526 PROCEEDINGS OF THE AMERICAN ACADEMY. 



the unmagnetized ones are apt to draw into contact and spoil the figure 

 unless kept several diameters apart. The balls are much more con- 

 venient than needles ; and as they give very nearly the same figures, 

 the law of force cannot be very different in the two cases. 



Professor J. J. Thomson 5 has discussed the stability conditions of a 

 ring of negatively electrified corpuscles within a sphere of positive elec- 

 tricity, and has given a method of calculating the minimum number of 

 such corpuscles required to hold an outer ring of a given number in 

 stable equilibrium. It is interesting to compare the figures actually 

 obtained with the results of the calculation. Complete agreement can 

 hardly be expected, partly because the calculated numbers are minimum 

 values and may represent in some cases forms of such slight stability 

 that they might be difficult to reproduce, but chiefly because the law 

 of force in the concrete case is quite different from the simple law of 

 electric attraction. With the floating balls only the horizontal com- 

 ponent of the central attraction is available in producing motion toward 

 the centre of the figure ; and as this is an increasing fraction of the 

 entire force as the distance from the centre increases, the pull on a 

 large outer ring is virtually increased and a larger number of balls will 

 be required to hold it in equilibrium. This is exactly what takes place, 

 as may be seen from the accompanying table, where for a considerable 

 number of balls the number inside the outer ring is almost always 

 larger than the calculated minimum. 



The configurations shown are those obtainable without much diffi- 

 culty, no special effort having been made to secure forms of very slight 

 stability. In fact, with perfectly clean balls and mercury it is not easy 

 to obtain many " isomers " unless the apparatus is very free from vibra- 

 tion, a figure which is quite stable enough to be photographed some- 

 times working itself over into quite another form after five or ten 

 minutes. The effects of surface* tension modify the results greatly, as 

 shown by A. W. Porter, 6 who was able to obtain a ring of fifteen mag- 

 nets without a central nucleus, in a dish of water filled to overflowing. 

 Lack of perfect equality in the balls will distort figures otherwise sym- 

 metrical, and if the mercury surface is even slightly dirty the inner 

 balls arrange themselves with nearly uniform spacing, without much 

 reference to the number in the outer ring. The white lines in the 

 figures have been drawn upon the negatives to mark the contours, and 

 are not a part of the experiment. The figures clearly show the periodic 

 nature of the structure, as has been noted from the first ; the larger 

 figures are obtained from the smaller by the simple addition of more 



» Phil. Mag., Ser. 6, 7, 237. 6 Nature, 64, 563. 



