April 27, 19 16] 



NATURE 



179 



:hogromia. The late J. D. Siddall was of the 

 Dpinion that his remarkable genus, Shepheardella, 

 shared this iridifiference to habitat, but did not 

 publish his conclusions on the matter. 



The twenty-five plates in colour and monotone 

 are worthy of the best traditions of the Ray 

 Society. Vol. iv., which will complete this 

 admirable work, will consist of two parts : the 

 first an addendum to vols. i. and ii., comprising 

 species recorded as new to Britain since their 

 publication ; the second, dealing with the Heli- 

 ozoa, will be the work of Messrs. Hopkinson and 

 Wailes. E. H.-A. 



MA THEM A TICAL TEXT-BOOKS. 



1) The Essentials of Descriptive Geometry. By 



Prof. F. G. Higbee. Pp. vi + 204. (New York: 



J. Wiley and Sons, Inc. ; London : Chapman 



and Hall, Ltd., 1915.) Price 75. 9J. net. 



I 2) Five-Figure Mathematical Tables. Compiled 



I by E. Chappell. Pp. xvi + 320. (London : 



! W. and R. Chambers, Ltd., 1915.) Price 55. 



net. 

 13) Mortality Laws and Statistics. By R. Hen- j 

 i derson. Pp. v+iii. (New York: J. Wiley I 

 1 and Sons, Inc. ; London : Chapman and Hall, 

 j Ltd., 1915.) 55. 6d. net. 



1^.) Arithmetic for Carpenters and Builders. By 



j Prof. R. B. Dale. Pp. ix + 231. (New York: 



] J. Wiley and Sons, Inc. ; London : Chapman 



•j and Hall, Ltd., 1915.) Price 55. 6d. net. 



;) Handy Logarithmic Tables. By Y. Uraguchi. 



' Pp. 7. (Tokyo: Y, Uraguchi, 1915.) Price 3d. 



"T*HE author assumes on the part of the 



-^ reader no previous knowledge of de- 



jriptive geometry, and only quite a superficial 



quaintance with ordinary plane geometry. The 



jurse follows mainly the customary lines, includ- 



i°f points, lines, angles, planes, surfaces, and 

 ^del-making. There are three reasons why its 

 neral character should commend itself to the 

 ♦ dinar}- student. First, the diagrams are 

 lerous, clear, and unusually large ; secondly, 

 style of exposition is admirably lucid ; and 

 lly, each chapter closes with a set of simple 

 cises ; it would be a distinct improvement if 

 ers were added, where possible. 

 - ) This book of five-figure tables includes 

 rithms of number and their reciprocals, anti- 

 irithms (called illogs), logarithms of loga- 

 ns (called lologs), anti-" logarithms of loga- 

 Tis " (called illologs), the trigonometric func- 

 s and their logarithms, and a table of various 

 -tants. To lessen, in using the lolog tables, the 

 nee of error which would occur from failure 

 lotice whether the logarithms are positive or 

 itive, numbers less than unity are shown in 

 and those greater than unity in black. This 

 wise precaution. The book is well printed 

 arranged in a convenient fashion. 

 ' The author sets out in scientific form the 

 Its of investigations into the duration of 

 -an life and the mathematical theory required 

 'n^- The book is a treatise for actuaries or for 

 "i3|iematicians interested in the theory of proba- 

 ! NO. 2426, VOL. 97] 



bility. The author has excluded the combination 

 of life corftingencies with the theory of compound 

 interest, annuities, etc., and has confined himself 

 strictly to life contingencies. 



After opening with an historical account of the 

 way in which mortality tables came to be com- 

 piled and improved, he proceeds to discuss the 

 construction and graduation of tables now in use, 

 and gives various modern tables in an appendix. 



(4) This small text-book is admirably suited to 

 meet the needs of the practical workman. It deals 

 with the elements of arithmetic, but includes also 

 a great deal of general and technical information, 

 such as the use of tools, cost of material, economy 

 of arrangement, and simple designs. The student 

 who reads and works thoroughly through its pages 

 will acquire a considerable store of valuable in- 

 formation : a worthy addition to an excellent 

 series. 



(5) These four-figure tables are printed on a 

 thickish sheet of paper, 7 in. high, 31 in. long, 

 folded into seven parts, and contain proportional 

 parts, logarithms of number and their reciprocals, 

 and anti-logarithms. W^e doubt whether they 

 possess any advantage over the ordinary forms 



OUR BOOKSHELF. 

 The Mathematical Theory of Probabilities and its 

 Application to Frequency Curves and Statis- 

 tical Methods. By A. Fisher. Translated by * 

 W. Bonynge. Volume i. Mathematical Prob- 

 abilities and Homograde Statistics. Pp. xx + 

 171. (New York : The Macmillan Co. ; Lon- 

 don : Macmillan and Co., Ltd., 1915.) Price 

 85. 6d. net. 

 It is remarkable that, in spite of the number of 

 older works in English on the theory of prob- 

 abilities and the great attention that has recently 

 been devoted to statistical method, no modern 

 work on the subject in our own language existed. 

 Mr. Fisher's work will do much to fill this gap. 

 After an introduction on the general principles 

 and the philosophical aspect of the subject, and 

 a somewhat slight historical sketch, he develops 

 the fundamental theorems of probabilities, the 

 laws of mathematical expectation, probability a 

 posteriori and Bayes's theorem, the law of large 

 numbers, and the theory of dispersion. This 

 theory is then applied to games of chance and 

 to statistical problems. A second volume is 

 promised on the theory of frequency curves. 



The treatment is very lucid — the chapter on 

 ^ayes's theorem may be selected as a marked 

 example — and the work will be of considerable 

 service to the statistical student. It is to be 

 regretted, however, that the author has not taken 

 up some of the more difficult problems of statis- 

 tical work and has stopped short at the elemen- 

 tary comparison of the actual dispersion of a series 

 with the combinatorial dispersion. 



There is no index, and it is to be hoped the 

 promised second volume will supply one. In a 

 future edition the spelling of proper names should 

 receive attention. 



