Oct. 6, 1887] 



NATURE 



551 



Large questions now present themselves as to transformations 

 which a distribution of turbulent motion would experience in an 

 infinite liquid left to itself with any distribution given to it 

 initially. If the initial distribution be homogeneous through all 

 large volumes of space, except a certain large finite space, S, 

 through which there is initially either no motion or turbulent 

 motion, homogeneous or not, but not homogeneous with the 

 motion through the surrounding space, will the fluid which at 

 any time is within S acquire more and more nearly as time 

 advances the same homogeneous distribution of motion as that 

 of the surrounding space, till ultimately the motion is homo- 

 geneous throughout? Probably, I think I may say certainly, 

 yes — at all events for a large class of cases. 



But can it be that this equalization comes to pass through 

 smaller and smaller spaces as time advances? In other words, 

 will any given distribution, homogeneous on a large enough 

 scale, become more and more fiiic-graitted as time advances ? 

 Probably^^j- for some initial distributions ; probably no for others. 

 Probably ^'«, for vortex-motion given continuously through all 

 of one large portion of the fluid while all the rest is irrotational. 

 Probably no for the initial motion given in the shape of equal 

 and similar Ilelmholtz rings, of proportions suitable for stability, 

 and each of overall diameter considerably smaller than the 

 average distance from nearest neighbour. Probably also no, 

 though the rings be of very diff"erent volumes and vorticities. 

 But .probably yes if the diameters of the rings or of many of 

 ihem, be not small in comparison with distances from neigh- 

 bours, or if the individual rings, each an endless slender filament, 

 be entangled or nearly entangled among one another. 



Again a question : If the initial distribution be homogeneous 

 and lEolotropic, will it become more and more isotropic as time 

 advances, and ultimately quite isotropic ? Probably yes for any 

 random initial distribution, whether of continuous rotationally- 

 moving fluid or of separate finite vortex-rings. Possibly no for 

 some symmetrical initial distribution of vortex-rings, conceivably 

 stable ; though it does not seem probable that there is any such 

 stability. 



If the initial distribution be homogeneous and isotropic (and 

 therefore utterly random in respect to direction) will it remain 

 so? Certainly jc'j>. 



We shall now suppose the initial motion to consist of a 

 laminar motion \_f{y), o, o] superimposed on a homogeneous 

 and isotropic distribution (Uq, z'oj '^''0) > so that we have — 

 when t = o, u = / iy) + Uo, v = v^, w = w^ ; 

 and we shall endeavour to find such a function, /(j, t), that at 

 any time, (, the velocity-components shall be — 



fiy, t) -f 11, V, w, 

 wfiere 11, v, w are quaatities of each of which every large enough 

 average is zero. 



With this assumption the equations of motion yield the fol- 

 lowing — 



feli)= -xzav^.^. 

 dt dy 



It is to be remarked that this result involves no isotropy, no 

 homogeneousness in respect to y ; and only homogeneousness of 

 rigime with respect io y and z, with no translational motion. 



The translational component of the motion is wholly repre- 

 sented by /(_>', t), and, so far as our establishment of the above 

 equation is concerned, may be of any magnitude, great or small 

 relatively to velocity-components of the turbulent motion. It is 

 a fundamental formula in the theory of the turbulent motion of 

 water between two planes ; and I had found it in endeavouring 

 to treat mathematically my brother Prof. Tames Thomson's 

 theory of the " Flow of Water in Uniform Regime in Rivers and 

 other Open Channels " (Proceedings of the Royal Society, 

 August 15, 1878). In endeavouring to advance a step towards 

 the law of distribution of the laminar motion at different depths, 

 I was surprised to discover the law of propagation as of distor- 

 tional waves in an elastic solid, which constitutes the conclusion 

 (rfmy present communication — 



— xzav (itz/ = 

 dt ^ 



dy 



Eliminating the first member from this equation, by the former, 

 we find — 



dfi * dt'' 

 Thus we have the very remarkable result that laminar dis- 

 turbance is propagated according to the well-known mode of 



waves of distortion in a homogeneous elastic solid ; and that the 

 velocity of propagation is -^ — R, or about '47 of the average 



velocity of the turbulent motion of the fluid. This might seem 

 to go far towards giving probability to the vortex-theory of the 

 luminiferous ether. 



