23 7 
1912-13.] Torsional Oscillations of Metallic Wires. 
distortions, the power characteristic of the outer metal should alone appear. 
But, the ratio of the tis for copper and zinc being nearly 2 : 1 , it can easily 
be verified that a sum of such terms cannot give results at all agreeing 
with the results of observation. On the other hand, one term alone, with an 
intermediate value of n, represents the actual results well. There seems 
to be a commingling of effects in regard to the dissipation of energy. 
§ 8. This also gives some justification of the treatment adopted in the 
paper of 1898, in which Hooke’s Law was postulated as an average for all 
of the types of groups suffering distortion and rupture, and the number 
of groups suffering rupture within a given very small change of twist 
might include many of these types. But, if we select as the characteristic 
of a “type” the shearing strain at which rupture just occurs, we may 
arrive at the same result by considering each type by itself, and then 
integrating over all types, provided that n be regarded as having the 
same value for each type. This gives an appearance of restriction, but 
the process derives support from the experimental fact just given above, 
and, in any case, it would throw light upon results which might be due 
to the condition of one type being dominative. For example, Mr Ritchie’s 
discovery of a sudden change in the value of n, when certain metals are 
heated to definite temperatures, seems to indicate a change of molecular 
structure. 
To make the development of any theory possible, subsidiary postulates 
regarding the conditions of rupture and re-formation of groups have to be 
made. In the former paper it was assumed that, for every group of given 
type which suffered rupture, a new group of the same type came into 
existence. This is analogous to the fundamental assumption of the kinetic 
theory, and is at least plausible as the expression of an average condition. 
In the following investigation it is also assumed that the characteristics 
of a type are not altered by ruptures of the constituent groups, the con- 
sequence of a rupture under strain being essentially the formation of a 
new (it might be the re-formation of the old) group instantaneously under 
no strain. In the former paper, the work was simplified by the postulate 
that there was no initial strain of any group, and that each old or new 
group of given type broke down under the same limiting strain in either 
direction of twist. But this condition required that all strain should again 
vanish when the angle of twist reattains its initial value, whereas it is 
known that negative twist is requisite to destroy the “ set ” produced by 
the positive twist. In the present investigation, simplification having been 
attained by dealing first with one type alone, this restriction is dispensed 
with. It is assumed that the initial condition is one of strain equilibrium, 
