June io, 1920] 



NATURE 



455 



The "Flight" of Flying-fish. 



I HAVE on frequent occ;isii)ns (in the Medit< rnmi'un, 

 the Red Sea, and the Indian Oc«'an) careful! v observed 

 with a field-jjlass ( x <S) the supposed " Hight '* of 

 rlving-fish, and have always concluded that the '"leap 

 and glide" th<'<)r\ is the (ornci one, with one or two 

 modifications. Dr. j. McN.nnara, in Nature for 

 June 3, p. 421, citt's Iinc tarts in support of the theor\- 

 of true flight, hut 1 nia> jioint out that all tlirsc ti\'r 

 facts can be otlierw isc int<rpreted. l-'h ing-tisli un- 

 doubtedly leap out of the water and gain their initial 

 imfH'tus by tail action, and when out of the water 

 the pectoral fins serve as planes. While gliding the 

 "ish can not only renew its iinnetus to a limited 

 >:tent by an occasional tlici-: of its tail aj^ainst th<' 

 rest of a wave, but, atji your correspondent says, can 

 ilso change the direction of its glide. T have, liow- 

 • \er, never observed a fish "come back in a direc- 

 tion opposite to the direction in which it set out," 

 and I am tolerablv certain that it could not do this 

 without re-immersion in the water, unless jx^rhaps a 

 strong wind were hlowini^ in tliis opposite direction, 

 l-^lyina-fish can c-ertainiy ris<' and fall duting tiie glide, 

 liut this, as well as change of direction, can be easily 

 <xp1ained by assuming inclinations of th<- plan* s of 

 the fins — a \^r\ different process from actual -win!.'"- 

 tlapping sufficient to cause flight. The tin> can, like 

 those of most fishes, move on their basis, hut T fail 

 to understand how, in the absence- of tin required 

 musculature, it can possibly be supposed that the fins 

 show " raoid movement, as in the case of hovering 

 flies and humming-birds." If seagulls can glide for 

 hundreds of yards, rise and fall, and change direction 

 without win£r-flapnin£/. why not flving-fish? In glid- 

 ing the outlines of the oectoral fins naturally appear 

 to be indistinct, because, (•omi)ared with the rest of 

 the bodv, the fins are thin and irregular in outline on 

 their posterior edj^e. 



Granting that the bodv can gain fresh impetus by 

 an occasional flick of the tail against a wave-crest 

 /"and this can be easilv seen to occur, and is certainly 

 less difficult to imderstand than the initial tail action 

 which enables the fish not onlv to emer'*e from the 

 water, but also to acquire an impetus which carries it 

 the greater part of its flidp"), and that the planes of the 

 wings can be inclined, all the movements of flying- 

 fish which I have observed are fullv intellitfible. 



W. N. F. Wooi:)i,ANn. 



■•Kismet," Lock Mead, Mai<lenhead, June 4. 



.\s another observer of Nature at -1 a 1 

 to differ entirelv from Dr. McNamara's (oni 

 the "flight" of the flying-fish. 



(i) Turning at an acute angle can be bri 

 l)V an extra puff of wind, and indicates n 

 the part of the fish. 



(2) It is impossible for a fl\ing-fish to fl, 

 toral fins as a bird does its wings. 



(3) The rise and 'fall over waves an < 

 forcing up or lowering of the air imniediati 

 surface of the water. 



(4) The impetus is quite sutVicient to s<inl 

 up to a height of 50 ft. or <\-<n mor<', and 

 the soar to 300 xards. Thev iiaiurall\ tloj 

 deck until dead. 



(5^ It is quite possible (though I ha\<' n. \ 

 for the tips of the fins to !>■ \it)rated b\ 

 during flight. 



The matt<'r has he.n ,l.:.h with ition 

 "Nature Not<-s for Ocean \ Ova-.rs, '• hv (", 

 Carpt'nter and mvself, and also in the Nan\ 

 z'me for Mav. 189a. and in the Shipping 

 April, iqoi. " The late Capt. Croniie, at n- 



NO. 2641, VOL. 105] 



iiusi beg 

 elusions on 



ught about 

 1 power on 



ip its pec- 



uf to the 

 \ over the 



llxin--tish 

 to <'\ii'nd 

 ahtiut on 



<-r seen it) 

 th«- wind 



fuUv in 

 ipt. .\lfred 

 ral Mafa- 

 World for 

 v request. 



niade •• 

 ttorpedo- 

 emphati 

 As in 

 sup<T-ki 

 \ii' of g 



earclul ohscixations from 

 1(1 sLihniarints, and was most 

 " -.//.v." 



sting problems, the help of a 



■d w ith a telephoto lens would 



David Wii.son-Rakker. 



Fellow-Workers. 



In Nau kk for juin 3, p. 416, Prof. DWrcy Thonip- 

 son r<f<rs to me and to my "fellow-workers" who 

 helped me to bring our "hopes to fruition" in con- 

 nection with the old malaria-mosquito business. .My 

 own memories remind me of seven vears' almost con- 

 tinuous soliiarv labour, during which time mv 

 numerous ■ f<ilow -workers " had man\ opportunities, 

 as good as mine or better, for doing tht- sam<' work, 

 but, oddlv enough, did not us*^ them ; and it w as not 

 until I had. solved the problem that they arrived on 

 the scene in a body, fullv armed with paper, pens, and 

 cameras, and resolved "to join the victory group" at 

 any cost. Prof. Thompson puts one of these gentlemen 

 in the i)laee of honour next to Pasteui- who. h\ the 

 wax-, had little to do with the develonni.nt of animal 

 parasitolof'v. 'i"he true b.istorv of th<> subjeet is given 

 in mv "Prevention of Mal-"-ia" (Murrav), and still 

 moretPMichantlv in Robert Koeh's letter to me, dated 

 Februarv- 10, t((or, and i)uhlisb.<'d in Scioicc Progress 

 for April. 10 17. 



But this is a detail: and I should like t(^ thank 

 Prof. Thompson for his kindiv references to my 

 medical verses, and for his interesting conspectus of 

 the medical poets. Oddlv enough, the dav after it 

 appeared in N.vtuke T lectured at the Roval Institu- 

 tion on "Science and Poetrv." and upheld the thesis 

 that a higher \;«w of both will show how frequentlv 

 and how close !\ th< \ are connected. But honestv 

 compels me to add that mv own interest in medical 

 matters is auite secondary, and a matter of duty 

 rather than of predilection. Ronald Ross. 



36 Harle\ House, London. N.W. i, June 4- 



The Approximate Evaluation of Definite Integrals 

 between Finite Limits. 



(i) Tin-: four-ordinale rule given in my letter pub- 

 lisht d in Nature of May 20, p. 354, viz. 



/"V(.ry.r= 1 !Ff ;„) + F(/„) + F(^'|j) + F(A);, 



is obtained by dividing the range into two and to 

 each half apphing the'simnU- two-ordinate rule, 



the parabolic 

 being 



r euhie ap 



M-'-l' + FfiV, 

 oxiniation for two ordinates 



/>:.,.v^1[f(3-^3),p(3Y3)J 



= l[F(o-2ii3) + F(o7887)]. . . (a) 

 (2) Closer approximations may be obtained by 

 dividing the range into a greater number of parts and 

 applying this rule to each, thus : 



f'F(.r:v/.r= I^V(xyx+ [Vci-y.r-H / V(.r)./.r 



=*[f>-(;>'-i>(T)'-/:K^rH 



+ I-' 



'l"he followiiii; t,ihl( show.s for se\<ral functions the 

 value of the iniigral and the approximate evaluations 

 from two, four, six, and eight ordinates : 



