760 



SCIENCE 



[N. S. Vol. XLni. No. 1117 



atoms, and that the orbital radius of tlie electron 

 whose vibration frequency would give the con- 

 vergence number is the true radius of the central 

 positive atom. 



Heydweiller has computed the atomic diameter 

 of a large number of elements from the volume 

 occupied by their dissociated ions in a very dilute 

 water solution. Heydweiller 's atomic radii are 

 accordingly here taken as the orbital radii of the 

 electrons whose vibration frequencies would give 

 the convergence numbers of Kayser's "Principal 

 Series" in the alkali metals, and the centripetal 

 forces required to hold these convergence electrons 

 in their orbits are calculated. Then, assuming the 

 inverse square law for the attraction between an 

 electron and its central positive charge, the force 

 of attraction upon an electron at unit distance 

 from the center of its orbit is calculated for each 

 element. 



If the central positive charges of the atoms 

 were the same for different elements, then these 

 central forces should be the same. They are found 

 not to be the same. 



The positive charges of these atoms have previ- 

 ously been computed by the writer from electro- 

 lytic data. The charges here computed are not 

 proportional to those formerly computed, henee 

 the assumption that the atoms of the different ele- 

 ments have different specific inductive capacities 

 seems to be justified. These specific inductive ca- 

 pacities may be computed by dividing the charges 

 of the atoms by the respective forces which they 

 exert upon an electron at unit distance. 



The specific inductive capacities are calculated 

 in this way for the thirteen elements for which 

 convergence numbers, atomic radii and atomic 

 charges have been computed. Since it is only for 

 the alkali metals that the convergence numbers 

 used are known to belong to the principal, or 

 inner, spectral series, it is only to these elements 

 that we can be sure that the above arguments 

 apply. However, the computed specific inductive 

 capacities are proportional to the serial numbers 

 of Rydberg for ten of the thirteen elements, and 

 for the other three, viz.; zinc, cadmium and thal- 

 lium, they increase with the serial numbers just 

 half as fast as they do in the case of the other 

 elements. 



The specific inductive capacities here computed 

 are also shown to vary with the same atomic prop- 

 erties which vary with the measured specific in- 

 ductive capacities of non-metallic elements. 



It is also shown that the specific inductive ca- 

 pacities of these elements are proportional to their 



respective atomic radii. This would make the 

 centripetal force upon electrons revolving about 

 and very near to these different atoms propor- 

 tional to the inverse third power of their orbital 

 radii. This is shown to be the relation that must 

 hold in order that the kinetic energy of different 

 electrons shall vary as their frequency, as is as- 

 sumed in Planck's Law and is apparently shown 

 in the case of electrons expelled by the action of 

 ultra-violet light upon metals. 



The relative specific inductive capacities which 

 have been calculated as above are given in the fol- 

 lowing table: 



Element k Element k Element k 



Li 35.9 Mg 134 Zn 190 



Na 127 Ca 196 Cd 255 



K 238 Sr 412 Tl 350 



Eb 437 Ag 466 



Cs 567 Cu 346 



Attention is caUed to the fact that if the orbital 

 radius of the outermost electron of a series be 

 taken as the atomic radius instead of the orbital 

 radius of the innermost electron, it will not change 

 the order of values of the specific inductive capa- 

 cities calculated as above. 



Following the discussion of this paper, the ques- 

 tion of a Pacific coast organization was taken up. 

 The chairman of the meeting reported that favor- 

 able replies had been received from the science in- 

 structors at the universities in Washington, Ore- 

 gon and Utah. It was decided to form an in- 

 formal organization to be known as the Pacific 

 Physical Society, looking toward the formation of 

 a section or branch of the American Physical So- 

 ciety in the near future. 



Ealph S. Mince, 

 Permanent Secretary 



SOCIETIES AND ACADEMIES 



THE AMERICAN MATHEMATICAL SOCIETY 

 The one hundred and eighty-fourth regular 

 meeting of the society was held at Columbia Uni- 

 versity on Saturday, April 29, 1916. The attend- 

 ance at the two sessions included fifty-one mem- 

 bers. President Brovm occupied the chair, being 

 relieved by Vice-president E. E. Hedxick. The 

 council announced the election of the following 

 persons to membership in the society: Dr. E. T. 

 Bell, University of Washington; Professor T. E. 

 Eagles, Howard College; Mr. Glenn James, Pur- 

 due University; Dr. J. O. Hassler, Chicago, lU.; 

 Professor G. N. Watson, University College, Lon- 

 don; Mr. J. H. Weaver, West Chester, Pa. Six 



