404 



SCIENCE 



[Vol. LV, No. 1424: 



TABLE II 

 Atomic and Ionic Eadii (X 10^) of the Alkali Elenientsi 



canee that the chance linearity of first 

 powers. The most recent values are those 

 of Henglein, whose procedure is very ques- 

 tionable inasmuch as he takes Fajans' values 

 for bromide and iodide ions and then 

 assigns values to chloride and fluoride so 

 that a straight line connects the molecular 

 volumes of the halides of any alkali metal and 

 the sizes of the substituent halogen ion. By 

 using the same process for determining the 

 sizes of the alkali ions it is of course possible 

 at once to write an equation by which the 

 molecular volumes may be calculated from the 

 constant size of the ion. Henglein quite nat- 

 urally observes a very good agreement between 

 calculated and experimental values. 



Table I indicates the definite progression in 

 size and properties from one member to the 

 next in such nearly perfect* families (or 

 groups) of elements as the halogens and the 

 alkalies. 



It is interesting in this connection to com- 

 pare the radius of the ammonium ion. Using 

 the distance between ion centers found by 

 Bartlett and Langmuir for the ammonium 

 halides, and subtracting the radii of the halo- 

 gen ions, the ammonium ion is found to have 

 a radius of 1.90 X 10"' cm., if Richards' 



8 According to the periodic table of Harking 

 and Hall the two groups of elements nearest the 

 group of rare gases, that is the alkali and halo- 

 gen groups, should be the ones in which linear 

 relations may be expected to hold for practically 

 all of the elements in the group. Such groups 

 may be designated as ' ' perfect. ' ' In this sense 

 groups 2 to 6 inclusive are imperfect, since a 

 considerable break in properties occurs between 

 the second and third elements in each of these 

 groups. 



values are used, or 1.76 X 10 — * with Davey's. 

 In either case this is also the radius of the 

 rubidium ion. That this equality is extended 

 to the molecular volumes and other properties 

 of both simple and complex ammonium and 

 rubidium salts may be shown by numerous 

 examples. 



Prom the above considerations it is at once 

 apparent that, by plotting the various prop- 

 erties of the halogens, both free and combined, 

 which are linear to the dimensions of the halo- 

 gens, a large number of possible new linear 

 relationships may be predicted. It has never 

 before been possible to ascribe such perfect 

 and simple constancy and dependency of 

 essentially all properties upon one fundamental 

 variable of matter. The definite increase in 

 size in passing from fluorine to chlorine to 

 bromine to iodine atoms is paralleled in a 

 linear fashion not only by all dimensions of 

 the atom free or in combination, neutral or 

 charged, but by practically every measurable 

 property. That this extends even to variations 

 in the electromagnetic stray fields which deter- 

 mine the strength of secondary valence forces 

 and complex salt formation, will be indicated 

 in a following paper. 



Exactly as has been done with the halogens, 

 the various properties of the alkali metals, 

 free and combined, may be related. The ionic 

 radii have been variously calculated as follows : 

 These values (with the exception of those of 



9 From ionization potentials. 



10 Other values are those of Born from heats of 

 hydration, Pleyer-Wegau from diffusion of metals 

 iu mercury, Stokes-Born from ion mobilities, 

 Gunther-Schulze from volume changes in permu- 

 tites and from polarization capacities, and Heyd- 

 weiller from ion refraction. 



