July i6, 1896J 



NA TURE 



251 



No. (4) remark that as long as there is any motion of the 

 heteroj^eneous liquid within the imperfectly elastic vessel 

 the liquid must be losing energy ; and the energy cannot 

 become infinitely small with any finite spherical portion 

 of the liquid homogeneous. 



(ii The initial motion of a heterogeneous liquid is 

 irroiational only at the first instant after being quite 

 suddenly started from rest by motion of its boundary. 

 Whatever motion be subsequently given to the boundary 

 the motion of the liquid is never again irrotational. Hence 



(2J If the boundary be suddenly brought to rest at any 

 time, the liquid, unless homogeneous throughout, is not 

 thereby brought to rest ; and it would go on for e\-er 

 with undiminished energy if the liquid were perfectly 

 inviscid and the boundar\- absolutely fixed. The ulti- 

 mate condition of the liquid, if there is no posi/ii'e surface 

 tension in the interfaces between heterogeneous portions, 

 is an infinitely fine mixture of the heterogeneous parts.' 

 And, if there were no gravity or other bodily force 

 acting on the liquid, the density would ultimately be- 

 come uniform throughout. Take, for example, a corked 

 bottle half full of water or other liquid with air above 

 it given at rest. Move the bottle and bring it to rest 

 again : the liquid will remain shaking for some time. 

 An ordinary non-scientific person will scarcely thank us 

 for this result of our mathematical theory. But, when we 

 tell him that if air and the liquid were both perfectly fluid 

 (that is to say perfectly free from viscosity), the well- 

 known shaking of the liquid surface would, after a little 

 time, give rise to spherules tossed up from the main body 

 of the liquid ; and that the shaking of the liquid, left to 

 itself in the bottle supposed perfectly rigid, will end in 

 spindrift of spherules which would be infinitely fine if the 

 capillary tension of the interface between liquid and air 

 were infinitely small, he may be incredulous unless he 

 tends to have faith in all assertions made in the name of 

 science. 



(3) If the boundary is an enclosing vessel of any real 

 material (and therefore neither perfectly rigid nor per- 

 fectly elastic), and if it is laid on a table and left to itself, 

 under the influence of gravity, the liquid, supposed per- 

 fectly inviscid, will lose energy continually by generation 

 of heat in the containing vessel, and will come asympto- 

 tically to rest in the configuration of stable equilibrium 

 with surfaces of equal density horizontal and increasing 

 density downwards. 



(4) \Vith other conditions as in (3), but no gravity, the 

 ultimate configuration of rest will be infinitely fine mix- 

 ture (probably, I think of equal density throughout). 

 Consider, for example, two homogeneous liquids of 

 different densities filling the closed vessel, or a single 

 homogeneous liquid not filling it. As an illustration, 

 take a bottle half full of water, and shake it violently. 

 Observe how you get the whole bottle full of a mixture of 

 fine bubbles of air, nearly homogeneous throughout. 

 Think what the result would be if there were no gravity, 

 and if the water and air were inviscid and the bottle 

 shaken as gently as you please ; and if there were per- 

 fect vacuum in place of the air ; or, if for air were substi- 

 tuted any liquid of density different from that of water. 



THE RETURN OF BROOKS'S COMET. 



r\K July 6, 1889, Mr. W. R. Brooks, of Geneva, New 

 ^-^ \'ork, U.S.A., discovered a somewhat faint, tele- 

 scopic comet at R.A. 356^, Dec. 1/ south, in the southern 

 region of Pisces. It had a short spreading tail, and was 

 moving slowly to the E.N.E. 



J " Popular Lecti 

 and 53, 54. See ali 

 the formation of c 

 inviscid incompressible fluid 

 fluid 



Es and Addres-ses," by Lord Kelvin, vol. i. pp. 19, 



Philosophical Magazine, 1887, second haif-ye.tr : " ( 



Ices by the motion of a solid through 



" On the stability of steady and of perioi 



and minimum encrgj- in vortex motion." 



NO. 1394, VOL. 54] 



Observations in a few days enabled the orbit to be com- 

 puted, and the small inclination (6') intimated that the 

 comet was probably one of short period. Th.s proved 

 to be the case after further observation, and t'nc time of 

 revolution was determined as about seven years. Otto 

 Knopf, from three positions obtained at Mount Hamilton 

 on July 8, at Dresden July 30, and at Vienna on August 

 19, deduced the period as 7'286 years. The comet was 

 followed until January 1890, and from the whole series of 

 observations Prof S. C. Chandler found a period of yo73 

 years, and that the orbit at aphelion approaches very 

 closely to the orbit of the planet Jupiter. From March 

 to July 1886, the distance of the comet and planet appears 

 to have been less than 10,000,000 miles. The theory was 

 suggested by Prof Chandler that the comet may be 

 identical with Messier- Lexell's comet of 1770 ; but Dr. 

 C. L. Poor, on reinvestigating the matter, found little 

 evidence in support of the idea. 



The possible connection of the comet with that of 1 770 

 is by no means the only interesting feature of this object. 

 On August I, 1889, Prof E. E. Barnard observed that 

 the comet was broken up into several detached fragments. 

 It had previously been seen single, and had been sub- 

 mitted to pretty general observation without anything 

 remarkable having been detected ; but on the night of 

 August I, it appeared to have been suddenly shattered by 

 some extraordinary forces or vicissitudes of a very 

 mysterious character. One of the smaller fragments, 

 together with the largest mass, remained visible for 

 several months, moving in concentric paths, and forming 

 a \ery interesting and rare telescopic spectacle. 



The comet was a fairly conspicuous object in tele- 

 scopes, but it was not visible to the unaided eye. Its 

 apparent motion was very slow, for early in November its 

 position was only seven degrees north of the place it had 

 occupied four months before. 



Dr. Poor fixed the next perihelion passage for 

 November 4, 1896, and an ephemeris was prepared by 

 Bauschinger for the spring and summer of 1896, as it 

 was expected the comet might be picked up some 

 months before its arrival at perihelion. This expectation 

 has been fully realised, for the comet was re-discovered 

 on the night of June 20 by M. Javelle, using the 

 30-inch refractor of the observatory at Nice. Its place 

 was almost identical with that given in the ephemeris, 

 and the re-discovery of the comet may therefore be 

 regarded as another triumph for mathematical astronomy. 



This comet should prove an extremely interesting 

 object in regard to its physical appearance and changes 

 of aspect. At the present time it is in Aquarius a little 

 west of Delta in that constellation, and its position during 

 the next few weeks will be nearly stationary. The 

 ephemeris by Bauschinger is as follows : — 



Thus the comet is likely to be visible throughout the 

 present summer and ensuing autumn, for its brightness is 

 gradually increasing, and it will remain in a favourable 

 position all the time. Its southern declination of more 

 than 18' is, however, rather unfortunate, as its altitude is 

 only about 20^, so that observers will require to watch it 

 from a position commanding a good open view of the 

 southern sky. W. F. Denning. 



