74 Prof. W. M. Thornton on the 



there is a suboscillation which displaces the minimum the 

 atomic weights of the last permanent elements are 207 and 

 208, lead and bismuth, whilst radium emanation (niton) has 

 222-4 and radium 226*4. 



4. It is plain from § 2 that the atomic formation oscillates 

 between two limiting conditions, that in which the density is 

 constant and a minimum, shown by the lower straight line 

 of fig. 1, and that in which the volume is constant and a 

 minimum, remembering that if it were possible to have zero 

 atomic volume, the maxima and minima of fig. 2 would lie 

 on parallel horizontal lines. There is a gradual adjustment 

 between the conditions of minimum density and minimum 

 volume. In the former the ratio of the mass to the volume 

 of the atom is constant, so that the closeness of packing of 

 the positive electrons within the atom is constant. In the 

 latter the ratio of mass to density is constant; the system has- 

 constant volume and is therefore elastic in the sense that at 

 the higher densities more electrons are packed into the same 

 space. 



As the internal cohesion is relieved by the successive loss 

 of units carrying positive electrons the atomic weight falls, 

 the volume expands to a maximum, declining again to a 

 minimum under the elastic forces of the remaining matter, 

 and any theory of atomic formation must be capable of 

 explaining the change of volume in so great a ratio as 

 13-75 to 1. 



5. It is to be observed that in the curve of atomic volumes 

 between csesium and osmium there is evidence of a sub- 

 oscillation, fig. 2, reaching a maximum at an atomic weight 

 of about 180, that of tantalum. Such an oscillation super- 

 posed on a regular periodic curve has the effect of displacing 

 the maximum of the wave on which it falls. The atomic 

 volumes with csesium as a maximum are clearly spaced un- 

 sym metrically, being more to the left than the earlier parts 

 of the curve would lead one to expect. Curve 1, fig. 2, is 

 the harmonic force which gives rise to the curve of observed 

 volumes ; curve 2 is that which would occur if there were no 

 such harmonic. The minima of the latter are close to 125 

 and 216, the cubes of 5 and 6. 



The origin of this harmonic, which plays so important a 

 part in the genesis of the higher elements, is clearly shown 

 in the curve of densities. The form of the part of the curve 

 in fig. 1 to the right of caesium is the same as that of G, fig. 3, 

 derived from a hysteresis loop symmetrical about the line of 

 mean values. In other words, the variation of atomic volumes 

 appears there to depend chiefly upon the periodic component. 



