1043 
Ca Tr oo 
A measurement of, i. e. the logarithmic decrement for unit time 
which might be carried out by photographic registration would lead 
to the knowledge of by equations (55) and (57). It is somewhat 
doubtful, however, whether this method is really practicable, in view 
of the circumstance that our eqnations are theoretically only applic- 
able after an infinite time; it is true that the experiments showed 
‘them to be practically valid after a very short time in the case of 
a periodic motion *), but a special investigation would have to show 
whether this would still be so in the case of an aperiodic motion 
or whether perhaps the decrement would only become constant 
after a long time, when the deviation has become much too small 
: eee ae 
for the purpose of measurements. If i did not reach constancy within 
the limits of the observation, the above equations for the aperiodic 
motion would not be of any practical use. 
_6. As with the periodic motion it is possible by increasing A’ or 
d 
diminishing M/ to make the decrement —, and thus 6", as also 6" 
ge 
(R'—R), so small that the expression (57) may be developed in a 
series according to powers of 6" (R'—R). The first term of this series is 
13 
RR 
(comp. $ 18 of the previous communication); so that, if no further 
terms are needed, the calculation of 1 becomes very simple. In that 
case the condition for aperiodicity would be 
13 
L= 8x R*y EO oe es (96) 
VMK < Aa Ry 
2 58 
aaa \i ee ieme a suo) 
7. Similarly to wv, LZ cannot become infinite (equation 57); on 
the other hand / can become zero and indeed the smallest value 
ae ; Sik NOPE 
of 6" for which Z becomes zero gives the upper limit of rie the 
1) According to an observation which was made in this connection with a 
sphere oscillating in a practically unbounded mass of water, with a time of swing 
of about 20 seconds, the logarithmic decrement had become constant already 
after one half oscillation. 
4 5 : : JS 
2) In the experiment with glycerine mentioned before, where p Was of the 
order 0,1, R =3, R=2, K=545, M=51, » = 1,2 and » = 10 about, b” (R'—R) 
was of the order 0,1, so that the expression (36) held with near approximation. 
The condition (58) is satisfied, and thus the motion was actually aperiodic. 
