140 PROCEEDINGS OF THE AMERICAN ACADEMY. 



of two marks on the volume tube of the gauge. The cathetometer is 

 used to learn when the setting is right, and to measure the mercury 

 column. 



Of course, the nearer the top of the volume tube one works, the 

 more serious the error made in setting becomes. Indeed, it is better 

 not to use a mark which is less than, say, 2 cm. from the top. 



Results. 



The following table gives the results obtained so far. In the first 

 column is given the gas pressure as measured by the McLeod gauge. 

 The pressure is expressed in millimeters of mercury. The gas em- 

 ployed in this case was air. In the second column the values of 

 the logarithmic decrement in the viscosity apparatus corresponding 

 to these pressures are given, and in the third the amount of torsion 

 given to the fibre of the transpiration instrument at the various pres- 

 sures to balance the force due to gas action on the vane. The signifi- 

 cance of the fourth and fifth columns will appear later. 



The table shows how slowly the logarithmic decrement decreases 

 at first as p is diminished. That there is an appreciable diminution 

 in I even when the pressure is great, e. g. 20 cm., is due to the fact 

 that the distance between the fixed and moving surfaces in the ap- 

 paratus is very small, and therefore the coefficient of slip, yS, is com- 

 parable with it. To put the matter in another way, I is large because 

 of the small distance between the plates, so that small relative changes 

 in it can be perceived. Yet the table shows that at a pressure of 

 5.8 cm. the resistance to the moving disk is only one half per cent 

 smaller than it is at atmospheric pressure. 



With falling pressure the rate of decrease of / increases, and for 

 pressures less than 0.01 mm. I and j(> become approximately propor- 

 tional. At such pressures the mean free path of the molecules of air 

 is over half a centimeter in length, and is therefore several times the 

 distance between the fixed and moving disks, so that the friction is 

 largely superficial. Figure 6 shows the relation between I and 2^ over 

 the range from where j) = 0.530 mm. to where p = 0.00085 mm, A 

 unit on the axis of abscissas represents a pressure of 0.01 mm., and 

 a unit on the axis of ordinates represents I = 0.00333. 



The resistance which the disk meets is due to at least two causes, 

 and we shall see that there is some evidence that there is a third. 

 There is first the friction of the air on the disk, and second, the fric- 

 tion in the suspending fibre. The former diminishes with decreas- 

 ing density of air, but the latter is a constant provided that the 

 temperature of the fibre is maintained constant, as was the case in 



