50 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65 



be of the same thickness for all atoms, since it abuts upon a positive 

 sphere which has the same normal charge density for them all. It 

 may be of uniform density, but it seems more natural to suppose 

 that its density falls off rapidly as 'the distance from its inner bound- 

 ary increases, 1 as shown in the diagram, where O represents the 

 center of the atom. With regard to its extent in the case of an 

 isolated atom there is no need to speculate. If it is to fulfill the 

 purpose for which its existence was assumed, it must be supposed to 

 have so low a charge density that magnetons do not lie in it, and 

 therefore its presence does not appreciably affect the values of fx—i 

 (§14). As being by far the most compressible part of the atom, the 

 envelope is the seat of the greater part of the volume change that 

 accompanies a chemical or physical change, and it may be supposed 

 to be compressed into a very small space when the forces between 

 atoms are strong. 



This envelope, the assumption of which will enable us to give a 

 qualitative explanation of practically all the observed volume rela- 

 tions, must be distinguished from the comparatively very dense layer 

 in which the valence magnetons lie as they surround the groups of 

 eight, and which owes its existence entirely to the presence of the 

 valence magnetons, being simply a less compressed part of the posi- 

 tive sphere proper (see §14). In the diagrams hitherto used in 

 this paper, both this layer and the envelope have been disregarded, 

 but they are represented in the more complete diagrams which are 

 given below for the atoms of Argon (3-/) and Iron (3y + 8) when 

 these elements are in the liquid and solid states respectively. Their 

 magneton numbers are 24 and 32, but because of the expanding 

 effect of the valence magnetons (which approximately trebles the vol- 

 ume : see §14), the volumes of their positive spheres, neglecting the 

 envelopes, are 24 and 96 respectively (in arbitrary units). These 

 are represented by the circles in the diagrams. The dotted hexagon 

 represents the total space, frequently duodecahedral in shape, that is 

 occupied by the atom when it is one of a cluster. In the case of 

 Iron, this space is shown as being only a little greater than the volume 

 of the positive sphere proper; i. e., about no units. The total space 

 for the Argon atom is therefore represented as having a volume of 

 about 430 units, to accord with the relative atomic volumes observed 

 for these elements. It may be seen that the distances across which 

 the interatomic forces must act are thus made to be about as we 



1 This gives the " thickness " a meaning even if the envelope is infinite in 

 extent. 



