528 PROCEEDINGS OF THE AMERICAN ACADEMY. 



and larger rings. With fifty-two balls the central nucleus changes 

 again from one to two, and the series continues much as before ; but 

 the figures are much crowded, and unless the balls are perfectly uniform 

 it is often difficult to decide just which ones go to form particular 

 rings. 



The preceding table presents the results as calculated by the Thomson 

 method and as photographed. It is curious that so many of the cal- 

 culated minimum numbers should be obtainable with ease ; with care 

 in manipulation of the balls I have obtained a number of others, but 

 not of sufficient stability to be photographed on the vibrating floor 

 where the experiments were carried out. 



