128 PROCEEDINGS OF THE AMERICAN ACADEMY. 



ence of pressure between the two sides of the plate, where the mean 

 pressure in the gas was 760 mm. His experiments established the 

 fundamental law that the difference of pressure reached is increased by 

 increasing the difference of temperature between the surfaces of the 

 porous plate, and that, given a certain difference of temperature, the 

 amount of the gas transpiring, or the height to which the difference 

 of pressure will grow, is governed by the relation between the mean 

 free path of the molecules and the diameter of the conducting space. 

 When, at a given pressure, the diameter of this space is diminished, 

 the difference of pressure attainable is increased. Since this is true, 

 it is readily seen that, when the transpiration spaces are large, it is 

 only necessary to reduce the density of the gas to get the same re- 

 sults as those obtained at greater densities with spaces of capillary 

 dimensions. 



Sutherland ^^ renews the theoretical discussion of this phenomenon, 

 and by a different method arrives at substantially the same result. His 

 result appears in an expression relating the difference of pressure to the 

 mean pressure, the coefficient of viscosity, the diameter of the transpira- 

 tion tube, and the mean velocity of the molecules. He then considers 

 the case of a circular vane of badly conducting material, placed in a 

 circular space, which it fits rather closely, and, assuming that in the 

 transpiration space thus formed the temperature of the gas is controlled 

 by that of the vane and the surrounding annulus, he deduces an expres- 

 sion for the force which will tend to push the vane out of the plane of 

 the annulus, when one side of the vane and the corresponding side of 

 the annulus are heated. His result is expressed thus: 



^^ Ap + B+ljp ^^^^ 



where F is the force on the vane in arbitrary measure, and 2^ the 

 mean pressure expressed in, say, millimeters of mercury. 



Sutherland has submitted his equation, with a considerable degree 

 of success, to the experimental test, using data accumulated by Crookes 

 in his work, on viscosity of gases at high exhaustions. Crookes meas- 

 ured not only the logarithmic decrement of the vane of mica men- 

 tioned above, but also the angle through which the vane was deflected 

 when the light from a candle was made to fall on the blackened half 

 of one of its surfaces. By measuring /'^and the pressure for three dif- 

 ferent pressures, the constants in (IV) can be determined, and then, 



" Phil. Mag., 42, 1896. 



