December 14. 1899] 



NATURE 



149 



OUR BOOK SHELF. 



Statistical Methods ; 7tnth special reference to Biological 



Variation. By C. B. Davenport, Ph.D. Pp. vii + 



149. (New York : John Wiley and Sons. London : 



Chapman and Hall, Ltd., 1899.) 



This little volume is a kind of " Molesworth " for the 



statistical biologist. Some two-thirds of the book are 



taken up with numerical tables (ordinates of normal curve, 



probability integral, gamma functions, squares and cubes, 



logarithms, &c.), a brief introduction, giving an outline 



of methods and formuUe, occupying only the first fifty 



pages. 



The idea is a good one, and the tables, collection of 

 formuhu, &c., are arranged in a handy form. The intro- 

 duction should, however, be subjected to revision before 

 the ne.\t issue. The sentence on p. 19, " Here x is 

 the actual deviation from the mean expressed in the 

 unit of the maximum," appears to be an abbrevia- 

 tion of ".r /or is the deviation from the mean expressed 

 in the unit of the standard deviation, and yly^ the 

 ordinate in the unit of the maximum," or some such 

 sentence. The _)'o on p. 22 should be defined as the 

 ordinate at the origin, not the mode ; it is not the modal 

 ordinate, e.i^., in Type IV. The methods of measuring 

 correlation do not necessarily depend on the assumption 

 that the frequency-distribution is normal (p. 30). The 

 author does not appear to have fully grasped the physical 

 meanings of correlations and regressions, as he speaks of 

 them as interchangeable (p. 36), for the correlation co- 

 efficient always measures the approach towards a single 

 linear law true for every case, and ranges only between 

 ± I, while the regression coefficient measures the average 

 alteration in one variable corresponding to unit alteration 

 in the other, and may take any value. The word 

 " binomial," on p. 38, appears to be a misprint for bi- 

 modal. On p. 33 we notice a lengthy method, quoted 

 from Duncker, given for reducing the product-sum ; this 

 should be replaced by the ordinary straightforward pro- 

 cess of reduction to the mean. The definition of the 

 probable error, on p. 14, needs revision ; it is not a 

 measure of " closeness of approximation to the truth," 

 but of degree of unreliability. 



In a subsequent issue the author might reconsider the 

 question of retaining some sections. New and untried 

 suggestions of measurements and indices are, in our 

 opinion, somewhat out of place in a reference pocket- 

 book. These remarks apply to some sections of chapter 

 i. and chapter iii. (" Index of Isolation "), &c., and from the 

 same point of view the brief chapter v. is hardly 

 necessary. 



The selection of tables seems very good ; the only 

 addition we would suggest is a brief table giving probable 

 errors of the correlation coefficient. 



Evolution of General Ideas. By Prof Th. Ribot 

 Translated bv Frances A. Welby. Pp. xi -h 231* 

 (London : Kegan Paul and Co., Ltd., 1899.) 

 Prok. Ribot is a leading exponent of the newer 

 experientialism which, having mastered the lesson of 

 evolutionist theories, declares for continuity through 

 transformism. All that he writes is lucid and suggestive, 

 and the course of lectures here translated is a character- 

 istic contribution to psychology. 



A dissociative act of attention brings some one element 

 in a presentation into high relief, while reducing the rest 

 by impoverishment to a residual form. This is abstrac- 

 tion, and, where we have a fusion of abstracted resem- 

 blants, we get generalisation. These processes have 

 three stages : first, that to be found in brutes, infants, 

 and deaf-mutes. With these we have the generic 

 image, best known through the composite photograph. 

 We have what is sometimes called inference from 

 particulars to particulars, and we have analogy. But 

 there is no use of the sign, no method involving sub- 



NO. 1572, VOL. 61] 



stitution. Second, a phase of mean abstraction, where 

 the image is associated with the word, increasing stress 

 being laid as we proceedXipon the latter, though it never 

 becomes a pure symbol. Third, a stage of advanced 

 abstraction, where the accompanying perceptual imagery 

 is already symbolic, while at last there is no conscious- 

 ness of any. 



The second stage is introduced by a chapter on speech, 

 which is of some interest. The third is discussed in 

 relation to Prof. Ribot's personal inquiries into types of 

 ideation. When asked for replies within a few seconds 

 as to what they experienced when such terms as " cause " 

 and "animal" were suggested, more than a hundred 

 persons gave answers, of which the visualisation of the 

 printed word, the sound of the spoken word, and alleged 

 vacuity were the farthest from unsymbolic picturing. 

 He seems not to have come across the"Je ne pense 

 qu'en parlant" type. His connection oi \!ti& flatus 7>ocis of 

 extreme nominalism with verbal imagery reminds us of 

 his clever association elsewhere of Berkeley's idealism 

 with visualisation. In his insistance that symbolic or 

 substitutional thought implies the actual existence of 

 that for which it is substituted, he shows the dependence 

 for him of psychological appearance upon a wider 

 psychophysiological reality, and effects the transition to 

 a future treatment of the unconscious. In a further 

 chapter Prof Ribot traces the development of such con- 

 cepts in the algebra of thought as space, time, cause. 

 Here, as in his account of the universal as such, he is 

 handicapped by the exclusion of epistemological and 

 metaphysical considerations. A short paragraph would 

 have shown the irrelevance of Kant's apriorism for a 

 psychology such as the present. The notes on meta- 

 geometry are too short if they are to find a place at all. 

 Some of his terms trespass on other people's rights, e.g. 

 "the logic of images," "schema." The translation is 

 well done, though probably "experiential" would be 

 better than " experimental " in more than one place. 



H. W. B. 



Handbook of Optics for Students of Ophthalmology. By 

 Prof William Norwood Suter, B.A., M.D. Pp. viii -f 

 209. (London : Macmillan and Co., Ltd.) 

 Optics: A Manual for Students. By A. S. Percival, 

 M.A., M.B. Pp. X 4- 399. (London : Macmillan and 

 Co., Ltd.) 

 Prof. Suter gives a simple and yet clear account ot 

 the science of optics, as applied to the most important 

 problems connected with ophthalmology. The study of 

 the eye as an optical system has many points of interest, 

 both for the physicist and for the medical student. In 

 many works on optics only scant consideration is given 

 to this part of the subject, so that the book before us 

 maybe said to fill a recognised gap in scientific literature. 

 Its value would have been greatly enhanced, however, 

 if measurements in connection with the various optical 

 constants of the eye had been considered in greater 

 detail. Mr. Shelford Bidwell's researches on the formation 

 of multiple images in certain circumstances, due to the 

 cellular structure of the eye, might have been mentioned 

 with advantage ; but it is, perhaps, hardly fair to criticise 

 a book of the dimensions of the one before us for errors 

 of omission. A serviceable index has been provided. 



In a few cases, the descriptions might have been 

 improved. Thus, on p. 42, line 7, the expression " the 

 planes perpendicular to the curved surfaces" should 

 read " the planes tangential to the curved surfaces." On 

 p. 37, line 10, the term "centre of the refractmg surface" 

 might be altered, with advantage, to the "centre of 

 curvature of the refracting surface." Mathematical ex- 

 pressions such as the following (see p. 44) are likely to 

 cause unnecessary trouble : — 



AF, 



:-.=^' 



