164 Equilibrium-Figures formed by Floating Magnets. 



more satisfactory than the wet and somewhat fussy experiment 

 with the corks and needles. 



The photographs illustrating this note were taken directly 

 from the floating balls by means of a mirror, and indicate very 

 well the degree of symmetry that can be obtained. 



I have adopted Mayer's notation in lettering them, the 

 letters a, b, c, d indicating decreasing degrees of stability. 

 The form shown in 4 d is so very unstable that it invariably 

 goes over into 4 a before it can be photographed ; accordingly, 

 I have reproduced it in ink. Its stability is about that of a 

 needle balanced on its point. 



The nature of the field has a good deal to do with the sta- 

 bility of certain forms. Often to form b' c requires the exercise 

 of the greatest care, while sometimes it will form itself without 

 any manipulation. 



A stable hexagon without a central particle, which was 

 the form that Lord Kelvin took the most interest in, in con- 

 nexion with the vortex mouse-mill, I have been unable to 

 produce, and so far as I know it has never been produced by 

 any one. Mayer figured three arrangements for eight particles, 

 but I have only succeeded in forming two, and I doubt if the 

 third can exist when the particles are as free to move as are 

 the balls on the mercury surface. A little viscosity, such as 

 we get when the mercury is not clean, makes all sorts of forms 

 stable. 



We can convert 10 a into 10 b by pushing in one of the 

 outside balls ; and as we go on increasing the number of balls, 

 we increase in general the number of possible arrangements. 



It is interesting, when we have a figure of thirty or forty 

 particles, to introduce a larger one ; for it immediately ploughs 

 its way to the centre, driving its smaller neighbours to the 

 left and right, and takes up a position directly over the pole, 

 the others then scuttling back into their places with all possible 

 haste. 



Possibly some of the phenomena of refraction can be repro- 

 duced by starting waves on a mercury surface on which a 

 50-ball figure floats. If this could be accomplished, it would 

 be better than the velvet strip and pair of wheels ; but it does 

 not seem very promising. 



Physical Laboratory of the University of Wisconsin. 

 Madison, March 3rd, 1988. 



