810 
PROFESSOR O. REYNOLDS ON CERTAIN DIMENSIONAL 
From which it appears that in the same gas 
see - .( 82 ) 
P 
when not limited by the solid objects. 
The general case of transpiration. 
95. The equation (78) is obtained on the assumption that 5 is so small compared 
with the diameter of the tube, that the layer of gas through which the influence of the 
surface of the tube extends may be neglected, and hence this equation cannot be taken 
as the law of transpiration when s~ comes to be limited by the diameter of the tube. 
And besides this, it is necessary to consider the value of u c , which cannot be done 
without considering the layer of gas throughout which the effect of discontinuity at the 
surface extends. 
In order to take the discontinuity at the surfaces 2 =Tc into account, the values of 
<x r (M) and cr-(Mu) must be taken from equations (53) and (54a). These values sub¬ 
stituted in equations (66) and (67) give equations which correspond to equations (69) 
and (70), but which involve the quantity q—q, which quantity it will be well to 
examine before proceeding to the substitution. 
The value of q — q. 
96. Remembering that q and s. 2 are taken respectively to represent the mean range 
of the quantity Q for the groups of molecules which have w respectively positive and 
negative, and taking ,sq s 2 to represent the values of «q q at the surface z=c, we may 
express -q—q as a function of s, c, and z. 
The fact that q=q=s when the point considered is without the range of the 
influence of the surface, shows that whatever may be the value of s\ — s' 2 , q—q 
gradually diminishes as the point considered recedes from the solid surface, until at 
some distance depending on s at which the mean range is unaffected by the surface 
s | —q= 0. It also appears from the fact of the gas being symmetrical about the 
axis of the tube that q— s 2 is zero at the axis, so that even if the value of q is limited 
by the surface, q approximates to q as the point considered approaches the axis of 
the tube. 
The definite manner in which q — q varies across the tube could only be deduced by 
taking into account the distribution of velocities amongst the molecules; but as q—q. 
must change after a continuous manner from one surface to another, we may take for 
an illustration, or even for an approximation, any law of variation which fits the 
extremes. 
Such a law is given by 
C—Z C + Z 
a x s — 
2c 
1 — e~ 
in which a L is a numerical factor depending only on the nature of the gas. 
q q —(sq s 2 ) 
(83) 
