(2) The authors of this small text-book have 

 succeeded in creating a "workshop atmosphere" 

 around this elementary course ; not only are the 

 problems of a practical nature, but the student is 

 frequently referred to drawings of simple forms of 

 mechanism, which illustrate and furnish the data 

 of the example set him. The range of the book 

 includes practical arithmetic, mensuration, graphi- 

 cal work, and simple algebraic processes. 



(3) This book is framed on the lines recom- 

 mended by the circulars of the Board of Educa- 

 tion, particularly in the first forty pages. It is 

 claimed that the requirements of the ordinary 

 leaving-school examinations are met, but the book 

 is so small that most teachers will find it neces- 

 sary to supplement it. There are comparatively 

 few examples, those given being mainly numeri- 

 cal. Regarded as an introductory course, this 

 small volume is of distinct merit. 



(4) Dr. Besant's treatise on dynamics is well 

 known to many generations of Cambridge men, 

 and its re-issue in an enlarged form will doubtless 

 be welcomed. Mr. Ramsey, who undertook a few 

 years ago, at the author's request, the editing of 

 part i. and the writing of part ii. of his treatise 

 on hydromechanics, has also found time to edit 

 and supplement this remaining volume. The 

 increase in size is considerable, partly owing to 

 additions to the text, but more to the very large 

 number of problems which are now incorporated. 

 Numerous illustrative examples are fully worked 

 out, and notes are frequently appended to them, 

 which the student will find instructive. We have 

 no doubt that men reading for the second part 

 of the Mathematical Tripos will find this volume 

 most helpful. 



(5) This collection of examples and papers is 

 conservative in typ)e. There is little note of origin- 

 ality either in arrangement or material. With 

 regard to bookwork, only the chief theorems are 

 inserted, and there is little explanatory matter. 



NO. 2364, VOL. 94] 



Part ii. includes progressions, variation, and 

 gradients ; part iii. contains the logarithmic and 

 exponential series. 



(6) This book, designed for first-year college 

 students in -America, corresponding roughly to the 

 last stage in the secondary schools of this 

 country, is intended to show the application of 

 simple mathematical principles and operations to 

 practical life. No great manipulative power is 

 demanded of the reader; the author's object is to 

 inspire him with new ideas and broaden his out- 

 look. The central thWie of the book is function- 

 ality. This is appli^y ta''^ power functions, ex- 

 ponential functions, and' periodic functions; the 

 fundamental transformations are treated from a 

 kinematic point of view, by translation, rotation, 

 and shear. The text is interesting throughout, 

 and the author has collected an admirable set of 

 practical exercises. 



(7) This treatise for engineering students deals 

 with the stability of bodies floating either in air 

 or water. There are two introductory chapters 

 which summarise the principles of rigid dynamics 

 and hydrostatics, specially needed for the course. 

 The author then passes to the stability of ordinary 

 ship-forms, and this occupies nearly half the book, 

 dealing with, among many other things, stability 

 curves, trim curves, stability at high speeds, 

 effect of wind and waves. In the next chapter he 

 turns to submarines, the action of rudders, trans- 

 verse stability, etc., and this is followed by the 

 consideration of floating docks, aircraft, and 

 caissons. The chapter on aircraft will probably be 

 of interest to a wider circle than any other part 

 of the book, and may be read independently. The 

 clearness of the diagrams deserves a special word 

 of praise. 



OUR BOOKSHELF. 



A First Book of Commercial Geography. By 

 T. Alford Smith. Pp. viii+151. (London: 

 Macmillan and Co., Ltd., 1915.) Price i5. 6d. 

 Mr. Alford Smith's book has many useful 

 characteristics. It is clearly written, has good 

 maps and diagrams, and a number of appropriate 

 pictures, and includes well-chosen and suggestive 

 examination questions. The scope of commercial 

 geography, however, as specified here, may not 

 appeal to all. The statement, for example, that 

 in order to understand commercial geography 

 it is necessary to know what processes an article 

 has to undergo in order to become an article of 

 commerce, needs cautious application ; it is a 

 fault of some larger and more advanced works 

 in this subject that, in the direction especially of 

 manufacture, they wander far outside geo- 

 graphical limits. And perhaps, on the other 

 hand, there is lacking in the book under notice 

 a sufficiently forcible exposition of the principles 



