I 



April 8, 1920] 



NATURE 



163 



) Elementary Calcuhis. By C. H. P. Mayo. 

 (With answers.) Pp. xx + 345 + xxxix. (Lon- 

 don : Rivingtons, 1919.) Price 10s. 

 ) Mensuration for Marine and Mechanical 

 Engineers. {Second and First Class Board of 

 Trade Examinations.) By John W. Angles. 

 Pp. xxvii+162. (London: Longmans, Green, 



(4) School Mechanics. Part i. School Statics. By 

 \V. G. Borchardt. (Without answers.) Pp. viii+ 

 266. (London : Rivingtons, 1919.) Price 65. 

 (i) npHIS text-book by three American authors 

 1 is best described as an elementary 

 mathematical melange. It ranges over a variety 

 of topics, but does not deal explicitly with the 

 calculus, though the fundamental process of the 

 latter is used. Great pains have obviously been 

 expended on the compilation, but it can scarcely 

 be described as an inspiring volume, and is not 

 likely to find favour in British schools and col- 

 leges. The authors state in the preface that they 

 desire to emphasise the fact that mathematics 

 cannot be artificially divided into compartments 

 with separate labels, and that they aim at show- 

 ing the essential unity, harmony, and interplay 

 between the two great fields into which mathe- 

 matics may properly be divided — namely, analysis 

 and geometry. It is to be feared that those who 

 are to become competent mathematicians must 

 continue to study the subject in compartments, 

 carrying on, of course, several sections simul- 

 taneously, leaving familiarity and time to show 

 the inter-relationship. None but the finished 

 scholar can fully appreciate and realise the inter- 

 twining of the branches. Only those who reach 

 the hill-tops see the harmony of the landscape and 

 the trend of the watercourses. There are several 

 interesting diagrams and historical references, 

 and also a number of good examples. The 

 volume is well got up and printed. 



(2) Mr. Mayo's well-printed and finished book is 

 meant for beginners, for general use in schools, 

 to be within the capacity of the average boy, and 

 also to meet the first requirements of those who 

 intend to specialise in mathematics. That the 

 book will realise all these aspirations is unlikely. 

 So early as p. 6 it presents the beginner with the 



expression U 



= 2, and discusses 



ith- 



metical approximations and negligible quantities. 

 The introduction to the subject is of that kind 

 which always leaves the student with the uneasy 

 feeling that the calculus is not quite all right, and 

 gives results just a little out. It is the belief and 

 experience of the reviewer that the opening peda- 

 gogics of the calculus must be simple and not 

 over-refined. The easy processes of finding the 

 NO, 2632, VOL. 105] 



gradients of chords of curves of the system y==x** 

 and of deducing therefrom the gradients of the 

 tangents are about all that the average boy 

 can grapple with for a considerable time. The 

 notation can be explained concurrently, and a few 

 easy steps lead on to simple integration and easy 

 applications. Geometry and intuition must be 

 relied on to give the start. The philosophy of 

 the limit is beyond the ordinary pupil. From the 

 school point of view the book covers a fairly wide 

 range, including triple integrals, singular points, 

 partial differentiation, and differential equations. 

 There are many good examples in it, derived from 

 geometry, physics, mechanics, etc., all likely to 

 stimulate a smart boy. In fact, it will probably 

 succeed much better as a second than as a first 

 course. 



(3) This is a book on mensuration intended for 

 the use of engineering students of various kinds, 

 as, for example, marine engineers preparing for 

 the First and Second Class Board of Trade Exam- 

 inations and for the Extra First Class Examina- 

 tion. It deals in a thorough way with the ordinary 

 elementary areas and volumes, such as those of 

 the rectangle, circle, ellipse, sphere, cone, and 

 cuboid, refers to the planimeter, explains Simp- 

 son's Rule, and discusses valves, specific gravity, 

 flow of water, etc. It includes also some calculus 

 and the theorems of Pappus. There is an abun- 

 dance of good examples in the book, both worked 

 and to be worked, so that any student who goes 

 through it conscientiously should conclude his 

 examinations successfully. 



(4) Mr. Borchardt's book is part i of a School 

 Mechanics, and deals with statics. It is intended 

 for the use of pupils preparing for the higher 

 mathematics, foi- entrance to Woolwich and 

 Sandhurst, and for the Senior Cambridge Local 

 Examination. The matter is arranged under the 

 following heads, according to the sequence given : 

 the lever, the parallelogram of forces, friction, 

 work and machines, centres of gravity, couples, 

 and general equilibrium. Then follow laboratory 

 problems and test papers. There are plenty of 

 illustrative examples in the text, and a copious 

 supply for the exercise of the student, mostly of 

 a numerical type. If the treatment of the subject 

 presents no fresh or original features, the book 

 is one which can safely be used. J. M. 



Our Bookshelf. 



The Romantic Roussillon: In the French Pyrenees. 



By Isabel Savory. Pp. xii + 214 + xxvi plates 



by M. Landseer Mackenzie. (London : 



T. Fisher Unwin, Ltd., 1919). Price 255. net. 



The author of this excellently printed work will 



not mind our saying at the outset that one of its 



chief charms is the series of pencil drawings by 



