October 4, 1894J 



NATURE 



5^9 



I 



stereoisomerism ; the essential part of it is retained in the 

 assumption that the carbon atom is stereo-chemically to be 

 regarded as lelrahedral in shape. If any student carries away 

 the notion tliat this is believed to be the actual shape of the 

 atom, there is no more mischief done than in that student's 

 case who gathers the impression that the two carbon atoms 

 united by an ethylene linkage are held together by two pairs of 

 forces which do not act along the line joming the two atoms, 

 but n-eet at an argle in empty space. G. S. TuRPIN. 



Hudderstield, September 24. 



Careless Writing. 



Prof. Tilden, in his review, published in Nature, 

 September 20, takes exception to the loose phraseology 

 adopted by writers on chemical subjects. This is, alas 1 only 

 too common. 



For example, in one of the best works on inorganic 

 chemistry, written by a Professor of Chemistry whose writings 

 are characterised by their logical clearness and philosophic 

 reasoning, one may read : — 



" When a molecule of hydrogen acts upon a molecule of 

 chlorine to form two molecules of hydrochloric acid gas, 

 44,000 c. of heat are evolved. " Of course, nobody can fail to 

 understand what is meant. But as the words stand, it is 

 certainly one of the most remarkable feats of science, and 

 makes us feel that some happy mortal has succeeded in retining 

 his faculties down to the degree of fineness, popularly ascribed 

 only to a certain species of " demon." F. G. DoN.S'AN. 



Holywood, Bellast. 



OS' THE DOCTRINE OF UISCOXTIXUITY OF 

 FLUID MOTIOX, IX COXNECTJOX WITH 

 THE RESISTAXCE AGAIXST A SOLID 

 MO VI X a THROUGH A FLUIDS 



II. 



§ 5. T X every case in which vacuum is formed a; an 

 ^ edge of a solid moving in an inviscid incom- 

 pressible fluid, under pressure constant at all infinitely 

 great distances from the solid, a succession of finite 

 individual vortices is sent from the edge into the liquid, 

 tind the motion is essentially unsteady. Each individual 

 vortex has a finite endless vacuum for its core instead 

 of the rotationally moving ring of fluid of the Helm- 

 holtz vortex ring. But it should be noticed that it would 

 not be rings of vacuum, but bubbles, that would in many 

 cases be first detached from the solid ; that by the 

 tumultuous collapse of bubbles they become rings ; and 

 that the case in which the collapse of a bubble, in our 

 ideal fluid, could be completed to an annulment of volume, 

 is of necessity infinitely rare ; and that the case in 

 which, when a bubble becomes a ring by the meeting 01 

 two points of collapsing boundary, there is exactly no 

 circulation through the aperture, is infinitely rare.- 



§ 7. In the case of our circular disc, it would be 

 circular vortex rings that, if the water were inviscid, 

 would be shed ofi" from its edge when the depth is less 

 than 63 feet. If the depth is very little less than 63 feet 

 these rings would be exceedingly fine, and would follow 

 one another at exceedingly short intervals of time. 

 Thus quite close to the edge there would be something 

 somewhat like Stokes' "rift," but with a rapid suc- 



1 Continued from p. 525. 



" The whole subject ot' the motion of an incompressible inviscid fluid with 

 vacuum on the other side of the whole or any part of its boundary is of 

 surpassing interest. Consider for example an open fixed basin, with 

 water pourcil into it and left not quite at rest under the influence of gravity ; 

 swinging slightly fromjside to side. let us suppose for example ; the water 

 perficlly inviscid, and vapour-less, but m.iy be either cohesional or cohesion- 

 less : and there being perfect vacuum over all its free surface. Vcrjr soon 

 it will certainly thr >w up a drop somewhere : and before very long it will 

 t>ecome covered withspin-drift and will thus illustrate Maxwell's important 

 allegation (which I believe t) be true tliough it has been much doubted), 

 chat any conservative system must "sooner or later " pass through every 

 possible conliguration. 



