IOWA ACADEMY OP SCIENCE 
189 
A METHOD OP DETERMINING WHETHER THE RESTORING TORQUE IS 
PROPORTIONAL TO THE TORSIONAL STRAIN DURING 
THE VIBRATION OP A TORSION PENDULUM. 
BY L. P. SIEG. 
During some experiments on the elasticity of a certain type of wires the 
question arose as to whether the restoring torque, during the actual vibration 
of the system was at all times proportional to the torsional strain measured 
from the zero position. It is easy to determine the answer to this question in 
the case of a static twist of the wire, but there seemed at first to be an unsur- 
mountable experimental difficulty in determining the answer for the case where 
the wire is actually vibrating. 
The question was finally solved in two ways; one a direct method, and the 
other an indirect one. Pirst as to the direct method. At the lower end of the 
wire tested, was fastened a light metal connecting frame and from the lower 
end of this frame was attached a steel wire. This steel wire was assumed to 
have regular elastic qualities. At the end of the steel wire was attached the 
vibrating mass, and on this mass was placed a mirror. Another mirror was 
attached to the frame connecting the two wires. These mirrors were adjusted 
so that they threw the focussed image of a pointer on a large 360° cir- 
cular scale. Suppose for simplicity that the two mirrors are adjusted to read 
the same zero value when the wires are at rest. Call this reading, r. Now 
imagine the loVer end of this compound pendulum to be twisted through some 
angle. The mirrors will now read different values. Let the reading of the 
lower mirror attached to the steel wire be n and of that attached to the con- 
necting frame be r 2 . The tv/o wires are twisted, and their twists act against 
each other. The twist of the steel wire will be r 2 — n, while that of the tested 
wire will be r 2 — r. Now if a series of values of the two twists is obtained one 
can plat a curve connecting the twist of the tested wire with that of the steel 
wire. Assuming that the restoring torque in the steel wire is at all times 
proportional to the twist, we have then a set of values for twist and restoring 
torque in the tested wire. By platting the above values one can readily deter- 
mine if their relation is a linear one. 
The question of technique at once arises, for it will be seen that in the above 
method a simultaneous reading of two separate spots of light must be taken. 
It was possible to do this at the turning points of the vibrations, by the 
close observation of two experimentors. In the intermediate positions of the 
spots of light their simultaneous positions were determined by taking an 
instantaneous photograph of the moving spots. A number of such plates were 
thus exposed, and afterwards a leisurely measurement of the positions was pos- 
sible. It may be stated, that while no specific data are to be given in this paper, 
the above tests were applied to a wire which possessed such peculiar elastic 
properties as to lead one to suspect different conditions during vibration from 
