1065 
gation was carried out both experimentally and theoretically ; in 
this paper are given the results of the experimental investigation. 
2. In order to settle experimentally, whether in the experiments 
previously described the velocities could be regarded as infinitely 
small, i.e. whether within the limits of the experimental errors the 
oscillation of the sphere, with the amplitudes then used, was a 
damped harmonic vibration with is logarithmic decrement independent 
of the amplitude, the limits of the amplitudes were in the first place 
widened as far as was possible with the arrangement for mirror- 
reading used. The scale had a length of 60 cms. and was at a 
distance of 153.7 cms. from the axis of the oscillating system, so 
that to right and left elongations could be observed to a maximum- 
amplitude of 5.5° (0.1 radian). The absolute accuracy of the readings 
was .00003 of a radian (0.1 mm. on the scale); amplitudes of 
.2° could therefore still be read with a relative accuracy of 1 °/, ; 
this accuracy was, moreover considerably raised by all elongations 
being observed both to right and left. 
The apparatus was the same as described in Comm. N°. 1495 and 
made use of in the determination of viscosities of mixtures of oxygen 
and nitrogen. The oscillating system was usually loaded with the 
aluminium cylinder, occasionally with the copper one. Various liquids 
were used in the vessel, in the first place water, afterwards liquids 
with smaller viscosity: benzene, carbon disulphide, ether*) and liquid 
air, and finally a mixture of water and glycerine, with a view to 
obtaining a set of observations with a liquid of higher viscosity. 
In contrast with what was found between the limits previously 
chosen (comp. Comm. N°. 1495 IV $3 and V $ 1), with the wider limits 
admitted this time the line representing log a as a function of t 
showed a distinct curvature especially between 20 and 30 ems. This 
fact seems to show that the angles of deviation used in the previous 
investigation were accidently near the limit of the range, where 
they may be looked upon as practically infinitely small. 
3. The oscillation of the sphere was thus not a pure harmonic 
damped oscillation and it was surmised’) that the movement would 
be a compound damped harmonic one, to be represented by the 
1) The benzene, carbon disulphide, and ether were commercial liquids; for the 
object of the above experiments it was unnecessary to work with perfectly pure 
liquids. 
2) This was aflerwards confirmed by the mathematical treatment of the problem 
(see next Comm.), 
