1071 
5. It follows from the foregoing discussion that in order to 
observe under such circumstances that the logarithmic decrement 
of the oscillations becomes independent of the amplitude within the 
limits of the errors of observation,') it would be necessary to go down 
to amplitudes about ten times smaller than those used so far, a 
method involving the difficulties just mentioned. 
It is not necessary, however, to look for a solution in that direction, 
as it has been found possible by a reliable extrapolation from a 
range, situated just above the limit of the practically infinitely small 
velocities, to derive the logarithmic decrement of actually infinitely 
small velocities with sufficient accuracy. In this manner the method 
of the observation of the damping of oscillations becomes a practical 
method for the determination of viscosities of liquids. 
By the aid of the data now obtained it becomes possible to correct 
the values for the viscosities of liquid mixtures of oxygen and 
nitrogen which were formerly found in Comm. N°. 1495, V. Although 
the elongations observed between the limits a= .07 and a= .02 
exhibited a practically constant logarithmic decrement, the formula 
(e) now found for liquid air shows that the mean value of the loga- ' 
dlog a 
rithmic decrement between those limits (i.e. the value of 7 
at a=.05 about or «= 5) is equal to 1.046 d,, d, being the value 
for infinitely small vibrations. Similarly it follows from the equation 
(g) found for gaseous air, that for a —= .06 (the mean amplitude at 
which the logarithmic decrement for the gaseous phase was deter- 
j ; ‘ Td loga 
mined in the experiments of Comm. N°. 1495) 7 = = 1d, 
Using these results we find for the mixtures of boiling point t°: 
t= 79.57 Jd = 0.03802 d, + J, = 0.00310 u = 0.909 1 = 0.001658 
82.34 0.04137 ze 1.003 0.001806 
17.91 0.03632 3 1.841 0.001615 
89,62 0.0443 | is 1.148 0.001858 
with a relative accuracy which may be estimated at zo . 
6. In plotting the elongations to right and left as read in the 
experiments of sections 3 and 4, the two lines containing the two 
') Unless very large times of swing are used (comp. § 1), which, however, in 
order to obtain moderate decrements would require a very high moment of inertia 
(comp. Comm. N°. 148c). The latter circumstance and also the extremely long time 
which each experiment would require in that case, render a large time of oscilla- 
tion undesirable. 
68* 
