1897-98.] Dr W. Peddie on Torsional Oscillations of Wires. 213 
value of the loss of energy per oscillation is independent of n, must 
exist. 
In the first series described in the present paper, the (constant) 
product of n and fr, has a value about one- half of the former, the 
diminution being due to a great change in the value of b , caused by 
the excessive fatigue employed. Excessive fatigue makes the value 
of n tend to unity. 
A recalculation of the constants in the formulae in Table I. of 
the first paper is made by the method now used ; and it is shown 
that, while nb is not constant, log .nb is a linear function of n — 
the two quantities increasing simultaneously. This implies the 
existence of a critical angle greater than that subsequently obtained, 
so that the critical angle is diminished by fatigue. 
It is further shown that log.fr may be regarded, in each series 
of experiments, as a linear function of n. With the observed 
values of n , it is impossible to tell which of log.fr or log.?zfr is 
more accurately a linear function of n — though both cannot he 
truly such a function simultaneously. The chief experimental 
result obtained is independent of this question. It is found that 
in every series of experiments , if conditions under ivhich n had the 
value unity are attainable , the value of b is absolutely constant. 
This seems to indicate a quantity which is dependent only on the 
nature of the substance of which the wire is composed. 
A modification of the apparatus was employed to compare the 
times of out and in motions during the oscillations. It was found 
that the time of inward motion exceeds that of outward motion 
through the same range. 
It is also shown that the magnitude of the total period of 
oscillation has no observable effect on the values of the constants 
in the equation given at the commencement of this abstract. 
In the first paper on this subject communicated to the Society, 
the equation just alluded to was deduced from t the assumption 
that the defect of the potential energy from the value which it 
would have in accordance with Hooke’s Law is proportional to a 
power of the angle of distortion. In the theoretical part of the 
present paper the assumption is made that molecular groups on the 
average obey Hooke’s Law in their distortions, and that definite 
groups have a definite limit of distortion beyond which they break 
