TBANSACTIONS OF SECTION A. 



491 



7. On an Experimental Illustration of Minimum Energy in Vortex Motion. 

 By Professor Sir William Thomson, M.A., F.B.8. 



This illustration consists of a liquid gyrostat of exactly the same construction 

 as that described and represented by the annexed drawing, repeated from ' Nature,' 

 February 1, 1877, pp. 297-298, 

 with the difference that the figure 

 of the shell is prolate instead of 

 oblate. The experiment was in 

 fact conducted with the actual 

 apparatus which was exhibited 

 to the British Association at 

 Glasgow in 1876, altered by the 

 substitution of a shell having its 

 equatorial diameter about f-, of 

 its axial diameter, for the shell 

 with axial diameter — of equato- 

 rial diameter which was used 

 when the apparatus was shown 

 as a successful gyi-ostat. The 

 oblate and prolate shells were 

 each of them made from the 

 two hemispheres of sheet copper 

 which plumbers solder together 

 to make their globular floaters. 

 By a little hammering it is easy 

 to alter the hemispheres to the 

 proper shapes to make either the 

 prolate or the oblate figure. 



Theory had pointed out that the rotation of a liquid in a rigid shell of oval figure, 

 being a configuration of maximum energy for given vorticity, would be unstable 

 if the containing vessel is left 

 to itself supported on imperfectly 

 elastic supports, although it would 

 be stable if the vessel were held 

 absolutely fixed, or borne by per- 

 fectly elastic supports, or left to 

 itself in space unacted on by ex- 

 ternal force ; and it was to illus- 

 trate this theory that the oval 

 shell was made and filled with 

 water and placed in the appara- 

 tus. The result of the first trial 

 was literally startling, although 

 it ought not to have been so, as 

 it was merely a realisation of 

 what had been anticipated by 

 theory. The fi'amework was held 

 as firmly as possible by one per- 

 son with his two hands, keeping 

 it as steady as he could. The spinning by means of a fine cord' 



- 7. tNCHES- 



round a small 



• Instead of using a long cord first wound on a bobbin, and finally wound up on 

 the circumference of the large wheel, as described in Nature, February 1, 1877, p. 

 297, 1 have since found it much more convenient to use an endless cord a little more 

 than half round the circumference of the large wheel, and less than half round the 

 circumference of the V pulley of the gyrostat ; and to keep it tight enough to exert 

 whatever tangential force on the V pulley is desired by the person holding the 

 framework in his hand, After continuing the spinning by turning the fly-wheel for 



