167 
making a second determination; by this procedure a reduction of 
the moment of inertia of the sphere to the temperature of liquid 
air was avoided. In this manner we found 7-—7, = 0.090. 
Afterwards according to the value of 4 which was ultimately 
arrived at, this difference appeared to be still about 10°/, too small ; 
this may be explained by considering that probably the friction of 
the sphere in the vapour close to the liquid may have given a small 
but appreciable increase of the time of swing'): we have there- 
fore thought it preferable to calculate the difference 7— 7, by means 
of the second equation 28), substituting for Z” the value obtained 
from the second equation (30) by means of the approximate value 
of 4 which is found by taking 7’= 7’). In this manner we found 
jae 
SU bh 00050 
7, 
and hence 
T—T,=0,105 , T, = 20,923. 
In caleulating ZL’ and LZ” the moment of inertia must be used 
which the vibrating system possesses, when the sphere is at the 
temperature of liquid air (80° K.). Taking according to HENNING’s 
measurements *) as the mean coefficient of expansion of brass between 
room-temperature and temperature of liquid air (a difference of about 
200°) the value of 0,00001644, the radius of the sphere at 80° K. 
becomes R= 1.921 *), and therefore K = 370.0 and A =173,2 + 
370,0 + 27,8 = 571,0. 
With #= 0.03975 it follows according to (28) that 
i ate 
This quantity, as explained (IV § 5), refers to the complete friction 
experienced by the oscillating system and from it the coefficient L’, 
corresponding to the friction of the liquid by itself has yet to be 
derived. For this purpose further experiments were made with the 
1) As the sphere was lowered to take the tension off the wire and came into 
contact with the liquid air, the latter boiled up with great vigour showing that 
the temperature of the sphere had risen considerably above that of the liquid air. 
Very likely this is an additional reason, why 7—T) was found too small. 
2) This will be seen to be the opposite procedure to that indicated in Comm. 
148) (p. 784). 
8) Ann. d. Phys., (4), 22, 631, 1907 
4) This is the equatorial radius (comp. V,§2); in view of the preponderance 
of the friction on the equatorial parts of the sphere it would be incorrect to take 
a mean between the two radii. A more exact treatment of the problem in which 
the very small deviation from the spherical shape would be taken into account 
could be considered as altogether superfluous for the present purpose. 
