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



When the condition of the gas varies from point to point, the 

 molecules are considered as consisting of two groups, one crossing 

 from the positive and the other from the negative side of the plane. 

 Considered in opposite directions, the mean characteristics (the 

 number, mass, momentum, or energy) of these two groups are not 

 necessarily equal. They may differ in consequence of the motion of 

 the gas, the motion of the plane through the gas, or a varying con- 

 dition of the gas, and the determination of the effect of these causes, 

 particularly the last, on the mass, momentum and energy that may be 

 carried across by either or both groups constitutes the extension of 

 the dynamical theory of gases. 



In order to take account of the difference in the two groups it is 

 assumed, and so far there is nothing new in the assumption itself, 

 that the group of molecules which crosses the surface from either side 

 Avill partake of the characteristics of the gas in the region from which 

 the molecules which constitute the group have come. The first direct 

 step in the investigation is the deduction from the foregoing assump- 

 tion of two theorems (I and II), supposing that there are no external 

 forces. Taking o-'(Q) to be the approximate value of <x(Q) obtained 

 on the assumption that the gas is uniformly in the mean condition 

 which holds at the point xyz, the theorems I and II admit of the 

 following symbolical expression : — 



KQ)=<(Q)-«{|V(Q) + ^(Q)+^(Q)}. 



Where s represents a certain distance, measured from the plane of 

 reference. 



This distance, s, enters as a quantity of primary importance into 

 all the results of the investigation. 



It is proposed to call s the "mean range of the quantity Q, so as to 

 distinguish it from the mean path of a molecule. 



. s is a function of the mean path, but it also depends on the nature 

 of the impacts between the molecules. It is subsequently shown that — 



from which it appears that s oo — . 



P - 



The dynamical conditions of steady density, steady momentum, and 

 steady energy are then considered. 



Putting 2(Q) for the value of Q in a unit of volume, in order that 

 2(Q) may be steady, we have — 



^<Q)+iU f (Q) + ^(Q)=0, 



ax ay az 



whence, by giving to Q the value M, the mass of a molecule, we have 



