231 
1912-13.] Torsional Oscillations of Metallic Wires. 
observations was really smaller than it. Thus the actual points, which 
could have been plotted had observations of the values of the two maxima 
been made, must have lain to the right-hand side of the cosine curve ; and 
so the time of the in -motion must have exceeded that of the out-motion. In 
the diagram, negative ordinates have been plotted as if they were positive. 
Fig. 4 exhibits results obtained with a copper wire. The second 
maximum value was 091 times the first. The full line represents a cosine 
curve with exponentially decaying amplitude. The separate points repre- 
sent the results of observation, the points next each maximum being 
taken on the full curve. The difference between the times of the in and 
out motions is quite well-marked, and exhibits the essential difference 
between the internal loss of energy in a distorted metal and the loss which 
occurs when a viscous resistance proportional to speed is active. 
§ 5. Fig. 5 shows results obtained with the same copper, the length of 
the wire being halved, while the maximum angle of twist was not much 
altered from its former value, so that the loss of energy per oscillation was 
greatly increased. The ratio of the second maximum angle to the first was 
now 0'68. The isolated points represent the results of observation, and 
were plotted by the process described in § 3. The difference between the 
times of the in and the out motions exceeds one-sixth of their average value. 
Fig. 6 exhibits similar results in the case of a zinc wire, in which the 
dissipation of energy was so great that the amplitude of oscillation fell to 
about one-half of its initial value in a single semi-oscillation. 
In each of these figures, the full curve represents a cosine curve whose 
zero point is at the point of inflection of a curve drawn freehand through 
the observed points. The dotted line is the axis of the cosine curve. 
The correspondence of the small oscillations of an elastic material such as 
steel with the simple harmonic law is well known ; but it seems to be a 
very remarkable thing that, in the case of a substance possessing so great 
viscosity * that the amplitude falls to one-half of its initial value in a single 
semi-oscillation, the law of oscillation should be very accurately simple 
harmonic from the extremity of the range inwards to the position of set 
(inflection), beyond that to the zero point, and almost as far beyond the zero 
on the negative side as the position of set is separated from it on the positive 
side. After that stage is reached, the deviation from the simple harmonic 
law takes place very rapidly. [A slight error, in either direction, in choosing 
the point of inflection, diminishes the accuracy of the correspondence 
greatly; so that the most suitable cosine curve is readily determined.] 
* Viscosity is here used merely to indicate internal resistance to relative motion of 
the parts. 
