lOO 



NA TURE 



[December i, 1904 



author is fully conscious of the serious embarrassments 

 of the position he has chosen, but braveh- attempts the 

 well-nigh impossible task of overcoming them. Thus 

 he says : — 



"If this book were written by a mathematician for 

 the mathematically minded, it would not need to be 

 one fifth as long. If read by such a one it may well 

 seem intolerably clumsy and inelegant." 



Whether he succeeds under these difficulties in 

 giving easily intelligible explanations may well be 

 doubted ; indeed, his language, though frequently lucid, 

 is often quite the reverse. Still, if the volume were 

 used as a text-book in the hands of an enthusiastic and 

 capable teacher good results might follow, but it re- 

 quires an optimistic disposition to believe that it would 

 prove more than superficially instructive, if it were 

 intelligible at all, to the mass of ordinary and un- 

 assisted readers. The author might, however, claim 

 a higher rank for it than he has done on the ground 

 that it teems with instructive illustrations by which 

 ever}'one may profit, and that it presents familiar ideas 

 from slightly new points of view, much to the 

 advantage of even well instructed readers. 



There is no science more handicapped bv cumbrous 

 and repellent terminology than that of the higher 

 statistics. Its ideas are not always intrinsically 

 difficult to grasp, but the phrases bv which they are 

 expressed are both ugly and unexpressive. The writer 

 believes that a student, however mathematically minded 

 he may be, would save himself time and annoyance if 

 he' prefaced his earliest studies by a few hours of what 

 might be called 'kindergarten exercises with beans, 

 acorns, or the like. By the process of sorting them 

 into arrays and picking out the medians, quartiles, 

 S:c., then by measuring them individuallv and extract- 

 ing from the measures the remaining statistical con- 

 stants, he would soon obtain a serviceable familiarity 

 with the more elementary technical terms and the ideas 

 they represent. It would be easy to devise a suitable 

 course that would prove a welcome help to students 

 who are enthusiastic about measurements, and it is 

 to be hoped that the next writer on popular statistics 

 will elaborate one. 



The author gives a large number of frequency 

 polygons, derived from a wide variety of data, which 

 are of interest. It is to be wished that attempts were 

 more frequently made to reduce the variously shaped 

 polygons obtained by experience into a few classified 

 types, to append to each type the names of the objects 

 that had been found to conform to it, and to analvse 

 the causes of its shape in each instance. It is difficult 

 to doubt that by so doing some desirable help would 

 be given to the interpretation of any new polygon. 

 It is perfectly true that almost any curve or polygon 

 may be built up in various ways by different types of 

 curve or polygons appropriately superposed, but ex- 

 perience alone will tell whether there is not a much 

 greater probability of such and such a type being due 

 to such and such combinations rather than to others. 

 Through these means many hypothetical sources of 

 origin might be found so rare as to be hardly worth 

 considering, and so the field of probable interpretations 

 would be narrowed. Speaking generally, the inter- 

 NO. 1831, VOL, 71] 



prctation of results is a branch of statistics that has 

 hitherto received less attention than it deserves. It 

 is no doubt a great thing to be able to describe groups 

 and to determine correlations between them with pre- 

 cision, but this is not all that is wanted. It is another ' 

 and even more important achievement to dissect and 

 anahse results and to discover the dominant causes 

 that produced them, but the art oL doing this seems 

 as yet inadequately developed and to offer a promising 

 field for research. F. G. 



OVR BOOK SHELF. 



Practical Cliciuislry, a Second Year Course. Bv 

 G. H. Martin, M.A. (N.D.). Pp. 41. (Bradford": 

 G. H. Martin, The Grammar School.) Price is. 

 Mr. Martin has arranged in an unpretentious form a 

 most excellent syllabus of experiments and examples 

 suitable for boys beginning the study of chemistry. 



It is satisfactory to find that, in a school of such 

 high standing as the Bradford Grammar School, the 

 science master has seen the wisdom of devoting a 

 whole year (it is to be hoped it will be extended to a 

 second year) to teaching the simple facts which under- 

 lie important principles without recourse to tests and 

 tables. 



One suggestion may be offered. If the book is to 

 have a wide circulation, which it certainly deserves, 

 it will be necessary to fill in the outline of experiments, 

 and perhaps to illustrate the results by actual ex- 

 amples, possibly in a companion volume. 



Boys cannot be expected to work out details of 

 apparatus in the short time allotted to science during 

 school hours if substantial progress is to be made. No 

 doubt the author has his apparatus set up and gives 

 an appropriate demonstration to the class, but this will 

 not help those teachers who wish to profit by the book 

 unless their technical difficulties are solved for them. 



J. B. C. 



Retouching. By .Arthur Whiting. Pp. xvi + qi. 



(London : Dawbarn and Ward, Ltd., 1904.) Price 



IS. net. 

 It ver}- often happens that photographic negatives 

 require a certain amount of careful manipulation 

 owing to defects caused by photographic methods, 

 scratches, &c. It is also desired sometimes to eliminate 

 small defects due to slight movement of the object, or 

 to alter or improve portions of the picture to attain a 

 desired end. The author has endeavoured in these 

 few pages to place before the reader the different 

 methods and devices that are in use to cope success- 

 fully with the various defects that may be encountered. 

 In the first instance the tools required are described, 

 and the special objects of each explained. The reader 

 is then shown how, in the case of portraits, to preserve 

 the likeness but yet to eliminate the blemishes caused 

 by optical or chemical or other action; he is here intro- 

 duced in a few words to the elements of facial anatomy. 

 The author has considered it necessary to insert 

 a special chapter on retouching portraits of pro- 

 fessionals, in which the main principle to be kept in 

 view is to produce a beautiful face. To attain such 

 an ideal, mouths are reduced, jaws cut down, ears 

 knifed, eyes enlarged, and various other surgical 

 operations performed. Working up draperies, retouch- 

 ing landscapes, preparing prints for the press, and 

 how to make a portable retouching desk, form other 

 topics for treatment. The book should serve as an 

 admirable guide to amateurs, and will be found useful 

 to those who go more especially into this class of work. 

 Numerous illustrations accompany the text. 



