1879.] Properties of Matter in the Gaseous State. 



317 



the condition of steady density, for steady momentum Q has severally 

 the values Mm, Mi', M.iv, and for steady energy Q=M(w 2 + v 2 + w 8 ). 



The equations of motion are then applied to the particular cases 

 which, it is the object of this investigation to explain. Two cases are 

 considered. 



The first case is that of a gas in which the temperature and pressure 

 vary only along a particular direction, so that the isothermal surfaces 

 and the surfaces of equal pressure are parallel planes ; this is the case 

 of transpiration. 



The second case is that in which the isothermal surfaces and 

 surfaces of equal pressure are curved (whether of single or double 

 curvature) ; this is the case of impulsion and the radiometer. 



Transpiration. 



As regards the first case, the condition of steady energy proved to 

 be of no importance, but from the conditions of steady momentum and 

 steady density, an equation is obtained between the velocity of the 

 gas, the rate at which the temperature varies, and the rate at which 

 the pressure varies, the coefficients being functions of the absolute 

 temperature of the gas, the diameters of the apertures, and the 

 ratio of these diameters to the mean range, which coefficients are 

 known for the limiting conditions of the gas, i.e., when the density is 

 either very small or very large. 



The most general form of this equation is — 



o -V*{*©fl-< £ )?Ki)}. 



in which Q is the mean velocity of transpiration along the tube, which 

 is taken in the direction of the axis of x. M is the mass of a molecule, 

 p the pressure of the gas, t the absolute temperature, and c the semi- 

 distance across the tube. 



In which A, m, m' depend only on the shape of the section of the 

 tube. 



- f is of the order — when - is zero, and is finite when - is infinite, 



s s s 



"1^— ^ an( l f 3 {~J are unu T when - is zero, and zero when - is infinite, 



