446 



NATURE 



[June i, lyii 



"The Calculus for Beginners," will present little 

 diniculty to those who arc suHiciently mature to be 

 able to appreciate the comprehensive work of the 

 present volume, and the consequent abbreviation of 

 analysis will render more prominent the principles 

 which are being illustrated. 



Owing to the general character of the structure 

 of this book, it is not until page 318 that we first 

 niret the systematic discussion of the equations of the 

 tluic species of conies, reduced to their standard 

 forms. These are taken together, and the import- 

 ance of parametric notation is shown here as in the 

 earlier parts of the book. We are glad to see that 

 Joachimsthal's section-equation is employed for tan- 

 gent and polar properties, not only because the 

 method is intrinsically instructive, but also on account 

 of its application to homogeneous coordinates. The 

 final chapter gives a brief sketch of the theory of the 

 general equation of the second degree, and a few pro- 



Eerties of confocal conies and curvature. The authors 

 ave excluded line coordinates, homogeneous co- 

 ordinates and invariants as being beyond the scope 

 of their work. We have no hesitation in describing 

 this text-book as an excellent introduction to Carte- 

 sian methods. 



Bathy-Orographical Map of the World on Gall's Pro- 

 jection. (Edinburgh and London : W. and A. K. 

 Johnston, Ltd., n.d.) Prices : Varnished, 125. ; un- 

 varnished, JOS. 

 In showing elevation on a map of the world generalisa- 

 tions are essential, but detail and accuracv must not 

 be sacrificed for tli,- sake of graphic effect if such a 

 map is to li.nc any i)i-actical value in teaching. On 

 this map three areas are distinguished in colour on 

 the land, above 5000 feet, 1000 to 5000 feet, sea level 

 to 1000 feet, and below sea level. The sooo feet line 

 has been inserted with considerable care, and gives 

 a fairlv true representation of the main regions of 

 high land, but some further distinction is needed be- 

 tween regions of great elevation, such as Tibet, and 

 moderate heights, such as the Drakensbergen. It 

 must be remembered that the principal use of a world 

 map of this kind will be in connection with the study 

 of climate. The absence of anv higher elevations is 

 agamst its use for, to take two examples, the study 

 of the influence of elevation on temperature and that 

 of high marginal ranges, such as the Himalavas, on 

 wmd movements and rainfall. That the map is in- 

 tended to be used in the studv of climate may be 

 judged from the fact that inset maps are given of 

 mean annual temperature and of rainfall. An excep- 

 tion must be made to the statement of the general 

 accuracy of the map with regard to the higher eleva- 

 tions in Canada and Alaska. The result of recent 

 observations has not been incorporated in the case of 

 N.E. Canada, N. and S. of Hudson Strait, in which 

 region are situated the highest mountains of the 

 eastern nart of N. America, and the accuracy of the 

 Rockies and coast ranges of the N.W. leaves much 

 to be desired when contrasted with that of the W of 

 the United States. 



The next contour is at 1000 feet, which, in the case 

 of countries such as .Africa, largely above that eleva- 

 tion, is at too distant an interval to give an adequate 

 representation of the land surface. A curious error 

 has been made in the case of Great Salt Lake, which 

 IS shown as below sea-level. The sea depths are 

 indicated at too, 2000 and 3000 fathoms, but it is 

 doubtful if these lines, which do not correspond to 

 those shown on the land, will be of much use for the 

 general studv of land forms. On the whole it must 

 be said that the map is of little use for advanced 

 geographical work, and is too crowded with unneces- 

 sary names for rlomentary teaching. 

 NO. 2170, VOL. 86] 



Flant'Animals : a Study in Symbiosis. By Prof. F. 

 Kceble. Pp. ix+103. (Cambridge: University 

 Press, 1910.) Price is. net. 



Although notices of two of the small volumes in this 

 series have already appeared in Naturk, it has not 

 been precisely indicated that they are early volumes 

 of a new series of short works, dealing with scientific 

 and literary subjects, and intended for the lay as well 

 as for the professional reader, that was initiated last 

 year by the enterprising University Press of Cam- 

 bridge. The contribution by Mr. Keeble is particu- 

 larly appropriate to the scries as it represents a com- 

 plete story, replete with instructive problems and a 

 definite piece of research that has entailed persistent 

 observation, ingenious experiment, and cautious in- 

 terpretation of results. 



The research covers the peculiar life-history of two 

 lowly worms, Convoluta roscoffensis and Convoluta 

 paradoxa, that inhabit the foreshores of Brittany, 

 where they were studied in the sea and in a small 

 laboratory. The first section of the book relates to 

 their structure, rhythmic movements, and periodic 

 seasons of reproduction, and contains an excellent dis- 

 cussion of their sense attributes as influenced by 

 light, gravity, and memory (mneme). The plant 

 element, in the shape of enclosed green or yellow- 

 brown cells, is considered in the second part of the 

 book, with regard to action, origin, nature, and sig- 

 nificance, leading to the conclusion that they arc 

 reduced algal cells of the family Chlamydomonadineae 

 Instructive as are the facts, quite as much so are the 

 observations, experiments, and arguments from which 

 the conclusions are derived. In fact, it is difficult to 

 say whether one admires more the patience and in- 

 genuity displayed, the careful sifting of evidence, or 

 the logical yet popular e.\position. The booklet 

 should be quite understandable to and interest non- 

 scientific readers, yet lew botanists will fail to glean 

 information and ideas from its pages. 



An Elementary Treatise on Conic Sections by the 

 Methods of Coordinate Geometry. By C. Smith. 

 New edition, revised and enlarged. Pp. x-l-449. 

 (London : Macmillan and Co., Ltd., 19 10.) Price 

 7^. 6d. 



The merits of this book are so well known that com- 

 ment is almost needless. Nearly thirty years have 

 passed since it was first published, and since then 

 a few additions have been made from time to time, 

 as experience has suggested. The latest edition is 

 considerably enlarged. The number of illustrative 

 examples has been increased ; a section on envelopes 

 has been inserted at the end of the chapter on the 

 parabola ; and a concise sketch of the theory of in- 

 variants of two conies is given in the concluding 

 chapter. There are many other minor additions 

 which will be found useful, such as occasional para- 

 graphs on points of book-work, which have been 

 hitherto regarded as problems, and three sets of 

 miscellaneous examples. 



For scholarship purposes in our opinion, this book 

 is without a rival. The earlier portions are scarcely 

 full enough for the novice, who probably requires a 

 more extensive numerical introduction to the subject. 

 But as soon as this initial stage is completed, it is 

 quite certain that he cannot do better than turn to 

 this text-book and read it from cover to cover. 



There are, of course, some features which are open 

 to criticism. The chapter on tangential coordinates 

 is so compressed that a student may fail to appreciate 

 the power of line coordinates and the analytical in- 

 iterpretation they offer of the principle of duality. 

 Again, many teachers would prefer a direct appeal 

 t> the methods of the cal^lus in tangent properties; 



