OF GASES AT HIGH EXHAUSTION'S. 
389 
measured by inches, and even feet,* and at exhaustions of this degree it is probable 
that Maxwell’s law would not hold good. 
MM. Kundt and Warburg found that for pressures between 760 millims. and 
1'5 millim. the coefficient of viscosity of air was constant, but at higher vacua it fell 
off. They, however, give no measurements of the amount of exhaustion obtained, 
simply speaking of Vacua I., II., III., and IV. 
637. As I have had considerable experience in working in high vacua, and am 
accustomed to measure with accuracy exhaustions up to the ten-millionth of an atmo¬ 
sphere and even higher, it has been proposed that I should continue these experiments 
on viscosity of gases at high exhaustions, at the same time obtaining as many other 
data and measurements as the apparatus can be made to afford. 
My experiments were commenced early in 1876, and have been continued to the 
present time. In November, 1876, I gave a note to the Royal Society on some 
preliminary results. Several different forms of apparatus have since been used one 
after the other, with improvements and complexities suggested by experience or 
rendered possible by the extra skill acquired in manipulation. The earlier observa¬ 
tions are now of little value, but the time spent in their prosecution was not thrown 
away, as out of those experiments has grown the very complicated apparatus now 
finally adopted. I will therefore not occupy time in describing earlier forms of 
apparatus, but will proceed at once to the one finally adopted. 
THE VISCOSITY TORSION APPARATUS. 
638. Plate 55, fig. 1, shows the general construction, fig. 2 (p. 390) an enlarged view 
of the torsion beam, &c., the same references applying to either figure, a is a glass 
bulb, blown with a point at the lower end, b, and sealed on to a long narrow glass 
tube c c. In the bulb is suspended a plate of mica, cl, by means of a fine fibre of glass, 
26 inches long, which is sealed to the top of the glass tube c c, and hangs vertically 
along its axis. The plate of mica is ignited and lamp-blacked over one-half, as shown. 
The tube c c is pointed at the upper end, e ; the points e and b are 46 inches apart, and 
are accurately in the prolongation of the axis of the tube. Sockets are firmly fixed at 
b and e to a solid support, so that when the tube and bulb are clamped between them 
* Thus, supposing the mean free path of the molecules of air at the ordinary pressure is the 10 ^ 00 th of 
a millimetre, at an exhaustion of the ten-thousandth of an atmosphere, the mean free path will he 1 millim. 
At one-millionth of an atmosphere the mean free path will be 10 centims., and at an exhaustion of one 
hundred millionth—by no means a difficult point to attain with present appliances—the mean free path 
will be over 30 feet. This rarefaction corresponds to that of the atmosphere at a height above the earth 
of a little more than 90 miles, assuming that its density decreases in geometrical progression as its height 
increases in arithmetical progression, and neglecting the small corrections for diminished gravity and 
temperature. As the height above the earth increases, the length of the mean free path of the molecules 
of air rapidly approaches to planetary distances; at about 200 miles height the mean free path is 
10,000,000 miles, whilst between 80 and 90 miles higher the rarity is such that the mean free path would 
extend from here to Sirius. 
3 E 2 
