186 
IOWA ACADEMY OP SCIENCE 
first give a brief description of the apparatus used and of the method 
of timing. The apparatus was the same described in one of the former 
paperst The torsional pendulum was supported from a firm brace 
bolted to the wall. The mirror attached to the suspended weight was 
exactly in the center of a complete circular scale, the diameter of the scale 
being 149.2 cms. This large diameter gave a space of 2.6 cms. to a de- 
gree, and so enabled one to read with accuracy to tenths and to esti- 
mate in the smaller amplitudes to one one-hundredths of a degree. The 
scale was of course really divided into double-degrees, because a twist 
of one degree of the mirror would give a displacement, 
of two degrees of the spot of light on the scale. The amplitudes of the 
vibrations were read by focusing the image of a wire, illuminated by 
an arc light, on the above described circular scale. It was possible by 
the use of the complete circle for a scale and the double mirror, to read 
all the amplitudes with the exception of a very few when the mirror 
was end on. This ecpiipment was a decided improvement over that 
used in the iireceding experiments, for in those some of the important 
amplitudes were obtained only by interpolation. The method of fas- 
tening the wire to the supports, and of attaching the v'arious moments 
of inertia was the same as that described in the former paper. To the 
upper rod holding the wire was attached a torsion head, graduated into 
degrees, and having adjustable stops. This device made it possible to 
set the wire into vibration, and to hold it at practically constant ampli- 
tude. The method of timing was, with only one or two changes, essen- 
tially the same as that explained in the former paper. In all cases, 
unless otherwise stated, the periods are in reality half-periods. To mahe 
perfectly clear how the periods were obtained, -the method will be brief- 
ly described. A drum geared to a motor running at nearly constant sp'eed 
wound tape from a roll, drawing it under a pen attached to the armature 
of an electo-magnet. A Bond and Son’s siderial break-circuit chrono- 
meter in circuit with the electro-magnet gave double-second marks on 
the tape. Connected with the recorder by a separate circuit was a 
tap key,' which was closed at the ends of each vibration. The periods 
were obtained by end readings instead of by center readings, in order 
to have periods match the corresponding amplitudes, these latter being 
of course measured at the ends of the vibrations. There were then re- 
corded on the same tape the times at which the turning points were 
reached, and also the double-second marks. When the amplitude had 
decreased to a value of from 15 to 20 degrees, the tape was abandoned, 
and the periods thereafter were obtained by the method of coiuci- 
2. — K. E. Guthe and L. P. Sieg, Phys. Rev. 30, 1910. 
