!76 



NATURE 



[January 6, 1910 



modern extensions, such as harmonic ranges and 

 coaxal circles, which now form a customary part of 

 the school course. 



(3) In this treatise the elements of coordinate 

 geometry are presented in a compact form. The first 

 twelve chapters are devoted to the treatment of the 

 line, circle, conic, and other curves, while the remain- 

 ing six deal with the line in space and the surfaces 

 of the second degree. The experience of the authors 

 has led them to introduce a number of changes in 

 the order of development of the subject. The equation 

 of the straight line is given, before the customary 

 work on lengths and areas; they advise the student 

 to read the chapter on the parabola before that on 

 the circle, thereby enabling him to see at an early 

 stage how analytical methods may be used to obtain 

 properties which are new to him. All mention of 

 pole and polar properties is deferred until after the 

 treatment of the general conic, and the application of 

 Cartesian methods to the investigation of loci is post- 

 poned to the final chapter of the first part of the 

 book. 



The section on solid geometry, while omitting the 

 more complicated analytical formulae, is sufficiently 

 thorough to enable the student to attack with success 

 any problem on the geometry of the conicoid of a 

 straightforward character. There are numerous exer- 

 cises and diagrams. In every respect this book is 

 admirably suited to meet the needs of those who are 

 reading the subject for the first time. 



(4) The range of work covered by Mr. Radford's 

 useful book includes the binomial theorem and the 

 exponential and logarithmic expansions. Quadratic 

 equations and graphical solutions are introduced at 

 the start, and logarithms appear at an early stage. 

 There are also ten book-work papers. 



(5) The papers set in recent examinations conducted 

 by the Civil Service Commissioners have included a 

 number of problems of a much more practical char- 

 acter than are to be found in the ordinary academic 

 text-book. That this type of question is both stimu- 

 lating and of real educational value is beyond question, 

 but up to the present there has been no convenient 

 collection of problems of this character. Mr. Fawdry's 

 book now supplies exactly what is wanted. Primarily, 

 it is intended for army candidates and students in 

 technical colleges, but many of the papers contain 

 practical questions of considerable intrinsic theoretical 

 dift'jculty, and may therefore profitably be set to boys 

 preparing for entrance college scholarships. A com- 

 prehensive set of revision papers adds materially to 

 the utility of this first-rate book. 



0\]R BOOK SHELF. 



Ant Communities and How they are Governed. ,4 

 Study in Natural Civics. By Dr. H. C. McCooli. 

 Pp. xvii + 321. (New York and London: Harper 

 and Bros., 1909.) Price 7s. 6d. net. 

 For thirty-two years Dr. McCook has devoted much 

 time and attention to the habits of American ants, 

 and has published many popular works on the subject, 

 in addition to the two large works on "The Agricul- 

 tural Ants of Texas" and "The Honev Ants of the 

 Garden of the Gods." In the present work, which is 

 NO. 2097, "VOL. 82] 



based chiefly on his own original observations, he 

 discusses the conditions of ant-life from a popular 

 standpoint ; and his sixteen chapters deal with such 

 subjects as fraternal confederacies, nesting architec- 

 ture, engineering, feeding the commune, language, 

 government, dependents, war, aliens, aphis herds, 

 slave-making, sanitation, &c. 



Britain is ver*' deficient, both as regards number of 

 species and number of individuals; but the American 

 species are more numerous, and the size of nests and 

 communities of many species is almost incredible. 

 Thus Dr. McCook writes : — " The large conical nests 

 of the mound-making ants of the Alleghanies, 

 Formica exsectoides vary in size from newlv-begun 

 colonies a few inches high to mature hills, measuring 

 thirty-seven feet in circumference at the base, though 

 rarely more than three feet high. Thev occur in 

 groups, and in one site near Hollidaysburg, Pennsyl- 

 vania, within a space of fifty acres, the writer counted 

 seventeen hundred well-developed mounds. At two 

 other localities in these mountains, similar groups 

 wore observed even more thickly placed. At "Pine 

 Hill," about thirty acres were occupied, of which five 

 were found to contain two hundred and ninety-three 

 mounds, an average of fift^'-nine to the acre, or 

 eighteen hundred for the whole section. At "War- 

 rior's Mark," another large settlement of nearlv two 

 hundred hills was visited. Experiments made in the 

 Hollidaysburg group proved that all therein formed 

 substantially one community, in complete fellowship, 

 although the individual mounds appeared to be con- 

 ducted independently " (pp. 3-5). 



Dr. Forei's comment on these observations is : — 

 " These ant kingdoms have in all probabilitv a popu- 

 lation of two hundred to four hundred million in- 

 habitants, all forming a single community, and living 

 together in active and friendlv intercourse " (quoted 

 at p. 8). _ 



Again, with reference to the cutting ants of Texas, 

 we read: — "A planter, in order to get rid of the depre- 

 dations of an immense commune near his residence, 

 had set his men to dig it up and utterly root it out. 

 In order to reach the central nest he had traced the 

 ants from a tree inside his home premises, which 

 they had stripped of leaves, to a point six hundred 

 and sixty-nine feet distant. The nest occupied a space 

 as large as a small cellar, the lowest and main cave 

 being as large as a flour-barrel. In this central cavern 

 were great numbers of winged males and females, 

 and innumerable larvae and workers. From this point 

 radiated the various avenues over which the leaf-cutters 

 marched on their raids " (p. 64). 



We could quote equally interesting passages from 

 almost every page of this fascinating volume; but 

 before concluding, we may note that Dr. McCook 

 attaches great importance to the sense of smell in 

 ants. 



The numerous text-illustrations are of unusual ex- 

 cellence. 



Sextant Errors. By Thos. Y. Baker. Pp. 32. 



(London : J. Griffin and Co., 1909.) Price is. net. 

 Mr. Baker has supplied a very excellent shillingsworth 

 for those who have occasion to use the sextant and 

 wish to understand it properly. Every text-book gives 

 the simple theory of the instrument, and the more 

 ordinary adjustments and tests for errors are generallv 

 enough understood, but when the complete theory of 

 an astronomical instrument, worked out on the sup- 

 position that no part is quite perfectly made, is re- 

 quired, then only such elaborate books as, for instance, 

 Chauvenet may be turned to with confidence. It will 

 be a great convenience to the sextant user to find in 

 this little book complete demonstrations, free from the 

 usual omission of steps, unnecessary for the writer of 



