498 Professor H. C. H. Carpenter [March 7, 



packing of that form was not by any means common in crystal struc- 

 tures, indeed it was not quite certain that it existed afc all ; it certainly 

 did not by any means represent the inevitable completion of crystal- 

 line effort ; in the crystal, therefore, the structure was not necessarily 

 or even probably the most rigid possible structure. The available 

 supply of internal cohesion was not all used up to secure maximum 

 rigidity. In the less closely packed assemblages of spheres it could 

 be imagined that by a small translation of the layers of molecules 

 relatively to each other, a more rigid structure might be produced. 

 If, for example, in an assemblage of spheres in which each was only 

 in contact with six others, a displacement occurred which brought 

 each into contact with twelve others, it was clear that the new struc- 

 ture would be at least twice as rigid as the original structure. . . . 

 It was believed that in the metals which crystallized in the regular 

 system, such as gold, silver, copper, iron, etc., the molecules were not 

 in closest packing ; in these metals the crystalline state w as one of 

 great mechanical instability and consequently of very small rigidity ; 

 as a result of that, disturbances by deformation caused very wide- 

 spread breaking down of the crystal structure with momentary lique- 

 faction of molecular layers and groups. If that occurred at a point 

 below the crystallization temperature, the newly solidified portions 

 could not receive their crystalline arrangement, and remained chilled 

 or frozen into a more rigid type of structure, a type in which the 

 available cohesion of the mass was more fully utilized than in the 

 crystalline state. ... In the case of ductile metals, flow under de- 

 forming stresses followed by re-solidification left a proportion of the 

 molecules in a condition of constraint, their freedom as vibrating 

 units being impaired. ... If then the available cohesion of the mass 

 could in that way be so effectively utilized that it could put a con- 

 straint on the vibration of the individual molecules, it was not at all 

 surprising that the molecules were so much more closely held by each 

 other, that a greater force was then required to move them over each 

 other under deforming stresses." 



In the hghtof investigations such as the foregoing, the hardening 

 of steel by quenching can be viewed from a broader standpoint than 

 was possible to earlier researchers. We know to-day that metals may 

 be hardened in four distinct ways : (1) pure ductile metals can be 

 hardened by cold work ; (2) these metals may be hardened by being 

 alloyed with one another, or with certain non-metallic elements such 

 as hydrogen, nitrogen, carbon, etc. ; (3) if these mixtures are ductile, 

 they may be further hardened by cold working, for instance a brass 

 (70 copper, 80 zinc) ; (4) certain of these alloys can be hardened by 

 chilling. The hardening of steel by quenching comes in this class. 

 It is important to remember that the rapid drop in temperature which 

 quenching produces may act in two ways : — {a) " It may stereotype 

 the form of chemical coml)ination or of structure, crystalline or non- 

 crystalline, which is in the condition of equilibrium at the tempera- 



