Maech 17, 1911] 



SCIENCE 



427 



Exposition of that year. A brief paper on the 

 subject was presented to the American Phys- 

 ical Society in 1903, and an abstract of this 

 paper was published in the Physical Review 

 for April, 1903, but the complete paper with 

 diagrams has not been published. The title 

 of the paper was " A Simple Geometrical 

 Principle and its Possible Significance in 

 Connection with a General Physical Theory," 

 and the principle referred to was stated as 

 follows : 



In an aggregation of an indefinite nuniber of 

 equal spherical bodies an arrangement giving 

 minimum total volume and perfect symmetry 



Three different arrangements of a group of 

 spherical balls of equal size were considered: 

 arrangement A, in which twelve of the balls 

 are grouped about a central one, so the sur- 

 rounding balls are tangent to the central one 

 and to each other throughout ; arrangement B, 

 in which twelve balls are symmetrically dis- 

 posed about and touch a central one, but no- 

 where touch each other, and arrangement C, 

 in which the balls have the cubical arrange- 

 ment, or the one in which the mutually tan- 

 gent planes form cubes. The following is 

 quoted from the published abstract referred 

 to above: 



The assumption is now made that the balls 

 come together in a collection under their mutual 

 attractions according to gravity laws. Tliey will 

 not assume or remain in arrangement C because 

 while this gives symmetry throughout it is not 

 the most compact possible and the equilibrium 

 of the collection would be unstable. 



Arrangement A, while the most compact pos- 

 sible for an indefinite number of balls in contact 

 throughout, is not entirely symmetrical. 



Arrangement B gives a perfectly symmetrical 

 disposition of twelve balls with respect to a cen- 

 tral ball but it is geometrically impossible 

 throughout a collection of a greater number than 

 thirteen. 



It is suggested that under the conditions as- 

 sumed the result will be that the balls will 

 assume no fixed arrangement, but that they will 

 be in continual relative movement, striving after 

 the unattainable arrangement that will give mini- 

 mum total volume, symmetrical disposition, and 

 therefore fixed stable equilibrium throughout. 



So far as I can now recall, I had not learned 

 of the Brownian movements at that time. I 

 certainly did not have this phenomenon in 

 mind when the paper was written. I have not 

 been able to make out that Professor Perrin's 

 paper contains any very clear explanation of 

 or theory as to the underlying cause of the 

 Brownian movements, or that it purports to 

 suggest such an explanation or theory, but the 

 relations between the actual phenomenon as 

 described and the above quoted speculation 

 seemed to me rather striking. 



In my mind the Brownian movement paper 

 tends to confirm the idea that the " simple 

 geometrical principle " above described is 

 deeply significant, if it is not indeed a general 

 and fundamental principle of physical phe- 

 nomena. John Millis, 



Col., Corps of Engineers, U. 8. Army 



FURTHER EARLY NOTES ON THE TRANSMISSION BY 

 FLIES OF THE DISEASE CALLED YAWS 



I HAVE previously published in Science ' 

 two notes on the transmission of this tropical 

 disease by flies. The earlier reference bears 

 date of 1769 from Guiana. The second, while 

 of much later date (1817), indicates that in 

 Brazil at that time the infection was conveyed 

 by a certain fly recognizable by its small size. 



Shortly after the publication of this second 

 note, I received a letter from Professor J. B. 

 Woodworth, leader of the Shaler Memorial 

 Expedition to Brazil in 1908-09, in which he 

 kindly called my attention to a further ac- 

 count of this phenomenon in Walsh's " Notices 

 of Brazil." While spending the recent holi- 

 days at Washington at work in the Library 

 of Congi'ess, I looked up this reference and 

 also found another and earlier statement. 

 Believing that these accounts may not be de- 

 void of interest and value, they are herewith 

 reproduced. 



The one referred to by Professor Wood- 

 worth is found in " Notices of Brazil in 1828 

 and 1829," by E. Walsh, published in Boston 

 in 1831. On page 224 of volume I. we read: 



A disease, called in the country bobas, is fre- 

 quently attended with fearful consequences. It 



'January 7 and November 4, 1910. 



