September 14, igi 1] 



NATURE 



345 



river flood and protect certain areas in time of the 

 inundation ; while no less important are the river- 

 training works to restrict the erosive action of the 

 river on its banks at points where it may damage 

 existing distributing works and towns or villages. 



The information so brought together should be of 

 much interest to irrigation engineers, and would have 

 been valuable to a wider circle if fuller material had 

 been provided for those not personally conversant with 

 the Punjab. The case of the gradual destruction of 

 the town of Dera Ghazi Khan on the west bank of the 

 Indus by the gradual erosion of its right bank fur- 

 nishes an interesting case of river action bv the annual 

 flood, and is illustrated by a series of ten plans showing 

 the disposition of the river at this point from 1882 to 

 the present time. 



Elsewhere general statements and descriptions are 

 in the majority, and we should have welcomed more 

 quantitative treatment of some of the interesting points 

 which are raised. The regimen of a part of a river 

 cannot be properly understood without some knowledge 

 of the whole, and the lack of this is especially apparent 

 in the first chapter, where a general map of the basin, 

 some information regarding its size, form, relief, 

 structure, &c, would have given a valuable setting to 

 the study of the utilisation of its water which follows. 

 The subjects of rainfall and discharge are dealt with 

 in two brief paragraphs, while we look in vain for 

 maps showing the distribution of the rainfall or dia- 

 grams explaining the variations of discharge at 

 different points and at different seasons. A number of 

 plans and diagrams illustrate the report, but in only 

 one case is the scale of the former indicated on it, 

 though in some other cases it can be found from the 

 text. References to other works on the Indus would 

 haw been a useful addition. H. G. L. 



ELEMENTARY STATISTICS. 

 An Introduction to the Theory of Statistics. By G. 

 Udny Yule. Pp. xiii + 376. (London : C. Griffin 

 and Co., Ltd., 191 1.) Price 10s. 6d. net. 



OF all the works a man may set himself to write, 

 the most difficult must surely be an elementary 

 text-book on statistics. The writer of a text-book on 

 almost any scientific subject has to face the difficulties 

 resulting from a recent rapid development of the 

 science of which he is writing, but in statistics he 

 has the further difficulty that many practical methods 

 have been reached by mathematical analysis that is 

 unsuitable for an elementary text-book. Nor is this 

 all, for the subject appeals to so many diverse interests 

 that points simple or useful to one student are merely 

 troublesome or inconsequent to another. 



Mr. Yule has made an attempt to explain some of 

 the methods used in practice, without demanding 

 much mathematical knowledge of his readers. This 

 course explains the advantages as well as the limita- 

 tions of his work, for it has enabled him on one 

 hand to display his natural facility of explanation, 

 and, on the other, it has debarred him from giving 

 more than a sketch of some of the most important 

 parts of the subject ; it has even led him to avoid 

 NO. 2185, VOL. 87] 



giving certain formulae and methods that are of 

 almost everyday use. 



The book is divided into three parts, the first of 

 which deals with the theory of attributes. We confess 

 that this type of statistical work does not greatly 

 appeal to us, for while good may be done with these 

 methods by a statistician of Mr. Yule's ability, we are 

 doubtful if the notation and formulae he gives are of 

 real help to a student. To most minds statistical 

 errors in reasoning, for instance, are best explained 

 arithmetically, and many of Mr. Yule's examples in 

 part i. will help his readers more than his algebra or 

 letterpress. The second part deals with the theory of 

 variables, "ideal frequency distributions," averages, 

 standard deviations, and correlation coefficients. 

 There is a chapter on partial correlation which should 

 be helpful to many readers, but we wish room had 

 also been found for an account of some of the most 

 recently discovered methods of calculating correlation 

 coefficients. The last part of the book deals with the 

 theory of sampling, and is mainly concerned with 

 probable errors. 



Possibly because of the mathematical work in- 

 volved, Mr. Yule does not deal with the fitting of 

 curves to statistical data, but a student who has 

 proceeded so far as to study partial correlations and 

 the correlation surface should, we think, have some 

 idea how to do this. The gap will perhaps be filled 

 in a future edition, and revision in some other re- 

 spects will, we think, also be wanted. For instance, 

 on p. 38 a formula is given for measuring the degree 

 of association, and if it is applied to the example of 

 imbecility and deaf-mutism on p. 34, the value is o'9, 

 indicating a high degree of association. On p. 213, 

 instead of giving the ordinary formula for working 

 out coefficients of correlation from fourfold tables, 

 Mr. Yule gives a simple expression which he implies 

 can be used in some cases. Unfortunately, in the 

 particular case mentioned above to which a student 

 might be tempted to apply it, the value, instead of 

 being about 0*9, is only o'o2, and gives quite a wrong 

 impression. It was, we think, a great mistake to give 

 the formula on p. 213, as it is open to considerable 

 criticism. 



Another example of a case where readers might be 

 misled occurs on p. 67, where a student might easily 

 misunderstand Mr. Yule's discussion of isotropic dis- 

 tributions, and think that they affected the calculation 

 of a coefficient of contingency. 



While we are very ready to admit that, within the 

 limitations he has placed on himself, Mr. Yule has 

 given much that is of interest and value, we also feel 

 that there is much in his work which lends itself to 

 criticism — more, in fact, than one would expect to see 

 in an elementary text-book. The two cases that we 

 have given above are merely examples of this, but 

 although we have felt it necessary to criticise, it is 

 a pleasure to add that we have been much interested 

 in reading Mr. Yule's work, and have throughout 

 appreciated his numerous arithmetical examples and 

 the trouble that must have been taken to arrange the 

 book in so clear a form and to supply it with such 

 excellent diagrams. 



