1665 
almost perfectly straight line, the inclination of which determined 
the logarithmic decrement. 
The angles of deflection were never taken greater than 4° and 
thus the deviations on the scale 20 cms. at the most '). The obser- 
vations were interrupted, when the amplitude of the swings had 
fallen to about 7 cms. *) 
4. The measurement of the time of swing. 
The time of swing was measured by graphical registration. 
At right angles to the telescope through which the scale was read, 
a second telescope was mounted, which was also pointed at tie 
swinging mirror through the intermediary of a glass plate placed at 
an angle of 45° in front of the first telescope in such a manner 
that both telescopes were always focussed on the same point of the 
scale. Through this telescope the times were observed at which the 
middle of the scale passed through the axis of the telescope, this 
point which corresponds to the position of equilibrium of the mirror 
being made visible by means of a conspicuous mark. These moments 
were registered by means of a morse-key and thus electrically trans- 
ferred to a strip of paper which travelled over a registering drum 
with a practically uniform speed of about 1 cm. per second. The 
registering pin was a glass tube with a fine drawn out point and 
filled with ink; it was attached to the extremity of a spring which 
could move between two small electromagnets. On pressing down 
the morse-key a temporary current passed through one of the electro- 
magnets and the pin was deflected through a small distance, so that 
the fine line drawn by the pin on the paper showed a sharp nick. 
In order to measure the times elapsed between the marks obtained 
a short current was sent every second through the second electro- 
magnet, so that the line drawn by the pin showed a series of 
1) With longer deflections the readings became too difficult on account of a too 
rapid movement of the scale. In how far the theory is applicable with the velocities 
which occurred in our experiments, is a point which we intend to investigate by 
working with an ordinary liquid under corresponding conditions (Comp. for this 
question: G. ZemPLéN, Ann. d. Phys. (4) 49, 39, 1916). 
2) It is easily seen, that there is a lower limit for the amplitude, which it would 
be unprofitable to exceed. This optimum must be reached, when 5 becomes a 
minimum, « being the absolute error of observation which can be made in the 
logarithm of the amplitude and # the number of swings. From this it may be 
inferred that when the experiment starts with an amplitude a, the series of obser- 
a 
vations must not be extended beyond the amplitude —. 
e 
