229 
1912-13.] Torsional Oscillations of Metallic Wires. 
In taking a record, the oscillations are started by means of a single 
out-and-in motion of the torsion head. The motor is started in sufficient 
time for its motion to become steady before the first maximum is reached, 
and the chronograph switch is closed also before the first maximum is 
reached. The reading: of a scale fixed round the rim of the oscillator 
is taken at the first and second maxima. The oscillations are then 
allowed to die down, and the reading corresponding to no twist is found. 
So the values of the two maximum ranges are obtained. 
A diagram is then plotted with suitable range and time scales, the 
instant of attainment of the first maximum being called zero, while that of 
the second maximum is the time of the semi-oscillation as obtained from 
the record. The two end points on the diagram are now correctly fixed ; 
but we do not know the instant at which the oscillation passed through 
its zero value, nor can we tell with accuracy from the apparatus the 
angular position of that zero relatively to the slits in the ebonite disc 
which determine the recorded angles. To surmount this difficulty, the 
intermediate points on the graph are plotted relatively to an arbitrary 
time and angle zero which cannot be far wrong. If these intermediate 
points do not now form a smooth, consistent graph with the end points, 
the whole intermediate set must be slid, without rotation, to a position 
which gives consistency. This was always found to be possible. 
§ 4. Fig. 3 shows results obtained with an iron wire. The experiment 
was the first made with the apparatus. No readings of angles were made. 
The instants of attainment of definite angular positions, counting from 
the instant of attainment of the first maximum as zero, were given by the 
record. A cosine curve, of unit amplitude and of the observed semi- 
period, was then plotted by means of points corresponding to the recorded 
instants; and the average drop of the oscillation, per recorded interval, 
between the two extreme recorded points within the two successive 
maxima was found. The two extreme points within the maxima being 
assumed to be identical with the corresponding observed points, the differ- 
ence of the ordinates of the two latter was divided into equal parts 
corresponding to the average drop per recorded interval, and the ordinates 
so found were plotted against the recorded times measured from the first 
maximum. The points so found are shown in the figure, the cosine curve 
being represented by the full line. It could not be predicted beforehand 
that these points would lie on the curve ; but, with the exception of one 
point obviously in error, it is evident that they do practically lie on it. 
Since the average drop of angle used is such that the second maximum is 
compelled to be equal to the first, the corresponding actual drop in the 
