78 



NA TURE 



[May 24, 1894 



the Protozoa, with which and the analysis of simple cell 

 structure the author's course commences, the student, 

 being told how to capture and mount his sample, 

 is asked, " How many different shapes can you dis- 

 tinguish?" "What variations in size?" "In color?" 

 and other questions of like order ; but when there follow 

 these (on p. 5 of the work), " How do these animals eat ?' 

 '• Digest their food?" " Breathe?" {sic) we confess to a 

 feeling of sympathy with the befuddled beginner. And 

 when, further, after an altogether insufficient preamble 

 and at the outset of his inquiry into the wide domain of 

 bioiogy, the tyro is asked, of the Amct-ba, " Is the process 

 [of tission] preceded by sexual union?" "How is 

 one sex distinguished from the other ? " and, ii propos of 

 the cerebral hemispheres of the frog, " Why are they 

 cal:ed hemispheres?" one's sympathy gives place to 

 pity for the student thus led astray. We entirely 

 disagree with the author's dictum that sooner or 

 later the student will have to learn to use the micro- 

 scope, and it matters little when he does so ; and 

 we further doubt the advisability of his interrogatory 

 method, when "the questions usually apply equally well 

 to sever.il related forms," particular species being said to 

 be " no: required." A training in elementary biology is 

 one in manipulation in a field beset with snares and pit- 

 falls, rendering it a primary necessity to teach the 

 beginner what to leave unconsidered. However, the 

 experiment, while not altogether new, is an interesting 

 one ; the book is carefully compiled, ?nd we await with 

 interest the verdict of lime upon the system which 

 it advocates. 



Notes on Ike Ventilation and Warming of Hcuses> 

 Churches, Schools, and other Buildini;s. Bv the late 

 Ernest H. Jacob, M.A., M.D. (Loridon : S.P.C.K., 

 1894) 



A MELANCHOLY interest is attached to this little manual 

 of health in the fact that its gifted author passed away 

 on .March I. His posthumous work shows what a pro- 

 mising life was cut short, and will serve as a memorial to 

 him. The idea that humin beings confined ia public 

 buildings should have pure air at a suit;il)le temperature 

 supplied them, has only in recent years been taken 

 seriously. It is notorious that in most churches there is 

 no attempt at proper ventilation, and they are only ex- 

 celled, as far as disregard for the laws of health go, by 

 many Nonconformist chapels with galleries, and mission- 

 roomi created by knocking two cottages into one. Dr. 

 Jacob's manual should be consulted by those who are 

 responsible for such buildings. Therein they will find 

 described the general principles by which buildings are 

 rendered healthy. The book should also be read bv the 

 householder, for he will learn from it how an ordinary 

 dwelling-house ought to be ventilated and better, will 

 find that it is an easy and not very costly business to 

 make the average English house less stuffy and more 

 healthy than it usually is. Indeed, all who desire in a 

 popuUr form information on the subject nf ventilation, 

 should procure this book, while architects and builders 

 would benefit the community by taking its lessons to 

 mind. 



LETTERS TO THE EDITOR. 



\Tm Elitor Jolt not holJ himtelf rtifioniihle for opinions tx 

 P'ttiiJ hy his corrtipon lints. Ifiilher can he unJtrtaki 

 la rtlurn. or to corriipond -,vilk Ihi rvriltrs of, rtjttti.i 

 m mnicripls inltnUd for this or any other, part of N ATURB. 

 j\'j nolift is laliin of anonymous couivsunications.] 



Rotating Shafts. 



In yoar account (Natuke, M.iy 10, p. 43) of Dr. J. Hopkin- 



•on'* "James K irre.l " lecture at ihc Insliiulion of Civil 



Engineet^, appear* Ihc followini; utalemcnl : " Another example, 



having a ceriaiii 'leijrce uf similarity with the case uf struti, it 



NO. 1282, VOL. 50] 



that of a shaft running at a high number of revolutions par 

 minute, and with a siil'stantia! dtst-ince between its bearings 

 . . . How will the shaft behave itself in regard to centrifrugal 

 force as the speed increases ? In this case, so long cis the shaft 

 remains absoltttely straight it 'vill not tend to he in any 7fay 

 affected by the centrifugal force, but suppose the shaft becomes 

 sli)>hlly bent, it is obvious to anyone that if the speed be 

 enormously high this bending will increase, and go on increasing 

 until the shaft breaks. In this case also we may use mathe- 

 matical treatment ; we find that the condition of the shaft is 

 expressed by a differential equation of the fourth order, and from 

 consideration of the solution of this equation we can say that if 

 the speed of any particular shaft be less than a certain critical 

 speed, the shaft will tend to straighten itself if it bemoment- 

 aiily bent, but that, on the other hand, if (he speed exceeds this 

 critical value, the bending will tend to increase with the 

 probable de>truclion of the shaft." (The italics are mine.) 



