328 REPORTS ON THE STATE OF SCIENCE, ETC. 
the elastic limit cannot be wholly regained by releasing the applied stresses, 
there is evidence to show that part of the difference may be regained by 
other methods. '!For example, since the electrolytic potentials of the strained 
and unstrained metals are different, a quantity of work may be regained by 
using electrodes of the two in a suitable cell. When a given mass of vitreous 
metal is replaced by an equivalent mass of crystalline, a quantity of electrical 
work is obtained, and any deficiency—such as would doubtless be found in 
experiment—may fairly be regarded as the equivalent of heat generated during 
the gliding motion of the second stage of straining. (2) While the great internal 
viscosity of the vitreous metal prevents recrystallisation at ordinary tempera- 
tures, the process may be accelerated by raising the temperature (above 400° C. 
in the case of steel). (3) General experience in the widest fields of research 
indicates that every change of physical or chemical state is inherently reversible, 
actually or by means of appropriate imaginary methods of operation. (4) In 
straining the metal elastically, up to the elastic limits at which the change 
occurs under different complex stresses, quantities of work are done on the 
metal in strictly reversible manners; and these quantities may be expressed 
in terms of the applied stresses and the elastic constants of the metal. 
Expression for the work done in the Reversible Stage of Strain, 
The reversible process now considered is the initial stage of strain, com- 
mencing when the crystalline metal—initially free from strain—is subjected to 
a gradually increasing stress, and terminating when the first molecules are 
projected out of the ‘crystalline lattice’ into the ‘vitreous assembly.’ It is 
evident that the process can be carried out isothermally, thus completing the 
conditions required for the application of thermodynamic principles. We have 
to attempt the problem of obtaining, in terms of the applied stresses, an 
expression for the work done on unit mass of metal suffering the change; or, 
alternatively, an expression proportional to this quantity. 
If the whole mass suffered the change, and were isotropic, and if the change 
involved no alteration of volume other than the elastic compression or 
expansion, the work done by the applied forces would be identical with the 
elastic strain-energy at the elastic limit; and would be given by the expression 
aipdl Poe ey eee dee ) 
WwW on (* +Y?+7Z?) i (YZ+ZX+4+XY) 
Part of this quantity of work, however, would be stored in the vitreous metal 
produced, in virtue of its elastic compression or expansion under the applied 
stresses. Thus the nett work corresponding to the change of state would be 
we_w— Ll Feseeey 
2K 3 
where K denotes the (unknown) modulus of compressibility of the vitreous 
metal. 
On the assumption that the change results in a change of volume, in ratio 
as measured free from stress, a further term may be introduced—analogous to 
the expression used in Thomson’s ‘ regelation’ theorem : Thus 
W"=W'—a ed) 
3 
The relation between the elastic limits would then be expressed by an equation 
stating that the quantity W” is constant, i.e. independent of the ratios between 
the stresses X, Y, and Z 
The problem is appreciably complicated by the non-isotropic character of 
actual crystalline metal; and by the fact that only a small proportion of the 
total mass actually suffers the change of state. On the probable assumption that 
the increase of volume a is only slight, the relative importance of the terms 
introduced for W’ and W” largely disappears; or on the not improbable 
hypothesis that the change involves a reduction of volume, the two terms may 
wholly disappear, leaving the strain-energy W as the constant governing factor. 
On this latter hypothesis we may picture the change of state as accompanied 
# 
