GASES ARISING FROM INEQUALITIES OF TEMPERATURE. 
253 
conditions of the gas at the surface, the expression in equation ( 22 ) is a much less 
accurate approximation to the actual distribution of velocities in the gas close to the 
surface than it is in the interior of the gas. We must, therefore, consider the surface 
conditions at which we arrive in this way as liable to important corrections when we 
shall have discovered more powerful methods of attacking the problem. 
For the present, however, we consider only terms of three dimensions or less, and 
we find 
Pi€i=—p{ 2rr ) 1 (Rd) 4 ( 1 +la 2 )'| 
P-2%2— p(27r)”“(R0) i (l+^a 2 ) J 
pi£ p 7 i = ^pR0a/3 — |p(27r)~ i Ptda 2 /3~j 
P 2 & 2 V 3— \p^ H" t>/>( 27r) -i R#a 2 /3 | 
(64) 
(65) 
Substituting these expressions in equation (63), and neglecting a 2 in comparison 
with unity, we find 
(2— f)pPv6a/3-\-f(2Tr)~ }:: pR l 6d 2 /3-\-2j'{2TT) *(1 +^a 2 )(lt^) i pv=0 . . . (66) 
If we write 
NfMIffllj-l).(67) 
and substitute for a/3 and a z /3 their values as given in equations (54) and (51), and 
divide by 2(pp)% equation (66) becomes 
_r( dv _ S A* cl ~ 6 \ _ 3 ^ d6 —o 
V ~'^\dx 2 JOdxdy) 4 pO dy~ ° * ‘ ‘ 
If there is no inequality of temperature, this equation is reduced to 
,dv 
v—G— 
dx 
■ ( 68 ) 
• (69) 
If, therefore, the gas at a finite distance from the surface is moving parallel to the 
surface, the gas in contact with the surface will be sliding over it with the finite 
velocity v, and the motion of the gas will be very nearly the same as if the stratum of 
depth G had been removed from the solid and filled with the gas, there being now 
no slipping between the new surface of the solid and the gas in contact with it. 
The coefficient G was introduced by Helmholtz and Piotrowski under the name 
of Gleitungs-coefficient, or coefficient of slipping. The dimensions of G are those of a 
line, and its ratio to l, the mean free path of a molecule, is given by the equation 
HO- 1 ). (70) 
Kundt and Warburg found that for air in contact with glass, G= 2 /, whence we 
find/=i, or the surface acts as if it were half perfectly reflecting and half perfectly 
absorbent. If it were wholly absorbent, G=f7. 
