146 Mr. 0. Reynolds on Thermal Transpiration 



means of taking account of the action of a solid surface on 

 the gas to which it is adjacent. 



When the idea of thermal transpiration first presented itself 

 I was acquainted with Maxwell's paper, and through this 

 knew of Clausius's work ; but I had not read his paper and 

 knew nothing of his method, so that I was not aware that he 

 had already introduced expressions for the inequalities of the 

 opposite groups of molecules in form of a series of ascending 

 powers of the mean path of the molecules, the coefficients 

 being the differential coefficients of the varying characteristics, 

 in the case of varying temperature. 



But having formed my conception of the mechanical 

 actions, from which I inferred the existence of the property 

 of thermal transpiration as the consequence of a definitely 

 dimensioned structure when the condition of the gas varied 

 in more than one dimension in space, my object being the 

 study of the dimensional properties which can only be studied 

 in three dimensions in space, I adopted a form of equation 

 which, while perfectly general, admitted of the expression of 

 the inequalities resulting from the variation of any charac- 

 teristic whatsoever of the gas for any group of molecules 

 distinguished by direction, in series of ascending powers of 

 the mean-range (or parameter of the dimensions of structure) 

 in three dimensions in space. 



This mathematical system admits of the consideration of 

 such discontinuity as results when the gas is bounded by a 

 solid surface. kSince at points in the gas of which the dis- 

 tances from the surface are small compared with the normal 

 mean-range, the range of any group leaving the surface is 

 limited by the distance of the point from the surface. 



The action on which thermal transpiration depends when 

 gas at constant pressure but conducting heat is bounded by a 

 solid surface parallel to the direction of conduction, say x, is 

 the sum of the mean components of momentum in the direc- 

 tion x of the two groups of molecules distinguished by the 

 signs of their component velocities parallel to x, which are 

 brought up to the surface by their component velocities per- 

 pendicular to the surface, say in direction z. If the com- 

 ponent momenta of these groups are equal and opposite, 

 then the condition of the gas at constant pressure will be 

 steady ; but if they are not equal and opposite, and if the 

 corresponding groups leaving the surface have equal and 

 opposite momenta in direction x of the surface, in consequence 

 of the action there will be a tangential force between the 

 surface and the gas. And it thus appears that, although the 

 prime cause of thermal transpiration is that relation between 

 the rates of variation of molecular velocities and density which 



