492 REPORT— 1880. 



V pulley of ^-inch diameter on the axis of the oval shell, and passing round a 

 large fly-wheel of three feet diameter turned at the rate of ahout one round per 

 second, was continued for several minutes. This in the case of the oblate shell, 

 as was known from previous experiments, would have given amply sufficient rota- 

 tion to the contained water to cause the apparatus to act with great firmness like a 

 solid gyrostat. In the first experiment with the oval shell the shell was seen to be 

 rotating with great velocity dming the last minute of the spimiing ; but the moment 

 it was released from the cord, and when, holding the framework in my hands, I com- 

 menced carrying it towards the horizontal glass table to test its gyrostatic quality, 

 the framework which I held in my hands gave a violent uncontrollable lurch, and 

 in a few seconds the shell stopped turning. I saw that one of the pivots had 

 become bent over, by j'ielding of the copper shell in the neighbourhood of the 

 stiff pivot-carrying disk, soldered to it, showing that the liquid had exerted a very 

 strong couple against its containing shell, in a plane through the axis, the efltbrt to 

 resist which by my hands had bent the pivot. The shell was refitted with more 

 strongly attached pivots, and the experiment has been repeated several times. In 

 every case a decided uneasiness of the framework is perceived by the person holding 

 it in his hands during the spinning ; and as soon as the cord is cut and the person 

 holding it carries it towards the experimental table, the framework begins, as it 

 were, to wriggle round in his hands, and by the time the framework is placed on 

 the table the rotation is nearly all gone. Its utter failure as a gyrostat is pre- 

 cisely what was expected from the theory, and presents a truly wonderful contrast 

 to what is observed with the apparatus and operations in every respect similar, 

 except having an oblate instead of a prolate shell to contain the liquid. 



8. On a Dlsturhing Infinity in Lord RayleigJi's Solution for Waves in a 

 Plane Vortex Stratum. By Professor Sir Willum Thomson, M.A., 

 F.B.S. 



Lord Rayleigh's solution involves a formula equivalent to 



0. 

 Where v denotes the maximum value of the y-component of velocity ; 



9 



„ m „ a constant such that ^^ is the wave-length : 



m 



„ T „ the translational velocity of the vortex-stratum when undis- 

 turbed, which is in the a-direction, and is a function of y ; 



2rr 

 „ n ,, the vibrational speed, or a constant such that — is the period. 



Now a vortex stratum is stable, if on one side it is bounded by a fixed plane, 

 and if the vorticity ( or value of — — ) diminishes as we travel (ideally) from this 



plane, except in places (if any) where it is constant. 



To fulfil this condition, suppose a fixed bounding plane to contain o x and be 



d T 

 perpendicular \a oy; and let —— have its greatest value when y = o, and decrease 



continuously, or by one or more abrupt changes, from this value, to zero &iy = a 

 and for all greater values of y. 



It is easily proved that the wave-velocity, whatever be the wave-length, is in- 

 termediate between the greatest and least values of T. Hence for a certain value 

 of y between and «, the translational velocity is equal to the wave-velocity, or 



as long a time as is judged proper, the endless cord is cut with a pair of scissors and 

 the gyrostiat is released. 



