318 Prof. 0. Reynolds on certain Dimensional [Feb. 6. 



and 



fJ^L \ and fJ x are zero when - is zero, and unity when - is infinite. 



All these functions varying continuously between tlie limits here 

 ascribed. Also — 



A,j depends on the nature of the surface of the tube, but not upon 



the nature of the gas. while 

 \. : and \ 3 may depend both upon the gas and the surface. 



From this equation, which is the general equation of transpiration, 

 the experimental results, both with regard to thermal transpiration 

 and transpiration under pressure, are deduced. 



Impulsion. 



In dealing with the second case, that in which the isothermal 

 surfaces are curved, the three conditions — steady density, momentum, 

 and energy — are all of them important. 



These conditions reduce to an equation between the motions of the 

 gas the variation in the absolute temperature and the variation in the 

 pressure, with coefficients which involve the ratio of the mean range 

 to the dimensions of the radii of curvature of the surfaces. The 

 equation corresponds to the equation of transpiration, and as applied 

 to the case in which heat is being conducted through a gas which is 

 constrained to remain at rest, the equation becomes — 



p-p, 2 ,M_g /t\ 



. , . /—a u 



or taking s= \/^-~ 



/t 2 M d 2 



p—pi being the excess of pressure in the direction of. and due to. the 

 variation of temperature. In the abstract of a paper read in April 

 last. Professor Maxwell gives an equation which, transformed into my 

 svnibols is — 



which only differs from mine in the coefficient — 3. As Professor 

 Maxwell indicates that he has obtained his result without taking 

 account of the tangential stresses, this difference is not a matter of 

 surprise. 



Besides the broad lines of the investigation which have been men- 

 tioned in this abstract, there are many minor points of which it is 



