4o6 



NATURE 



\.Y 



1912 



Stithllilx 



I/../ 



\ 1 , 1 ( ' I n i 1 1 . 1 1 1 • n H 1 < 



5i. IHl. 



THIS booU. in (■(■inniuii uiili mlin ptilplislii .1 in.iili'- 

 in.ilir.i! |i,i|)ris nt I'mt. l>i\,iii, lunt.iiiiv imicll 

 utii;iii.il \Miil<. It !■- u'-ll u>irlli stu(l\, noi nuTcIy 

 \<\ in.illuin.ilii i.in-. lull .il^u In .ill inii i .-^icd in tin- 

 |it .id ifi' 'it .i\i.i!iiiii .111(1 in till' (li-^i^^n (if llvinj^ 

 iiKii-hii!' 111(1 inlru(hi(liiin the .-tuthor 



iiuli(Mii>- 111- n.i-'Mi-. i..i uiuliii.ikiiiL; ilii- iiuf<tii.jn- 

 lion, .uui his ilcsirr to ni.ikc the luxik piaiiicilly iisi-- 

 ful. 1 1 will !>'• univiT>,illy .i^rfcd, .nui the conclusion 

 i> ((Uitinnid hv cxpciicncc, that the ^nat.si difficultios 

 which niusi he suiindunlcil in connection with .liTi.il 

 navigation aris,- troin l.icic of exact know Irdi^r ol the 

 |)riiici|)lis of (Knamical stahilitv a-, .iiiiiliccl to the 

 nioliuiis of aeroplanes. I'p to date it is jnohahlv cor- 

 rect to say that individual skill oft. n appan mly 

 almost insfinrfive on the part of airmen, and tlieir 

 immediate readiness to .uM when sudden iiiier^>iuirs 



arise, pl.l\ the i^re.ltest |iart in the s.'ite ("oiuluci ot 

 .leri.il in.'ichines. In f.ict, h.ivin^ rcj^ard to cndK-ss 

 possible variation.^ in the conditi<ins whi(li .ire, and 

 will be, encountered in .lerial n.ivii.^,ilion, these per- 

 SOn.iI cjiialilies will ,iK\a\s remain essential to 

 success. Oir the other h,ind. there cm he no dispute 

 but that subst.uiti.al advant.ii;es m,i\ t'e i.^.iined from 

 the results of work done h\ m.itliem.iticians liki> Lord 

 Rayleifijh, Sir (leorfje Greenhill, and Prof. Hrwin. 



It is true th.it ;ill niatheinatic.il investi^ali<Mis must 

 bo h.ised on certain .'issuiiifMions ; and, hecausi- of our 

 imperfect knowledge of atmospheric phenomena, errors 

 have been, and will be, made in these assumptions, 

 and important considerations may be omitti-d in fram- 

 ing equations. In consequence of these limitatittns 

 mathematici.ins tun .1 risk of claiming more for their 

 conclusions tluiii they are really worth. Prof. Hrv.in 

 himself has not escaped entirely free from this dan^i r 

 in previous utterances on the subject of aviation ; but 

 in the book under review he puts the case for mathe- 

 matical inquiry in ;i form to which no one \\\\\ take 

 exception. Tlu> jiass.ii^e is of sufBcient interest to 

 justify quotation, and the mcrre so because it strikes 

 the keynote of the book itself : — 



" In this book attention is concentrated on the 

 mathematical aspect of the prqblem for sev( ral reasons. 

 In the first place, there is no obvious alt(rnativo 

 between developing the mathematical theory fairly 

 thoroughly and leaving it altogether alone ; any 

 attempt at a via media would probably lead to 

 erroneous conclusions. In the second place, the 

 formula- arrived at, even in the simplest cases, are 

 such that It is difficult to see how they could be estab- 

 lished without a mathematical theory. In the third 

 place, th(Me is prohahlv no lack of competent workers 

 interested in the practical and experimental side of 

 aviation, and, under these conditions, it is evident 

 that the balance between theory and practice can be 

 improved by throwincf as much weight as possible on 

 the math<inatical side of the scale. I>astly. it is hoped 

 to advocate the claims of aeroplane equilibrium and 



NO. 2204, VOL. 88] 



.f-iKIliiv .-It an «»ducational subject sui'^'bl'' for study 



'.ersitifs a!on),(side with .su' 'as of 



ith'in.itii s .iiid math' in.iii' • - .is 



I huoM; between purely nialhe- 

 id experimental research in 

 ronnecfidii with th- d< \ rjopmcnt of aviation, the latter 

 method w<pu! i ! . It IK he preferred. No .such choice 

 has to be I ice progress can only be 



achieved if 1.. ,„;,.;,.„ r.( ,„-.ii,..^,...;,-.,| 



an.ihsis with • 



Re.idc rs of i' a !)•• impressed 



with the sii^'^^ sages in which 



results ot mathi ni.i'.ii .1] soluti(jns of difficult problems 

 .ire dis( ussed. ICven if ;ill the mathematical processes 

 in the book cannot be follow. d hy practical men, their 

 attention may well he tuni.-d to its pages, and they 

 c.-iruiot f.iil to d.-rive instruction .and obtain guidance 

 ther.from in d.'l.-rminint; dir.-ctions in which further 

 experimental r.-se.irch m.i\ mo-i adv.nit.ageously be 

 imdertaken. 



Prof. JMx.an .inticip.ites "that tti>- siicc-stul .i.-ro- 

 pl.an.- of the future will possess inherent, not auto- 

 matic, st.ihility, mov.ible parts being used only for 

 the purposes of steering." He considers the use of 

 gvrostats, pendulums, or other movable parts which 

 ar. intended to provide automatic stability to be un- 

 ci, sir.ihle, because such parts are liable to get out of 

 ord.r, while "they increase the degree of treedoi 

 of the machines and add to the number of conditio: 

 which have to be. satisfied for stability." There 

 sound common sense in this observation, and its fori 

 has been emphasised by e.xperience in submarine- 

 After many attempts to devise and apply means for 

 automatic control of longitudinal stability, it has been 

 universally aj^reed that manual control by competei 

 steersmen is on the whole to be preferred. The cas 

 of the submarine is, of course, vastly simpler, and 

 the conditions of service loss compler •>" ' ^ >-. .ki.. 

 th.in are those to which .liri.il m.tchir, 

 but the principle holds good in both ii--taius. in, 

 " human element " is all-important. 



It is both unnecess.iry and undesirable to attempt 

 anv detailed description or criticism of the mathe- 

 matic.il chapters of this book. They are marked both 

 t)V an ability and a compactness which are not sur- 

 prisini^ to those who know the character of Prot. 

 Mr\. Ill's m.ithematical papers. He has had the ad- 

 vant.ii^e of help from Mr. E. H. Harper and other 

 gentlemen, to whom due .acknowledgment is made 

 and by whom the whole of the formulae have bee 

 checked. Prof. Bryan hopes that the formluae are 

 correct, but modestly adds :— " It is impossible to be 

 too careful in a matter where a mere slip of a sign 

 might change stability into instability." Readers are, 

 therefore, invited to chock the formul.-v for them- 

 selves — an invitation which may have an attraction 

 for mathematicians, but not for all who will study 

 the results recorded in these pages. 



The volume is admirably produced, and it consti- 

 tutes a valuable addition to the series of "Science 

 Monographs," to which it belongs. 



Special interest now attaches to the subjects treated ; 



