2 so 



NATURE 



[July i6, 1896 



B. Todd, Treasurer Roy. Soc, Mr. R. Trinicn, Prof. 

 Unwin, Prof. Van't Hoff, Gen. Walker, Prof. Weiss, 

 Mr. C. Welch, Dr. Wynne. 



Sir Joseph Lister, in giving the toast of ".Science in 

 all Lands," remarked tliat it would be impertinent in such 

 company to dwell on the advantages which science con- 

 ferred upon humanity or upon the pleasures which she 

 gave to those who had the privilege of cultivating her 

 various branches. They were agreed that if the mighty 

 project upon which the conference had met was brought 

 to a successful issue it would very greatly promote the 

 advance of science. 



The toast was responded toby the Italian Ambassador 

 (General Ferrero), who said that England had always 

 taken a leading, sometimes the first, place in science 

 from the days of Newton to those of Lord Kelvin, and 

 the Royal .Society had worthily represented the nation 

 in its work for the advancement of science. 



Prof. Mach also responded, remarking that men of 

 science recognised no distinction of race or nationality, 

 and they were all glad to co-operate with Englishmen in 

 a work in which all men of science were interested, 

 especially as the work was done under the auspices of the 

 Royal Society. 



Dr. Billings proposed " Success to the Conference and 

 the Catalogue " in a humorous speech. He suspected 

 that classification began in the Ark. Science was now 

 getting so large and various that the projected summary 

 would be of e.xtreme value ; but he did not quite know to 

 what it would lead. If their object in carrying out this 

 catalogue were achieved, they might anticipate a 

 time when men and things and thoughts also would be 

 catalogued. They might look forward down the vista of 

 years to the time when a stranger in Hyde Park would 

 see a passer-by with such a number as 26053, ^"d would 

 then at once appreciate his status in every respect, and 

 when the novelist would proudly show that his heroine 

 had twenty-six points in her character, while a rival 

 writer had only achieved nineteen. 



Prof. Darboux, Prof. Mobius, and Prof. Forel briefly 

 acknowledged the toast. 



The Treasurer of the Royal Society (Sir John Evans) 

 proposed " The Guests," and expressed the hope that the 

 deliberations of the conference would be ultimately 

 successful. 



Sir Donald Smith, High Commissioner for Canada, 

 responded. 



The Belgian Minister proposed "The Royal Society," 

 which he said, was the mother and model of all similar 

 societies in Europe, and was based on the principle that 

 science knew nothing of nationality. The president was 

 a great master of antiseptic surgery ; if he could only 

 introduce the principles by which he was so distinguished 

 into the realm of politics and international relations he 

 would be one of the greatest benefactors of the human 

 race. 



The President, in response, said the society was proud 

 to take the lead in so important a work as that of the 

 Conference. It had given him personally much satisfac- 

 tion to learn that the Conference on the first day had been 

 exceedingly successful, and there was no doubt that if 

 this movement was carried out, as they hoped it would 

 be, it would prove of great help to science in all its 

 branches. 



ON THE MOTION OF A HETEROGENEOUS 

 LIQUID, COMMENCING FROM REST WITH 

 A GIVEN MOTION OF ITS BOUNDARY?- 

 T U.SE the word " liquid " for brevity to denote an in- 

 ^ compressible fluid, viscid or inviscid, but inviscid 

 unless the contrary is expressly stated. A finite portion 

 of liquid, viscid or inviscid, being given at rest, within a 



1 Read at the Royal Society of Edinburgli, by Lord Kelvin, on April 6. 



NO. 1394, VOL. 54] 



bounding vessel of any shape, whether simply or multiply 

 continuous ; let any motion be smiifeiih produced in 

 some part of the boundary, or throughout the boundary, 

 subject only to the enforced condition of unchanging 

 volume. Every particle of the liquid will instantaneously 

 commence moving with the determinate velocity and in 

 the determinate direction, such that the kinetic energy 

 of the whole is less than that of any other motion which 

 the liquid could have with the given motion of its 

 boundary.' This proposition is true also for an in- 

 compressible elastic solid, manifestly : Cand for the ideal 

 "ether" of Proc. R.S.E., March 7, 1890 ; and Art. xcix. 

 vol. iii. of my Collected Mathematical and Physical 

 Papers). The truth of the proposition for the case of a 

 viscous liquid is very important in practical hydraulics. 

 As an example of its application to inviscid and viscous 

 fluid and to elastic solid consider an elastic jelly standing 

 in an open rigid mould, and equal bulks of water and of 

 an inviscid liquid in two vessels equal and similar to it. 

 Give equal sudden motions to the three containing 

 vessels : the instantaneous motions of the three contained 

 substances will be the same. Take, as a particular case, 

 a figure of revolution with its axis vertical for the con- 

 taining vessel and let the given motion be rotation 

 round this axis suddenly commenced and afterwards main- 

 tained with uniform angular velocity. The initial kinetic 

 energy will be zero for each of the three substances. The 

 inviscid liquid will remain for ever at rest ; the water will 

 acquire motion according to the Fourier law of diffusion 

 of which we know something for this case by observation 

 of the result of giving an approximately uniform angular 

 motion round the vertical axis to a cup of tea initially at 

 rest. The jelly will acquire laminar wave motion pro- 

 ceeding inwards from the boundary. But in the present 

 communication we confine our attention to the case of 

 inviscid liquid. 



The now well-known solution - of the minimum problem 

 thus presented, when the bounding surface is simply con- 

 tinuous, is, simply ; that the initial motion of the liquid 

 is irrotational. That the initial motion must be irro- 

 tational'^ is indeed obvious, when we consider that the 

 impulsive pressure by which any portion of the liquid is 

 set in motion is everywhere perpendicular to the interface 

 between it and the contiguous matter around it, and there- 

 fore the initial moment of momentum round any diameter 

 of every spherical portion, large or small, is zero. But 

 that irrotationality of the motion of every spherical por- 

 tion of the liquid suffices to determine the motion within 

 a simply continuous boundary having any stated motion, 

 is not obvious without mathematical investigation. 



Whether the boundary is simply continuous, or multi- 

 ply continuous, irrotationality suffices to determine the 

 motion produced, as we now suppose it to be produced, 

 from rest by a given motion of the boundary. 



Now in a homogeneous liquid acted on by no bodily 

 force, or only by such force (gravity, for example) as could 

 not move it when its boundary is fixed, the motion started 

 from rest by any movement of the boundary remains 

 always irrotational, as we know from elementar)' hydro- 

 kinetics. Hence, if at any time the boundary is suddenly 

 or gradually brought to rest, the motion of every particle 

 of the liquid is brought to rest at the same instant. But 

 it is not so with a heterogeneous liquid. Of the following 

 conclusions Nos. (i), (2), (3) need no proof. To prove 



1 Cambridi;c and Dublin Mathcmalkal Journal. February t84C>. This 

 is only a particular case of a general kinetic theorem for any material system 

 whatever, communicated to the Royal Society, Kdinburgh, April 6, 1863, 

 without proof (Proceedings, 1862-63, p. 114), and proved in Thomson and 

 Tail's " Natural Philosophy," sec. 317, with several examples. Mutual 

 forces between the containing vessel and the liquid or ela.stic solid, such as 

 are called into play by viscosity, elasticity, hesivity (or resistance to sliding 

 between solid and solid), cannot modify the conclusion, and do not enter 

 into the equations used in the demonstration. 



a Thomson and Tait's " Natur.il Philosophy," sec. 3t2. 



■' That is to say, motion such that the mnment of momentum of every 

 spherical portion, large or small, is zero round every diameter. 



