STRAIN ON THE PHYSICAL PROPERTIES OF MATTER. 
807 
ments were repeated again and again until the logarithmic decrement became sensibly 
constant in the different experiments.^ 
In reducing the observations, the following plan was adopted in those cases where 
the decrement of the amplitude was comparatively slight. Suppose that a L , b 1 ; 
a 2 , b . 2 ; <x 3 , b.,, and « 4 are seven consecutive readings,! the six corresponding arcs from 
rest to rest will be b 3 -fo 
2? ^2 -\-b 2 , & 2 +« 3 , ct 3 -\-b 3 , & 3 +« 4 . The means of a x +K 
h 3 +« 4 .5 ^iT a - 2 ’ c h + ^3 i O- 0 + b 2 , & 3 +a 3 , were written down, and if these agreed well 
with each other, which was almost invariably the case, the logarithm of the total mean 
was taken. Now, say that n single vibrations have taken place between the end of 
this and the beginning of the next seven consecutive readings, the difference of the 
logarithms of the first and second total means wall, when divided by n+6, give 
the mean logarithmic decrement for a single vibration. When the decrements of 
amplitude were comparatively large, the following mode of reduction v ? as used 
Suppose a x , b 1 ; a. : , b»; ci 3 , b.,, and to be, as before, seven consecutive readings, so 
that the arcs from rest to rest are a 1 -\-b 1 , b 3 -\-a 2 , Uo + ho, fn+« 3 , a 3 -\-b 3 , and h 3 + a 4 : 
the difference of the logarithms of a 1 -\-b 1 and b. ? -\-ao ; of ^d-% and a 3 + h 3 ; of a 3 + b. 2 
and & 3 +a 4 , were put down, and, if they agreed well, the mean of these differences, 
divided by three, was taken as the mean logarithmic decrement of a single vibration. 
The following experiments will furnish illustrations of the methods pursued in the 
two cases, and wall also give a fair idea of the accuracy to be attained. 
* This is very necessary, as sometimes, from slight fluctuations of temperature, the internal friction is 
very variable. I have not unfrequently had to go on experimenting for a couple of hours or more before 
the logarithmic decrement became constant. 
f In the earlier experiments seven readings were taken; in the later ones eleven readings. 
