235 
1912-13.] Torsional Oscillations of Metallic Wires. 
The result is very significant in connection with the view of G. 
Wiedemann, that the loss of energy is due to the work done in shifting 
the position of set from one side of the zero point to the other. Its 
possibility was suggested by the theoretical considerations given below 
(§ 9 ). 
Theoretical Discussion. 
§ 6. The experimental data upon which a theoretical discussion must be 
founded are those described in the preceding paragraphs, and the now 
well-established fact (see Ritchie, Proc. R.S.E., vol. xxxi. p. 424, vol. xxxiii. 
pp. 177, 183) that the law of the decrement of the range, y, of oscillation, 
as the number of oscillations, x, increases, is very accurately given by the 
relation y n (x-\-a) = b, where n, a, and b are constants, together with other 
known facts regarding the statical and kinetic laws of deformation of a 
solid, e.g. those of “ set.” Any theory must be of “ molecular ” type, the loss 
of energy being, in great part at least, due to the rupture of molecular con- 
figurations. These may, of course, take place on a finite “ crystalline ” scale. 
§ 7. In previous papers (Phil. Mag., July 1894; Trans. R.S.E., 1898) it 
has been shown that, when the fractional decrease of the range per 
oscillation is not too great, the above formula can be deduced from the 
assumption that the loss of energy per oscillation is proportional to a 
power of the angle of twist measured from the position about which the 
oscillations take place and towards which they converge as their amplitude 
decreases. In the latter paper an attempt was made to express this loss 
in terms of the work done in distorting molecular groups which break 
down when the distortion becomes too great. Two factors have then 
essentially to be considered : (1) the law of force to which a group is subject 
during distortion, and (2) the law regulating the number of groups which 
break down per unit volume in a given small range of distortion. Regard- 
ing the law of force, at least when the individual groups are of invisible 
dimensions, nothing is known except as an average, in which case Hooke’s 
Law is fundamentally applicable. But it is probably legitimate to 
postulate that the number of groups of any one type, per unit volume, is 
so great, and that the nature of the interconnections is such, that Hooke’s 
Law may be assumed to apply to each type on the average. The only 
quantity then remaining undetermined is the number of groups of given 
type which break in a given small range of distortion. In order to deduce 
the above empirical law, it is necessary to assume either that this quantity 
is proportional to a power of the distortion, and that the power is the 
same for all types, or that the quantity when averaged over all types is 