NO. 1 30 1, VOL. 50] 



cession of vacuum rollers, as it were : and no slipping 

 between the portions of the fluid on its two sides. 



§ S. At greater depths than 63 feet, if the water had 

 absolutely no viscosity,' the motion would be continuous 

 and irrotational, as described in § 4, text and fool-note : 

 but any degree of viscosity, however slight, would, if the 

 edge were infinitely sharp (instead of having a radius of 

 curvature of I 2000 of an inch, as has our supposed disc), 

 give rise to a stale of motion in its neighbourhood some- 

 what like to Stokes' rift,- " a surface of discontinuity 

 extending some way into the fluid," but with the 

 difi'erence that there is no slip of fluid on fluid. A trail 

 of rotationally moving liquid, a Helmholtz' '■ vortex sheet " 

 of exceedingly small thickness, is thus left in the wake 

 of the circular edge ; which, while becoming thicker as 

 it gets farther from the edge, becomes rolled up in a 

 wildly tumultuous manner, giving the appearance of an 

 irregular crowd of detached circular ring-vortices. This 

 crowd follows the disc at an ever diminishing speed and 

 widens outward farther and farther, and inwards en- 

 croaches more on the comparatively undisturbed middle 

 of the wake, as it is left farther and farther behind the 

 disc. 



g 9. Whether as in § 7 for an ideal inviscid incom- 

 pressible fluid, or as in § S for a natural liquid such as 

 water, the " wake," that is to say, the fluid on the rear 

 side of the plane of the disc, as far as it is sensibly 

 afiected by the motion of the disc, must be as described 

 in the last sentence of § S. The rear of the wake is 

 always moving forwards, that is to say, following the 

 disc ; but at a'Continually diminishing speed. Hence, if 

 the disc has been set in motion from rest some finite 

 time, /, ago, the whole wake must be included between 

 the plane from which the disc started, and the plane in 

 which the disc is now, at the time when we are thinking 

 of it. These two planes are at the finite distance, \'t. 

 asunder. In other words the wake extends to some 

 distance less than \7, rearwards from the disc. 



§ 10. The shedding oft' of vortex rings from the edge 

 of the disc, to follow in its wake at less speed than its own, 

 essentially gives a contribution to negative pressure on the 



rear side of the disc equal to ' Ik ; where 2>c denotes 



at 



the sum of the circulations of all the coreless ring vor- 

 tices, or of all the rotationally moving liquid, which have 

 or has left the edge since the beginningofthemotion. This, 

 with the commonly assumed velocities of the fluid on the 

 t'vo sides of the rigid plane, seems insufficient to account 

 for the excess of observed pressure above that calculated 

 for a long blade by Lord Rayleigh's formula ' referred to 

 in my letter to N'.\turi;, "Towards the Efficiency of 

 Sails, !k.c." and leaves some correction to be made on 

 those assumed velocities. But the working out of this 

 interesting piece of mathematical hydrokinetics must be 

 deferred for a continuation of the present article in which 

 supposed discontinuity of fluid motion, extending far and 

 wide, as taught by many writers in many scientific papers 

 and textbooks since Stokes' infinitesimal rift started it 

 in 1847, will be considered. Kelvin. 



( To be continued.) 



MR. SCOTT ELLIOT'S RUiVEXZORI 

 EXPEDITIOX. 



ABOUT three years ago, in Nature (November 5, 

 1S91), I gave an account, rescued from an .American 

 periodical, of the botanical results, slender enough it is 

 true, but not without interest, of the Emin Relief Ex- 



1 Viscosity is resistance to change of shape in proportion to tlie speed o 



the change. 



-Stokes, *' Mathematical and Physical Papers." vol. i. p. 3to. 



^ In lines (^ and 10 of the printed letter (Naturk, Aug. 20. 1S94, p. 426), 

 for "something like five or ten." substitute 4 S. I unfortunately had not 

 Lord Rayleigh's formula by me at the lime th; letter was written. 



