192 
MR. A. A. GRIFFITH ON 
is not necessarily so. If. for instance, a small thickness of material at the interface 
between two crystals were to increase in volume, it could not be said without proof 
that tensile stresses would not be set up thereby, in addition to compressions. In 
some cases, in fact, it is obvious that there must be tensions. Thus, if the outer layer 
of a sphere increases in volume, the matter inside must be subjected to a tensile stress. 
The effect of overstrain on the density of metals is at present under investigation 
at the Royal Aircraft Establishment. The work is not yet sufficiently complete for 
detailed publication, but it may be mentioned here that the expected change in density 
has been found, and that the results already obtained are such as to leave little room 
for doubt that this change is in fact the cause of fatigue failure in metals. Thus, in 
overstraining mild steel by means of a pure shearing stress, a decrease in average 
density of as much as 0-25 per cent, has been observed. 
Some progress has also been made in the direction of estimating the internal stresses 
set up as a result of the change in density, and it has been found that an average change 
of the magnitude mentioned above could give rise to a hydrostatic tensile stress in the 
cores of the crystals, of the order of 30,000 lbs. per sq. inch. 
Dealing now with materials whose molecular sheet-formations are curved, it is at 
once evident that all yield, or slide, phenomena must be absent, as possible gliding 
planes do not exist. Thus, this case, though geometrically more complicated, is 
practically much simpler than that in which the sheets are plane. The theoretical 
properties of materials having the curved type of formation appear to correspond 
exactly with those known to belong to brittle “ amorphous ” substances. Exactly 
as in the case of crystalline materials, elastic after-wmrking is explained by the inferor 
stability of molecules near the boundaries of the units of molecular configuration, but 
elastic hysteresis should not occur. If adequate precautions are taken to avoid secondary 
tensile stresses, fracture of short columns in compression should occur at stresses of an 
altogether higher order than in the case of crystals. In this connection it may be 
remarked that the compressive strength of fused silica is about 25 times as great as 
its ordinary tensile strength. 
It appears from the foregoing discussion that the molecular orientation theory is 
capable of giving a satisfactory general account of many phenomena relating to the 
mechanical properties of solids, though closer investigation udll perhaps show- that 
•the agreement is in some cases superficial only. Such questions as the effects of unequal 
cooling, foreign inclusions and local impurities, and the behaviour of mixtures of 
different crystals, have not been dealt with ; it is thought that these are matters of 
detail wfhose discussion cannot usefully precede the establishment of the general 
principles on which they depend. 
9. Practical Limitations of the Elastic Theory. 
It is now possible to indicate the directions in which the ordinary mathematical 
theory of elasticity may be expected to fail when applied to real solids. 
