IN TORSIONAL OSCILLATION 117 



most cases it was found that the value of n was greater in 

 the line drawn through the points corresponding to the 

 smaller oscillations. 



EXPERIMENTS ON BRASS WIRE 



In the present series of experiments brass was the material 

 most studied in detail, and, for the purpose of experiment, 

 lengths of brass wire, approximately one millimetre in 

 diameter, 1 were used. The length was in each case chosen 

 so that, from clamp to clamp on the torsion apparatus, there 

 should be exactly one foot of wire. It was found in a subse- 

 quent experiment, however, that change of length had no effect 

 on the constants a and n, although b might differ considerably. 

 In an experiment on 6 inches of brass wire, the values of a 

 and n were found to be equal to those got with 12 inches of 

 the same wire. The reason can readily be seen, as follows. 



If we postulate that the loss of potential energy in a 

 breaking down of molecular groups is proportional to a power 

 of the angle of torsion, we can approximately write (Peddie, 

 Phil Mag., July 1894) the loss of energy per swing in the 

 form kydy=py m dx. 



Now, in a wire of half length, k is doubled for the same value 

 of y ; and the loss of energy, with the same y at half length, 

 is half of what it would have been in the wire of whole length 

 at 2y. But in the wire of whole length at 2y the loss is 



p2 m y m dx. 



Thus -2kydy=p2 m - l y m dx 



- kydy=p2 m ~ 2 y m dx, 



M " 



1 '0975cm. 



