~l 
= 
w 
Persistence of Molecular Velocities. 
after collision, 
Tall gayie es 
(25k + 6h? +1) 
1 Vu(L +22) 
of which the value is found to be 
I 1 ids 
i (1 =f Ree loSai(4/ 24 »), 
or “4()6. 
§ 3. If we denote this quantity by 0, we see that, roughly 
speaking, a molecule which has travelled a distance in a 
given direction since its last collision, may be expected to 
have travelled a distance 0% on its previous free-path, 0? on 
the free-path preceding this, and so on. It may therefore be 
supposed to have travelled a total distance 
Ge ee Cee ct 2 ee eee ei 
in this direction, and the value of this series is 1 « a: 
§4. Thus, in the diffusion of gases, we must regard 
the “free-path”’ of the usual formula as of length 
(1—@)-! times that contemplated by the simple theory. 
Putting 0=-406 we find that (1—@)—'=1°684. 
§ 5. In the problems of viscosity and conduction the case 
stands differently. Diffusion may be regarded as a transport 
of qualities, and velocity and conduction as a transport of 
quantities. There is the essential difference that the qualities 
associated with a molecule—its chemical composition in the 
present instance—cannot be affected by collision, whereas 
the quantities associated with a molecule—quantities of energy 
and momentum respectively when dealing with conduction 
and viscosity—are altered by collisions. As a simple hypo- 
thesis, we may suppose that at each collision, half of the 
excess of either quantity is imparted to the colliding molecule. 
We then replace expression (ii1.) by 
i oe Se rn at ee 
| 
— ee 
ee ee ee PS ee eer | 
of which the value is oe The simple free-path must 
2 
therefore be multiplied by a factor (1—430)-*, of which the 
value, on taking @=:406, is found to be 1°2947. 
This correcting factor leads to the formule: used in the 
preceding paper. 
a 
