THE PHENOMENA OF RUPTURE AND FLOW IN SOLIDS. 
195 
then the general criterion of rupture shows that the crack cannot spread unless the 
material is subjected to a certain minimum stress, which is greater the smaller the crack. 
Thus, reducing the size of the crystals increases the stress necessary to cause the initial 
crack to extend. There is therefore a critical size of crystal for which the stress-range 
necessary to spread the crack is equal to that necessary to start it. Until the refining 
has reached that stage it can have no effect on the magnitude of the safe stress range, 
but from that point on the range must increase progressively with refinement until the 
limit is reached, as before, when each “ crystal ” contains but one molecule. 
It therefore appears that refining is one avenue of approach towards the ideal state 
of maximum strength. Strangely enough, another line of argument suggests that the 
reverse of refinement might be effective in securing the desired result, in certain special 
cases. If a wire is required to withstand a simple tension, it seems that the best 
arrangement is that in which the strongest directions of all the molecules are parallel to 
the axis of the wire. This is equivalent to making the wire out of a single crystal. 
The theoretical tenacity would not be obtained, however, if the gliding planes made 
with the axis angles other than 0° C. and 90° C., as yield would occur. 
If, in passing from the normal crystalline to the strong fine-grained state, the necessary 
orientation of the molecules were performed in accordance with some regular plan, 
the resulting configuration would possess some kind of symmetry, and the material 
might therefore exhibit crystalline properties. In cases where a substance exists in 
nature in several different crystalline forms, of which one is much stronger than the 
others, it may be that the strong modification is of the fine-grained type here considered. 
Thus, diamond may be a fine-grained modification of carbon. If this view is correct, 
it suggests that the transformation of carbon into diamond requires, firstly, the existence 
of conditions of temperature and pressure under which diamond has less potential 
energy than carbon ; and, secondly, the provision of means for causing relative rotation 
of the molecules. In the attempts which have so far been made in this direction, 
attention seems to have been concentrated on satisfying the former requirement, the 
possible existence of the latter one having been overlooked. The most obvious way 
of satisfying it, if the mechanical difficulties could be overcome, would appear to be 
the application of suitable shearing stresses in addition to the hydrostatic pressure. 
11. Application of the Theory to Liquids. 
A detailed discussion of the properties of liquids, in the light of the present theory, 
would scarcely fall within the scope of this paper. One prediction which has been 
made, however, and which has been verified experimentally, affords such a remarkable 
confirmation of the general theory that it is felt that no apology is necessary for 
introducing it here. Consider a solid composed of molecules whose attraction is a 
function of orientation, the molecules being arranged in groups, in accordance with 
the theory outlined in the preceding pages. If the temperature of this body be supposed 
to be increasing, it will be seen that at some temperature the kinetic reactions due to 
VOL. CCXXI.-A. 2 E 
