June 8, 191 1] 



NATURE 



479 



undergone continuous and marked improvement, is 

 certain of a cordial welcome. 



We may at once state that the book is no other 

 than it purports to be — a reprint of three lectures, 

 the first on instruments, the second on survey methods, 

 and the third on maps and map-making. It is in 

 no sense a text-book on the science of surveying. It 

 is, for example, not the sort of book that the prac- 

 tical surveyor would take into the field, nor would it 

 be of much value to the student who has passed the 

 elementary stage. 



Its true function, we take it, is identical with that 

 of a lecture, not to instruct, but rather to stimulate 

 curiosity, not so much to teach as to show that there 

 are things worth learning. A book of this class has 

 a tendency to fall into a difficult category, being too 

 technical for the ordinary reader and too simple for 

 the expert. At the same time, we may frankly recog- 

 nise that as regards this particular subject there are 

 a large number of persons — travellers, oflficers, and 

 officials, whose duties take them into the uncharted 

 regions of the world — to whom a little knowledge 

 of survey methods is a valuable acquisition but who 

 have no desire or capacity to prosecute their studies 

 further. 



To these and to all others who de^re a general 

 acquaintance with a science which must always re- 

 main of great practical importance and of considerable 

 human interest, we can cordially recommend Mr. 

 Reeves's book. 



The first chapter, dealing with the history and 

 development of surveying instruments, profusely 

 furnished with illustrations, as indeed is the whole 

 book, will be found full of curious information. The 

 treatment of modern instruments is perhaps too com- 

 pressed to be thoroughly satisfactory and has a 

 tendency to degenerate into a mere catalogue, wherein 

 the various instruments are briefly described, but no 

 adequate attempt is made to estimate their relative 

 merits or defects. Thus the prismatic sextant is 

 mentioned as an " improvement " on the ordinary form 

 without a hint that, as a matter of fact, it was 

 found to be no improvement, and has passed entirely 

 out of use. 



The book is well printed and misprints are not 

 common. We scarcely know whether the spelling 

 s^eodecist fp. 24) is intentional; if so, we must enter 

 a protest against it. 



The specimen maps are reproduced with the uniform 

 excellence of style that we are accustomed to in the 

 R.G.S. publications. 



In conclusion we may direct attention to the map 

 on p. 131, showing relief by "stereoscopic " colouring, 

 i.e. a system wherein the varying altitudes are shown 

 by an ordered sequence of spectrum colours, the high 

 ground red and thence descending through greens and 

 yellows to a blue sea. The effect of relief on such 

 a map is very good. The eye naturally adjusts itself 

 as in viewing near and far objects so that the tops of 

 the hills appear nearest and the bottoms of the valleys 

 farthest from the observer. A neglect of this principle 

 of spectrum colours is a marked defect of the recently 

 published half-inch Ordnance Survey map of England, 

 NO. 2 171, VOL. 86] E. H. H. 



MATHEMATICAL TEXT-BOOKS. 

 (i) Elements of Plane and Spherical Trigonometry. 

 By Prof. D. A. Rothrock. Pp. xi+ i47 + xiv + 99. 

 (New York : The Macmillan Co. ; London : Mac- 

 millan and Co., Ltd., 1910.) Price 6s. net. 



(2) Homogeneous Coordinates for Use in Colleges and 

 Schools. By Dr. W. P. Milne. Pp. xii+164. 

 (London : E. Arnold, 19 10.) Price 5s. net. 



(3) A Geometry for Schools. By F. W. Sanderson 

 and G. W. Brewster. Pp. X4-336. (Cambridge: 

 University Press, 19 10). Price 3s. 



(4) Analytic Geometry. By Prof. N. C. Riggs. Pp. 

 xi + 294. (New York: The Macmillan Co.; Lon- 

 don : Macmillan and Co., Ltd., 19 10.) Price -js. 

 net. 



(i) npHIS volume contains a fairly through treat- 

 X ment of the numerical aspects of plane and 

 spherical trigonometry. In addition to this, a certain 

 amount of attention is directed to elementary identity 

 work, and some indication is given of the higher 

 analytical developments of the subject, based on 

 Demoivre's theorem, in the concluding chapter of 

 the first part of the book. It is unfortunate that the 

 symbol ei« is regarded as equivalent to exp(i«). 

 This is the source of much error in the minds 

 of students, and from the earliest stage it is most 

 desirable to emphasise the distinction between the 

 two forms. With this exception, the mode of pre- 

 sentation is excellent. There are numerous exercises 

 and problems, but at present no answers are given. 

 This is a serious omission, and it should be rectified 

 in a new edition. Five-figure tables of logarithms and 

 trigonometric functions are appended to the book. 



(2) The utility of homogeneous coordinates when 

 carefully employed, is undeniable. It so often hap- 

 pens that their properties are sketched in a brief 

 chapter at the end of treatises on Cartesian methods, 

 thus leading the reader to believe that the subject 

 is one of small value and importance. It is, of 

 course, a misuse of this instrument to apply it to 

 metrical results, except in very special circum- 

 stances ; but its application to properties of a descrip- 

 tive character is particularly instructive and illuminat- 

 ing. The present volume contains, in a remarkably 

 small compass, a comprehensive account of the sub- 

 ject, treated in exactly the right way. Its wealth of 

 detail will be invaluable to the teacher, who will 

 probablv prefer to make selections for his pupils. 

 The correspondence between point and line coordinates 

 is worked out in a thorough fashion, and the part 

 played bv ideal and imaginary elements is clearly 

 indicated. Such work as this is well within the 

 range of the scholarship class in secondary schools, 

 and it arouses keen interest, mainly because analysis 

 is verv properly subservient to principle. There is 

 an admirable collection of examples. We wish the 

 book all the success it unquestionably deserves. 



(3) The plan of this book agrees to a large extent 

 with the recommendations made in the Board of 

 Education circular on the teaching of geometry. The 

 proofs of the fundamental congruence and parallel 

 theorems occupy a subordinate position, thus making 

 it possible for the student to onss rapidly over the 