But a difficulty remains unsolved : a possible rearrangement 

 of vortices within each wave, giving rise to dissipation of the 

 wave-energy. 



The mathematical investigation appears in full in the 

 October number of the Philosopical Magazine, with some slight 

 farther considerations regarding this virtual viscosity, and the 

 question of what, if any, distribution of vortices can either have 

 no tendency to the vitiating rearrangement, or can, with the 

 requisite fine-grainedness, be slow enough in the vitiating re- 

 arrangement to allow the propagation of waves of light to go on 

 through a hundred million million miles of space, or a million 

 times the earth's distance from the sun. 



The Committee of the Section reported that at a meeting of 

 the Committee it had been resolved, on the motion of Prof. 

 Gustav Wiedemann, of Leipzig, seconded by Sir William 

 Thomson: — "That this Committee of the Mathematical and 

 Physical Science Section of the British Association hereby 

 convey to Dr. Joule their sense of the great loss sustained by the 

 Section in consequence of his inability to take part in this meet- 

 ing of the British Association in his native city, and express their 

 sincere regret at the cause of this loss, and their hearty sympathy 

 with him in his illness. The Committee take this opportunity of 

 recording their appreciation of the splendid work of this most 

 painstaking and conscientious seeker after truth, who, with his 

 discoveries, has led the way in the greatest advance in knowledge 

 made in this age, and, by his life, has conferred on mankind a 

 precious example for their admiration and imitation." 



SCIENTIFIC SERIALS. 



American Journal of Science, August. — History of the changes in 

 the Mount Loa craters (continued), by James D. Dana. In this 

 paper the history of Kilauea is continued from January 1840 to the 

 end of 1886, during which period sufficient facts were accumulated 

 for a widened and apparently final explanation of the method of 

 filling the pit. The eruptions of 1849, 1855, 1868, and 1886 

 are fully described, and the whole subject is illustrated with 

 maps of the burning mountain at various dates during the period 

 under consideration. — On some phenomena of binocular vision 

 (continued), by Joseph Le Conte. In this paper, the twelfth of 

 the series, the author deals with certain peculiarities of the 

 phantom images formed by binocular combination of regular 

 figures. The phenomena here described, none of which have 

 hitherto been satisfactorily accounted for, are all explained by 

 the law of corresponding points, justly regarded as the most 

 fundamental law of binocular vision. — Chemical integration, by 

 T. Sterry Hunt. In this paper the author deals more fully with 

 several points connected with chemical metamorphosis, which 

 were more briefly noticed in his recently published work, en- 

 titled "A New Basis for Chemistry." — Studies in the mica 

 group, by F. W. Clarke. In this paper the author deals with 

 specimens of muscovite from Alexander County, North Caro- 

 lina ; of lepidomelane from Baltimore and Litchfield, Maine ; 

 of iron biotite from Auburn, Maine ; and of iron mica from 

 near Pike's Peak. 



SOCIETIES AND ACADEMIES. 

 London. 

 Institution of Mechanical Engineers, September 30. — 

 Mr. E. H. Carbutt, President, in the chair. — A supplementary 

 paper by Major Thomas English, R. E., on the initial conden- 

 sation in a steam cylinder, was read and discussed in connexion 

 with the paper by the same author on the distribution of heat 

 in a stationary steam-engine, read at the spring meeting on 

 May 17, an abstract of which has already appeared in Nature 

 (vol. xxxvi. p. 115). The supplementary experiments were 

 carried out in a portable engine of ordinary type, the cylinder of 

 which was jacketed on the cylindrical portion but not at the 

 ends. The steam was admitted directly from the boiler into the 

 steam chest, and the quantity required for each experiment being 

 small compared with the capacity of the boiler, no question of 

 priming or condensation before admission can arise. The con- 



