CIIK?\IISTRV AND CRYSTALLOCRAPH V 



215 



If it be objected to the scheme that the equivalent spheres 

 ought to be separable, the assumption may be made that such 

 central aggregates of spheres are slightly coalesced. This idea 

 is the same as Pope's conception of the elimination of interstitial 

 space between his spheres. Another objection which seems at 

 first more formidable is that my carbon tetrahedron of spheres 

 occupies too much bulk to take the place of Pope's carbon 

 spheres (which have the same volume). The circumscribed 

 sphere to my tetrahedral arrangement has a radius = ( I + y' f ) 

 times the radius of the " equivalent-spheres " (the volume beirig 



Fig 1. — Aggregate of methane molecules * 



II times that of a sphere), and it might be supposed that the 

 assumption of half-sized equivalents {i.e.. semi-valent) would 

 explain the facts better; but as a matter of fact the hollows 

 between these equal spheres allow of such exact close packing 

 that the tetrahedron of spheres above described seems to repre- 

 sent the carbon atom even better than Pope's scheme does. 



It will be desirable to show how this theory fits in with 

 some of the concrete cases discussed by Barlow and Pope. 

 Taking methane first, and examining Pope's assemblage which 

 represents it, we find its unit to be a cu be of carbon spheres 



* In the figures the dark spheres represent Z of ato nic weight 3 



