1666 
regularly spaced nicks to the other side. The seconds were auto- 
matically registered by a second-pendulum which had been previously 
compared by means of the same registering-apparatus with the clock 
which serves as the time-instrument to the whole laboratory *). 
Relatively to the second-marks the times of passage could be read 
with an accuracy of about 0.01 of a second. On account of the 
personal error of observation the accuracy was however smaller, 
but it was found to be possible after some practice to keep the 
error at the moment of passage through the zero below 0.1 of a 
second. From a series of observations which usually contained 
about twenty complete swings the time of swing could thus be 
derived with a relative accuracy of sooo. 
5. The frictional couple produced by the liquid. 
From the values of the decrement d and the time of swing 7’ 
thus found the moment of the frictional forces acting on the oscil- 
lating system may be derived. From the observations it appears 
that the motion of the system is a damped harmonic one and thus 
corresponds to the equation: 
da 
dt? 
da 
at 1g —— = Ma ='0)7) 4 nn eer (AE) 
dt ; 
where K is the moment of inertia of the system, Ma the torsional 
_ da at : 
couple and LZ zj the moment of the frictional forces. We have also 
C 
found before ®, that in second approximation (which is sufficiently 
accurate in our experiments) 
L 2d 
K — T e « ° Oa whoa 0 : . e (28') 
0 
where 7, is the time of oscillation of the system, when there is no 
friction, and L’ the real part of Ls; for the imaginary part L'2 the 
equation 
NAV Age, da T—T, 
=a ee ere tice en HO 
RG peor TE Re) 
holds also with sufficient approximation. From the equations 28’ L 
can thus be calculated. 
This is, however, not yet the quantity Z occurring in the formulae 
1) The agreement between the two instruments was such that the time-measure- 
ment could be determined with a relative accuracy of one tenthousandth. 
2) Comp. Communications N°. 148b, p. 777. 
3) Ibid, p. 778. 
