402 



SCIENCE 



[Vol. LV, No. 1424 



their constituents, as will be shown later in 

 detail. 



The present paper will be limited to a con- 

 sideration of these relationships in the ease of 

 the elements and simple compounds, and will 

 indicate briefly some of the most interesting of 

 a large number of eases which show the above 

 simple relationship. 



While the writer was working upon the more 

 extended and general set of relations given in 

 this letter, the above mentioned paper by Biltz 

 appeared. In this he exhibited the volume rela- 

 tions which may be used as a basis for the 

 general discussion. Biltz found that if the 

 atomic volumes of certain of the noble gases 

 (argon, krypton, and xenon) are plotted along 

 one axis in a two dimensional plot, the atomic 

 voliunes of the three corresponding halogens 

 give one straight line, the three alkalies an- 

 other, the three members of group 4B another, 

 and the three members of group 4A, a fourth 

 straight line; while in all of the other groups 

 there is a departure from linearity. It may 

 he noted that the alkali and halogen groups on 

 the one hand, and groups 4 A and B on the 

 other, are equidistant from the group of the 

 rare gases of the atmosphere in the periodic 

 table of the elements as represented by Harkins 

 and Hall. The facts found in this work are 

 beautifully in accord with wihat might be ex- 

 pected from this particular model of the peri- 

 odic system. 



The relations found by the writer are much 

 more general than those given in the preceding 

 paragraph. Tims it is found that if the atomic 

 volumes of the five alkali elements are plotted 

 on one axis (as the X-axis) of a three dimen- 

 sional rectangular coordinate system the atomic 

 volumes of the four halogens on the Z-axis, 

 and the molecular volumes of the alkali halides 

 on the Y-axis, practically all of the points (all 

 except some of those for ccesium), lie quite 

 nearly on a plane z = bs + cy + d %ohich 

 passes nearly through the origin. Thus the 

 relationship is very much more simple than 

 has heretofore been suspected. 



It is even more remarkable that when 

 instead of the molecular volumes of the salts, 

 other properties are plotted on the T-axis, it is 

 found that in a very large number of cases the 



surface, while not a plane, is of the extremely 

 simple form known as a doubly ruled surface. 

 Commonly the surfaces found may be ex- 

 pressed by the equation z = axy -{- bx -\- cy -{- d. 

 For the molecular volumes of the alkali halides, 

 the following expression, in which z is the 

 molecular volume, x the atomic volvune of an 

 alkali metal, and y the atomic volume of a 

 halogen, holds rigorously: z = .0074a:j/ + 

 .3655a: -f y — 9.07 = .WMQxy + .3345a; -f 

 .9442?/ — 7.49. 



Since it is difiEieult to present the character- 

 istics of these remarkable doubly ruled sur- 

 faces in a very simple way, the discussion of 

 the present paper will be given in terms of the 

 projections of these surfaces on the various 

 coordinate planes. Simply to present one ex- 

 ample, the two dimensional plot for the halo- 

 gens may be considered. If the atomic vol- 

 umes of the four members of the halogen 

 group, fluorine, chlorine, bromine, and iodine, 

 are plotted along one axis of a plane rectangu- 

 lar coordinate system, and along the other any 

 of a large number of properties of other groups 

 of elements, of other properties of the halogens 

 themselves, and of compounds in which they 

 are substituents, perfectly linear relationships 

 are found, for which simple equations may be 

 derived and calculations made with which 

 reputable experimental data agree quite accu- 

 rately. Some of these properties linear to the 

 halogen atom dimensions may be briefly enum- 

 erated as follows : atomic volumes, atomic 

 radii, viscosities or boiling points of the rare 

 gases; atomic volumes of the alkali metals and 

 alternate members of group 4; for the ele- 

 mentary halogens, the molecular diameters, 

 melting points, boiling points, critical tempera- 

 tures, latent heats of fusion and vaporization, 

 normal potentials, cubical coefficients of ex- 

 pansion, atomic frequencies, magnetic suscep- 

 tibilities, cohesional dimensions, \/a and b of 

 van der Waals' equation, and the heat of 

 formation of ions from the elements; for the 

 hydrogen halides, the molecular volumes and 

 diameters, boiling points, melting points, crit- 

 ical temperatures, latent heat of vaporization 

 and the energy of ionization; for organic com- 

 poiinds, the atomic volumes of the halogens in 

 combination, the atomic refraction for the D 



