126 



NATURE 



\Jwie 7, 1888 



convey, through reading-lessons, some of the more 

 attractive elementary facts of science ; and, if we may 

 judge from the degree of success attained in " Sea-side 

 and Way-side," the volumes are likely to be cordially 

 welcomed in many primary schools in England as well as 

 in the United States. The author has taken, as the 

 subjects of her lessons, crabs, wasps, bees, spiders, and 

 shell-fish ; and she has contrived to put into the simplest 

 and most direct language a great deal of really useful and 

 entertaining information. Almost all children find some- 

 thing to interest them in what they are told about the 

 habits of animals, and it is not improbable that these 

 bright and pleasant lessons will implant in a good many 

 young minds the seeds of an enduring love of natural 

 history. 



Reminiscences of Foreign Travel. By Robert Crawford. 

 (London : Longmans, Green, and Co., 1888). 



Mr. Crawford is already favourably known as the 

 author of "Across the Pampas and the Andes." The 

 present volume will maintain his reputation as a traveller 

 who knows how to observe what is most significant in the 

 countries he visits, and who possesses the faculty of re- 

 producing his impressions in a lively and attractive 

 narrative. His reminiscences relate to Canada, Austria, 

 Germany, Sardinia, Egypt, Algeria, and various other 

 lands ; and in every chapter he records something that 

 most readers will find fresh and interesting. The most 

 instructive sections of the book are, upon the whole, those 

 relating to Canada and Algeria. 



LETTERS TO THE EDITOR. 



[The Editor does not hold himself responsible for opinions 

 expressed by his correspondents. Neither can he under- 

 take to return, or to correspond with the writers of, 

 rejected manuscripts intended for this or any other part 

 of Nature. No notice is taken of anonymous communi- 

 cations. .] 



Dr. Giglioli and Lepidosiren. 



Dr. Giglioli asserts, in his interesting letter published in 

 the last issue of Nature (p. 102), that the Lepidosiren whose 

 capture he records is "the fifth specimen known." Reference 

 to his earlier remarks (Nature, vol. xxxv. p. 343), concerning 

 that which he regards as " the fourth known" specimen, shows 

 that while he has acknowledged the examples of Natterer and 

 Castlenau, he has apparently overlooked that of Bibron and 

 IL Milne-Edwards, recorded in 1840. Readers of Nature 

 interested in this wonderful creature, now apparently verging on 

 extinction, will find a resume of all that is topographically 

 important concerning the last-named and the three previously 

 recorded specimens in the Zoolog. Jahrb. for 1887 (pp. 575 to 

 583). For this welcome communication, to which a full biblio- 

 graphy is appended, we are indebted to Dr. G. Baur, of Yale 

 College Museum, U.S.A. It forms one of the series of historical 

 miscellanea with which he has enriched our recent literature ; 

 and, if the conclusions at which he (in common with Briihl) 

 arrives are sound, Dr. Giglioli's "fifth" specimen will be in 

 reality a sixth. 



Zoologists in general will unite in congratulating Drs. Rodriguez 

 and Giglioli upon their recent acquisition ; and while hoping for 

 a repetition of the same, they will eagerly await the results of 

 the promised "future study." G. B. Howes. 



South Kensington, June 2. 



"A Text-book of Biology." 



Will you allow me to point out that the reviewer, in your issue 

 of May 17 (p. 52), apparently misunderstands the object of my 

 " Text-book of Biology " ? The work is not meant to supplant 

 lectures, but to aid them, by reducing for the student the wearisome 

 labour of note-taking, and by enabling the teacher to enlarge 

 where necessary, and to treat the subject from other points of 

 view, running meanwhile less risk of addressing an audience of 

 mere scribblirg-machines. 



The review alsD implies that a previously published work 



covers the same ground as the present book. This, however, is 

 not the case, as my book deals with the Botany as well as with the 

 Zoology of the course. 



I cannot but think that the reviewer is led by his enthusiasm 

 into the common mistake of demanding that the ordinary "pass" 

 man shall follow the same course as the specialist. I suppose 

 that the University of London prescribes at the Intermediate Pass 

 stage a portion, not too small, of Biology, which shall form part 

 of a general course of science adapted to the average student, and 

 to the time at his disposal ; perhaps your reviewer will kindly 

 explain, less vaguely, what other system he would propose to 

 substitute ? J. R. Ainsworth Davis. 



Aberystwyth, May 24. 



Resistance of Square Bars to Torsion. 



The attention of writers on Applied Mechanics should be 

 called to the error continuously repeated in about thirty editions 

 of the late Prof. Rankine's different works which have appeared 

 during the last thirty years. The error is still reproduced in 

 quite recent works of other writers : Prof. Ewing's article, 

 "Steam-Engine," in the Encyclopaedia Britannica ; Prof. 

 Unwin's "Elements of Machine Design"; Prof. Alexander's 

 " Elementary Applied Mechanics " ; &c. 



It is stated that the moment of resistance of a square bar to 

 torsion appears from Saint -Venant's investigations to be — 



0-281 fh\ 



where/" = maximum intensity of stress, and h = side of the 

 square. This formula is also quoted at discussions of Institu- 

 tions of Engineers and accepted without dissent. It is easily 

 seen to be wrong, because the moment of torsion of a round bar 

 of equal area is only 



0*282 fh\ 



The error is reproduced in the text of Prof. Cotterill's " Applied 

 Mechanics," but is corrected in an appendix, where the author 

 says Rankine gives the formula without further explanation. 

 The explanation is that on the old theory the torsional moment 

 of inertia was — 



h* 



which had to be multiplied by the maximum intensity of stress 

 and divided by the corresponding radial distance — namely, from 

 the centre to the middle of the side, giving the moment of 

 resistance 



= f!l 

 3 



on the old theory. (Rankine was aware that the maximum 

 stress does not occur at the angles, as in Coulomb's method. ) 



Now, in Saint- Venant's " Memoire," the torsional rigidity of a 

 square bar is proved to be the fraction 



0-843 



of the fallacious result of the old theory. Rankine accordingly 

 wrote 



0843 x l- = o-28i/7; 3 



as the true moment of torsion. 



But the toi sional rigidity determines the amount of twist, and 

 not the maximum stress. A few pages farther on, Saint-Venant 

 gives the correct formula, equivalent to 



0208 //A 



It seems strange that the tiLnted author of the expressive dis- 

 tinctions strain and stress should himself have taken the formula 

 for the strain instead of that for the stress. The reason is, that 

 up to that dale (Todhunter's " History of Elasticity ") the strain 

 and stress were supposed to be proportional to each other. 



Abstracts of Saint- Venant's researches are given in Sir 

 William Thomson's article " Elasticity," in the Encyclopaedia 

 Britannica, Thomson and Tait's "Natural Philosophy," and 

 Minchin's '* Statics." Strange that in all of these the method 

 is given which determines the strain to be 0843 of the old 

 fallacy, while nothing is said about what is of more importance 

 in Applied Mechanics, the maximum stress, nor the moment of 

 resistance to torsion, as given above. 



Perhaps this hint may be attended to in future editions. 



T. I. Dewar. 



Engineering Academy, 721 Commercial Road, E. 



