September 19, 1907] 



NA TURE 



517 



deciding to adopt this type of construction in any given 

 case. An excellent index adds much to the value 

 of this book for reference purposes, which will prove 

 a welcome addition to the library of every architect 

 and civil engineer. T. H. B. 



Water-works Management and Maintenance. By W. D. 

 Hubbard and Wvnkoop Kiersted. Pp. vi + 429. 

 (New York: J. \\'iley and Sons; London: Chap- 

 man and Hall, Ltd., 1907.) Price 17s. net. 

 This book is divided into three parts, the first dealing 

 with the methods and principles of developing, im- 

 proving, and storing water supplies ; the second with 

 the maintenance and operation of waterworks; and 

 the third with water rates, and depreciation and 

 valuation of waterworks property. 



Although this book treats of American practice, and 

 cannot be regarded as a te.xt-book for experts, yet it 

 contains a great deal of information useful to those 

 having the designing and management of water- 

 works for urban districts. 



The authors point out that in selecting a source from 

 which a supply can be obtained a knowledge of the 

 physical characteristics of the territory from which 

 the water is to be obtained is the first consideration ; 

 a chemical analysis is necessary to detect impurities ; 

 and as drinking water is a medium througli which 

 the bacilli of certain diseases may be imbibed, and 

 infection thus widely disseminated, a rigid bacterial 

 e.xamination has now become a recognised necessity. 



Chapter i. treats of ground water supply and wells, 

 the percolating capacity of soils, rate of filtration 

 through sand, and purification works. The second 

 chapter deals with water supply from rivers, and the 

 means of fitting it for domestic use. The third 

 chapter describes the class of engines in use for pump- 

 ing, the other chapters treating of plans and records, 

 service connections, meters and fittings, fire protection, 

 financial management and accounts, water rates, and 

 depreciation. 



Attention is directed to the subject of electrolysis, or 

 the effect that the introduction of street railways 

 worked by electricity has had on the water mains ; and 

 illustrations are given showing the effect of electrolysis 

 on the cast-iron mains. As a result of electrolytic 

 action the metal of the pipes becomes in some cases so 

 softened that it can be cut with a knife. Cast-iron is 

 affected the least, wrought-iron next, mild steel the 

 next, then high carbon steel, and lead the most. The 

 salts in the ground also have a varying effect, the 

 order of activity being chlorides, nitrates, and sul- 

 phates. The drier the soil the more resistance it 

 offers to the passage of the current. Wasting of the 

 lead in the joints also leads to leakage and eventual 

 failure of the i)ipe by the blowing out of the lead. 

 Pictures from Nature's Garden; Stories from Life in 

 Wood and Field. By H. W. Shepheard VValwyn. 

 Pp. 311; illustrated. (London: John Long.) Price 

 6s. 

 To the naturalist the chief point of interest in this 

 little volume is undoubtedly centred on the illus- 

 trations, which are reproductions from photographs by 

 the author. Among these we may specially refer to 

 one of a dormouse asleep (p. 34), which, so far as w-e 

 know, is unique, and certainly of great interest. The 

 photograph of a sleeping bat, apparently a pipistrelle 

 (p. 27), is likewise excellent, as is also one of a 

 Japanese or Manchurian sika-deer, with the white 

 " chrysanthemums " on the buttocks fully expanded 

 (p. 306). In both these instances it is a pity that the 

 names of the species depicted are not given. As to the 

 text, we venture to think even the author himself 

 would admit that it is scarcely of a nature demanding 

 detailed notice in the columns of this journal. 



R. L. 



NO. 1977, '^OL 76] 



LETTERS TO THE EDITOR. 

 [The Editor does not hold himself responsible for opinions 

 expressed by his correspondents. Neither can he undertake 

 to return, or to correspond wilh the writers of, rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous comtnunications.] 

 On Correlation and the Methods of Modern Statistics. 

 In N.vture of August 29 (p. 401) appeared some account 

 of a (liscussion at the British Association on modern 

 methods of treating statistics. The following paragraph 

 occurs : — 



" Mr. A. R. Hinks, who was somewhat sceptical as to 

 the general applicability of the new methods, inquired 

 what meaning could be attached to the value 0'3 of the 

 correlation coefficient in such cases as y = \ogx. He also 

 gave an example in which questionable conclusions had 

 been arrived at by the method, the reason being that 

 certain groups of stars had been studied for special pur- 

 poses, while others had been neglected." 



The obvious answer to the first part of Mr. Hinks's 

 inquiry is that no meaning could be attached to the par- 

 ticular value 0-3 unless we were told what part of the 

 relation y = log.v it referred to, and then it would have 

 a quite definite but limited meaning. Every statistician 

 trained in modern methods in the case of statistics belong- 

 ing to new material plots his regression lines and tests 

 the approach to linearity in his material. When he finds 

 any orderly system, but no approach to linearity, he 

 naturally tests the dependence of his characters by the 

 correlation ratio. That test applied to Mr. Hinks's case 

 of two absolutely correlated variables y = logj: gives 

 unity or perfect correlation, as we might anticipate. 



Writing to Mr. Hinks for further information as to the 

 bearing of the second part of his criticism, he tells me 

 that the report is too brief to be intelligible, and owing to 

 his courtesy I have been provided with a fuller report of 

 his speech, in proof, for the Journal of the Royal 

 Statistical Society. The " questionable conclusions " 

 reached by the method of correlation to which he refers 

 occur in " a recent paper published under the auspices of 

 Prof. Karl Pearson " (Winifred Gibson, Monthly Notices 

 R.A.S., vol. Ixvi., p. 445), and the special point to which 

 Mr. Hinks refers is the result reached by Miss Gibson for 

 the relationship between parallax and photometric magni- 

 tude. The point is an extremely interesting one, and that 

 must be my excuse for ventilating the matter in the pages 

 of Nature. Mr. Hinks makes two criticisms, the first as 

 to method and the second as to matter. 



First, as to Method. — Mr. Hinks says that if the stars 

 were uniform in size and brilliancy, the parallax and 

 magnitude relation would be logarithmic, and consequently 

 the coefficient of correlation would not be unity. " He 

 understood that in such a case it was proper to use corre- 

 lation ratios, but not correlation coefficients. If this was 

 so, he would ask the exponents of modern methods to 

 erect a very large and conspicuous danger signal to keep 

 astronomical statisticians from falling into such a trap." 



Now Miss Gibson's paper was, I believe, the first to 

 place modern statistical methods before astronomers, and 

 the statistician may well make slips in a new field. But as 

 to method; what does she actually do? She calculates 

 (i) the correlation coefficient between magnitude and 

 parallax, (2) the correlation coefficient between parallax and 

 amount of light, and finding both small, she plots (3) the 

 regression line, and calculates the correlation ratio, and as 

 this takes a value of 04, she points out that the corre- 

 lation coefficient is not the suitable measure in this case. 

 In other words, she puts up the very danger signal which 

 Mr. Hinks requires ! I fail entirely to see how Mr. 

 Hinks's remarks as to the logarithmic relation apply to 

 Miss Gibson's work. She has treated the matter correctly 

 from the statistical standpoint, and her paper shows that 

 she was fully aware of the possibilities attached to a 

 logarithmic relationship, which she more than once cites. 



Secondly, as to Matter. — Here Mr. Hinks is on -safer 

 ground, but one in which I fancy astronomers have been 

 guilty of a considerable amount of circular reasoning. 



Thev start from the hypothesis that magnitude is very 

 closelv related to parallax, and when the statistician shows 

 that the best determined parallaxes show no continuous 

 relationship between parallax and magnitude, they turn 



