208 BRIDGMAN. 



that the thermal agitation consists merely of a swinging back and forth 

 within the atom of the heavy nucleus, and that the restoring force on 

 the nucleus is proportional to a linear function of its displacement. 



This completes the list of those substances which are known or pre- 

 sumed to crystallize in the cubic system, and for which therefore the 

 assumption is justified that the linear compressibility is the same in all 

 directions. Of the above list all except three have been definitely 

 proved to be cubic. These three are Sr, Ur, and Tl. Sr resembles Ca 

 chemically and is probably cubic. With regard to Ur there is not 

 much basis for estimate. We have seen above that it is highly 

 probable that Tl is not cubic because of the discrepancy between my 

 value of the compressibility calculated above on the basis of uniform 

 compressibility in all directions and that of Richards. 



Metals Crystallizing not ix the Cubic System. 



Xi"> system except the cubic enjoys in general the property of having 

 the same compressibility in all directions under hydrostatic pressure. 

 It is, however, possible that there should be such relations between the 

 elastic constants as to give this property to particular metals crystal- 

 lizing in other systems, or it may be that the difference of compressi- 

 bility in different directions is so small that experimentally it is not of 

 importance. Xow a study of crystal models makes it seem highly 

 probable that in the hexagonal close packed arrangement of spheres 

 the compressibility is the same in every direction. In fact the hexag- 

 onal and the cubic close packed arrangement of spheres are the same 

 as far as the adjacent layers of atoms are concerned, so that any de- 

 parture of the elastic properties of the hexagonal from that of the 

 cubic close packed arrangements can be due only to forces between 

 atoms separated from each other by at least one intervening atom, 

 and these forces are presumably weak. Xow of the metals studied 

 here, magnesium crystallizes in the arrangement of hexagonally close 

 packed spheres. (Of the metals listed above as cubic it will be found 

 that Hull has evidence that two, cobalt and cerium, may also crystal- 

 lize in the hexagonal system, but since the hexagonal arrangement in 

 which these crystallize is the close packed arrangement of spheres, the 

 compressibility would be expected to be the same in all directions, so 

 that the possibility of the existence of two forms introduces no compli- 

 cations in the case of these two metals. I 



It is probable therefore that the method of linear compressibility 



