IOWA ACADEMY OP SCIENCE 
187 
dences. Upon the tape record, the chronometer times of the turning* 
points were recorded in hours, minntes, seconds and hundredths of a 
second. Supposing that t is this recorded time for the 5th vibration, 
and that U is the time for the 25th vibration, then t’-t is the time 
elapsed between these two vibrations. This difference divided by 20 
is used as the period of vibration of the mean SAving; in this case, the 
15th. In this Avay the errors arising from individual observations are 
diminished; and AAdiile this method is not an exact one, nnmerons tests 
have shoAAm that it giA^es essentially correct values. A sample of one of 
the curves connecting period and vibration nnmher is given in Fig. 1. 
The figure shoAvs hoAv Avell the observed values fit a smooth curve, and 
hoAV in most. cases it Avas unnecessary to correct the period readings. 
To see if there AA^as any Amriation in the relation betAveen amplitude 
and period ; this variation, if any, being possibly due to the magnitude 
of the initial amplitude, the following experiments Avere performed. 
The Avire Avas annealed at dull red heat by a current of 2.5 amperes, 
for about 30 seconds. Care was taken not to alloAv the Avire to vibrate 
through more than 15 or 20 degrees after this treatment. The Avire Avas 
then carefully tAvisted through a certain small amplitude and timed by 
the method described above. After a rest of a day the Avire Avas tAvisted 
through a larger amplitude and timed as before. This aa^s continued AAuth 
constantly increasing initial amplitudes until at the sixth observation 
the total ampliude of swing had reached a value of 788 degrees. This 
Avas an amplitude from the zero position of 394 degrees, and a tAvist per 
centimeter of length of the Avire of 9.8 degrees. The results of this set 
of experiments are giAmn in table 1, and graphiially shoAvn in Fig. 2. 
