OCTOBEK 23, 1914] 



SCIENCE 



599 



about twice that space of solid tables and 

 diagrams. It has three noteworthy char- 

 acteristics. 



The first is the excessive labor involved in 

 calculation. In a few instances, for example, 

 in the case of the tables X„ X, and 1 — r^ to 

 facilitate the calculation of the probable errors, 

 it has been possible to arrive at constants of 

 the greatest usefulness with a minimum of 

 simple arithmetic. But in the great majority 

 of cases, each entry has cost heavily. It is 

 probably safe to say that the difficulties of 

 computation have been far greater than in the 

 majority of published tables. 



The second remarkable feature of the book 

 is originality of contents. For the most part, 

 volumes of tables are largely made up of old 

 material which has long since become common 

 property. Practically, the whole of this quarto 

 is strictly new. In only a few eases have 

 materials already published been better 

 adapted to meet the needs of statisticians. 

 Thus the tables of logarithms of the Gamma 

 function have been adapted from those of 

 Legendre; the table of angles, arcs and deci- 

 mals of degrees is based on Button's mathe- 

 matical tables; after the table of logarithms 

 of factorials had been completed, similar 

 tables issued in 1824 were discovered and used 

 as cheeks. 



The third distinguishing feature of the 

 volume is that it represents the work of a 

 single laboratory and its associates under the 

 leadership of the one who has finally brought 

 the colossal undertaking to completion. 



The cost of publication has been very great ; 

 it has been made possible only by distributing 

 the expense of setting and moulding over a 

 period of years of first publication in Biome- 

 trilca. Thus the completion of the tables has 

 largely depended upon the possibility of main- 

 taining Biometrika. Though this has been 

 given such protection as copyright affords, it 

 has been practically impossible to prevent 

 piracy of tables already issued and so to make 

 possible the completion of the series. The 

 editor remarks with a bitterness which is fuUy 

 justified by his experience of the last few 

 years : " It is a singular phase of modern sci- 



ence that it steals with a plagiaristic right 

 hand while it stabs with a critical left." 



The volume is indispensable to all who are 

 engaged in serious statistical work. 



J. Arthur Harris 



Crystallography. An Outline of the Geomet- 

 rical Properties of Crystals. By T. L. 

 Walker. New York, McGraw-Hill Book 

 Co., 1914. Pp. xiv + 204, 213 figures in text. 

 So many elementary treatises on crystallog- 

 raphy have appeared in the American press 

 within the last five years that a new one would 

 seem to be justified only by the introduction of 

 some essentially new feature. Such a justi- 

 fication is certainly to be claimed for this brief 

 work by Professor Walker in which a discus- 

 sion of the geometrical properties of crystals 

 is based on the gnomonic projection as em- 

 ployed in the methods of Goldschmidt. 



After brief consideration of the process of 

 crystallization in very elementary terms there 

 is given in Chapter TV. an account of the 

 gnomonic projection showing how by its means 

 a graphic representation of the relations of 

 crystal faces may be obtained; how numerical 

 symbols for the forms and values for the axial 

 elements may be read directly from it ; and how 

 the regular arrangement and spacing of the 

 projection points illustrate the laws of sym- 

 metry, of constancy of crystal angles and of 

 the rationality of parameters. The chapter 

 also contains instructions for preparing both 

 gnomonic and stereographic projections from 

 two-circle goniometrie measurements as well 

 as an account of the conventional axes of 

 reference and the derivation of Miller's index 

 symbols. 



This chapter seems to the reviewer an 

 admirable presentation to the beginning stu- 

 dent of the difiicult subject of the mathe- 

 matical relations of crystal faces. No ade- 

 quate account of Goldschmidt's very useful 

 methods exists elsewhere in the English 

 language and these methods are here very 

 happily welded to the conventional ones which 

 they illuminate. It is to be regretted that the 

 author did not supplement his account by a 

 statement of Goldschmidt's energy theory of 



