March 31, 1916] 



SCIENCE 



473 



and distant from each other r, have charges 

 Q^ and Q.,, the spheres having a common 

 potential F. Their attraction for each other 

 will be 



A =K- 



= K 



16 -^Rmi' 



R1R2 



V 



Here K is the value of ISTewton's constant of 

 gravitation, as it would be determined by the 

 method of Cavendish or Boys, if V were zero 

 absolute. 



If V is not zero, and the second term is 

 omitted, the last equation might be written 



?R2V 



. „ / , a; \ 16 -RmfR: 



In this equation ^[1 — (a;/)100)] is the 

 gravitation constant that would be determined 

 under such conditions. Both K and x would 

 remain unknown quantities. 



Equating these two values of A 



V = i^R,RiP^ 



If V is measured in volts 



V = iOirRiRiP^Kic 



If B^'=10, R, = l, p=. 11.35 and Z = 

 6.6576 X 10-' 



V = 3.68 V^ 



This result shows that if these two spheres 

 have a common potential which differs from 

 absolute zero by 3.68 volts, the value of K as 

 determined by the Cavendish method will be 

 in error by one per cent, of the above value 

 which is that of Boys. If V were =i= 8.23 volts, 

 an error of five per cent, would result. If V 

 were 36.8 volts the two spheres would cease to 

 attract each other. The absolute zero in V 

 would be the common potential of the two 

 bodies, when their attraction for each other 

 is a maximum. 



Storm clouds and the electrified atmosphere 

 are continually acting inductively upon the 

 earth's surface. The potential difference at 

 the ends of a flash of lightning may amount to 

 thousands of millions of volts. Aside from 

 such disturbances, we are wholly in the dark 

 concerning the average potential of the earth. 



It is evident that the smaller the masses 

 used in such determinations, the greater will 

 be the possibility of error in the result, when 

 the potential term is ignored. 



It seems very probable that we do not know 

 the real value of the gravitation constant. 



Francis E. ISTipher 



SOCIETIES AND ACADEMIES 



THE AMERICAN MATHEMATICAL SOCIETY 



The one hundred aud eighty-second regular 

 meeting of the society was held at Columbia Uni- 

 versity on Saturday, February 26, extending 

 through the usual morning and afternoon sessions. 

 The attendance included forty-three members. 



The president of the society, Professor E. W. 

 Brown, of Yale University, occupied the chair, 

 being relieved by Professors H. B. Fine, T. S. 

 Piske and H. S. White. The following persons 

 were elected to membership: Mr. L. E. Armstrong, 

 Stevens Institute of Technology; Professor Grace 

 M. Bareis, Ohio State University; Professor G. A. 

 Chaney, Iowa State College; Mr. J. E. Davis, 

 Pennsylvania iState College; G. H. Hardy, M.A., 

 Trinity College, Cambridge, England; Mr. Harry 

 Langman, Metropolitan Life Insurance Company, 

 New York City; Mr. E. D. Meacham, University 

 of Oklahoma; Dr. A. L. Nelson, University of 

 Michigan; Mr. Elmer Schuyler, Bay Eidge High 

 School, Brooklyn, N. Y. Six applications for 

 membership were received. 



The society has recently taken over the stock of 

 the Chicago Papers and Boston Colloquium Lec- 

 tures, heretofore in the hands of The Macmillan 

 Company. All publications of the society, so far 

 as in stock, are now obtainable directly from the 

 main office. The New Haven Colloquium was pub- 

 lished by the Yale University Press, and is sold by 

 them. 



The List of Members of the society for 1916 has 

 just been issued. Copies may be obtained from 

 the secretary. 



The following papers were read at this meeting: 



T. H. Gronwall : "A functional equation in the 

 kinetic theory of gases (second paper)." 



T. H. Gronwall: "On the zeros of the functions 

 P(«) and Q(e) associated with the gamma func- 

 tion. ' ' 



T. H. Gronwall : ' ' On the distortion in con- 

 formal representation. ' ' 



C. A. Fischer : ' ' Equations involving the deriva- 

 tives of a function of a surface." 



