More recent investigators in Germany have attacked the problem mathematically. Among these may be mentioned Edith Einstein in 1922. She found an expression for the pressure be tween two plates, one of which was hotter than the other. Using the Maxwell-Boltzman law for the partition of the energy among the three translational degrees of freedom of the mole cules, she arrived at the result that the normal component of the pressure is proportional to the gas pressure and to the square of the rate of flow through the gas.
In 1926 Sterntal, starting with the same assumptions but intro ducing the possibility of internal vibratory motion which may absorb energy and applying the Maxwell-Boltzman laws to all these degrees of freedom, showed that the normal pressure is proportional to the first power of the rate of flow of heat instead of its square.
His result is in fair agreement with experiment, while the terms which E. Einstein obtained were second order ones about io,000 times smaller.
Consider two parallel plates in an enclosure in which the gas pressure p is sufficiently low for the distance between the plates to be small compared with the mean free path of the molecule. Let and be the absolute temperatures of the plates and T that of the containing vessel, then the pressure p' between the plates is related to p by the formula If one of the plates is at the same temperature as the containing vessel, i.e., if equals T, we have The excess pressure F which tends to move the plates is - - It is assumed that the molecules take on impact the temperature of the plate; this, probably, is not quite true so that the formula is only an approximation.
Knudsen designed a number of gauges, most of which depended on a sudden change of temperature brought about by an ad mission of steam to one portion of the instrument. During the interval before radiation and conduction have established equality of temperature throughout, repulsion of a small moving part occurs; this motion is taken as a measure of the pressure. Other gauges have been devised by Angerer (1913), by Woodrow (1914) and by Schrader and Scherwood (1918), in which electrically heated strips repel small suspended vanes.
Oeuvres, ii. p. 667 ; Crookes, Phil. Trans. (1876), p. 325; Schuster, Phil. Trans. (1876) ; Reynolds, Phil. Trans. (1876) ; Pringsheim, Ann. der Phys. (1883) , p. 32 ; Nichols, Phys. Rev., No. 4 (1897), P. 297; Nichols, Astrophys. foam., 13 (1901), P Ioi; Hull, Science, 16 (1902), p. 175; Webb, Phys. Rev. 3o (19m), p. 0. Reynolds, Proc. Roy. Soc. (1874) ; E. Einstein, Ann. der Phys., 69 (1922), P. 245; Sterntal, Zeit. fiir Phys., 39 (1926), P. 341; Knudsen, Ann. der Phys., 32 (19o9), p. 8o9. Some of these gauges are described in detail in Vacuum Practice by Dunoyer. Also Gerlach and Westphal, Verh. der D. Phys. Ges., 218 (1919) ; Gerlach, Zeit. fiir Phys., 207 (1920) ,• A. Einstein, Zeit. fur Phys., 27 If. (1924), p. 1; Hettner, Zeit. fur Phys., 16 345 (1923) ; 27 12 (1924) ; 37 179 (1926).