400 
MR. W. CROOKES OK THE VISCOSITY 
without a sudden change in direction. They evidently meet the top line of zero 
pressure long before the logarithmic decrement of 0’00 is reached. This means that in 
an absolute vacuum there would still be a measurable amount of viscosity. This is 
probably due to the viscosity of the glass torsion fibre, for it has been ascertained that 
glass is not perfectly elastic, but will take a permanent set if kept under constraint for 
a considerable time. I give an instance which has come under my own notice. In 1862 
I purchased a piece of glass lace, and some spun glass from which the lace was made. 
The spun glass is in long straight threads, about O'OOl. inch diameter, and has 
occasionally been used for torsion fibres. The fibres of which the lace was made were 
originally straight, but the twists and bends in which they have been kept for 
eighteen years have permanently altered their direction, and on dissecting a portion 
of the lace the component fibres remain distorted and bent, even when free to resume 
their original shape. 
Were glass perfectly elastic the logarithmic decrement in an absolute vacuum would 
probably be equal to zero: there would then be no diminution in the arc of vibration, 
and the torsion fibre once set swinging would go on for ever. 
VISCOSITY OF AIR. 
653. The mean of a very large number of closely concordant results gives as the 
logarithmic decrement for air for the special apparatus employed, at a pressure of 760 
millims. of mercury and a temperature of 15° C., the number 0'1124. According to 
Maxwell the viscosity should remain constant until the rarefaction becomes so great 
that we are no longer at liberty to consider the mean free path of the molecules as 
practically insignificant in comparison with the dimensions of the vessel. 
My observations show that this theoretical result of Maxwell’s is sufficiently near 
the actual fact in air to confirm the accuracy of his reasoning, although there is a 
variation showing that disturbing influences are at work which make the coefficient of 
viscosity (taken as proportional to the logarithmic decrement) not quite constant. 
The results are embodied in the following table and diagrams. 
The first half of Table I. gives the viscosity of air, in so far as it is represented by 
the log. decs., at pressures intermediate between 760 millims. and 0'76 millim. (1000 
millionths of an atmosphere). In order to avoid the inconvenience of frequent refer¬ 
ence to small fractions of a millimetre, I now take the millionth of an atmosphere* 
( = M ) as the unit instead of the millimetre. The second half of the table is therefore 
given in millionths, going up to an exhaustion of 0’02 millionth of an atmosphere, the 
highest point to which I have carried the measurements, although by no means the 
highest exhaustion of which the pump is capable. 
At the high exhaustions, in addition to the observed results, I have given the 
calculated mean free path of the molecules. 
* 1 m = 0'00076 millim.; 1315V89 M = 1 millim. 