The italicised statement seems to imply that a certain operat- 

 ing cause may have absolutely no eflect, which cannot of 

 course be the meaning Dr. Hopkinson intended to convey. 

 Most engineers, it is to he hoped, are aware that the natural 

 tendency of the material of the shaft is to retire from the axis of 

 roation, and that this is necessarily associated with a slate of 

 strain and stress throughout the shaft, whether straight or bent, 

 for all speeds of rotation. Dr. Hopkinson must, I think, have 

 had his mind so fully occupied with the idea of rupture through 

 instability, worked out by Prof. Greenhill,' that he overlooked 

 the fact that his language suggests the non-existence of the 

 more commonplace and essential elastic phenomena. 



So far even as rupture is concerned, Ur. Ilopkinson's state- 

 ments are, I believe, incomplete. The ordinary strain and 

 stress developed by rotation in a shaft may, as I have shown 

 elsewhere,- exceed the limits of safety before a velocity is 

 attained at which, on the Greenhill theory, instability becomes 

 possible. This is the more likely to happen the shorter the 

 cylindei and the thinner its walls, if it he hollow ; but even in 

 a solid iron cylinder of length eight or nine times its diameter — 

 —a very substantial distance in a thick cylinder — the strain 

 developed would be such as to merit an engineer's careful 

 attention before a critical velocity was reached associated with 

 instability. 



I am somewhat doubtful whether Dr. Hopkinson's remarks 

 on instability il-elf are altogether satisfactory. On the niathe- 

 milical theory there appear in reality to be a series' of critical 

 value^:, if any, at which instability may occur. Supposing the 

 velociiy gradually raiseil, it seems possible, IlieorelicaHy, for 

 the shaft to safely suimount the first crisis. It then would ap- 

 pear to remain unexposed to instability until the approach of the 

 next higher critical velocity, and so on. 



As Dr. Hopkinson says, Prof. Greenhill's instability theory 

 leads to a differential equation of the fourth order. The soluiion 

 of this equation is, however, dominated by the terminal con- 

 ditions*, at the ends or bearings of the shaft, and unless these 

 l)e correctly assigned the numerical results deduced from the 

 theory are untrustworthy. This is, I think, one of those points 

 where the praclical experience of tiie engineer isa most essential 

 auxiliary to the analysis of the mathematician. 



Kew Observatory, May 11. Charles Chrke. 



In order to shut out every possibility of ambiguity, I might 

 have said, instead of " sub..taniial distance between the bear- 

 ing*," "distance between the beaiings very great in comparison 

 with the diameter of the shaft," and In the next sentence quoted 

 it would perhaps have been clearer if I had said " will not be 

 broken by centrifugal force." Hut 1 do not think that in fact I 

 could be misunderstood by anyone. 



It was hardly desirable th.at I should touch upon the terminal 

 conditions, or upon the possibility of stability between the 

 critical values, in a paragraph introduced for illustration and 

 not for detailed information. 



Hut Mr. Chrce's ietter does remind me that I neglected to 

 refer to Prof. Greenhill's name in this connection. This I 

 should have done with the greatest pleasure, but, unfortunately, 

 for the moment I forgot that it w.is he who had worked on the 

 problem. I write this no'e in order to make the acku'iwledg- 

 ment. J. IIoi'Ki.nson. 



' Instilution of Mechanical Enginetrs. I'roitedingi, iE8j. pp. i82->o» 

 -Camb Phil. Soc /'»w<'.rf/»fi. Feb. 8, 1891, pp. 383 •■/«•/. 

 ^ Ste Phil. Mnr Auguit l3.j3, pp. 165-67. 



■•See Comb. Phil. Sjc. I'rocttdingi, I.e. f. yia, ani I'hil Man- I.e. 

 pp. 164.65. 



