1886.] Professor Tait on the Kinetic Theory of Gases. 
23 
where p is the density, and A. the mean free path. The product pX. 
is the same at all temperatures, so that the viscosity is as the square 
root of the absolute temperature. 
(3) The steady linear motion of heat in a gas is next considered, 
temperature being supposed to be higher as we ascend, so as to 
prevent complication by convection. It is assumed, as the basis of 
the inquiry, that : — 
Each horizontal layer of the gas is in the “ special ” state, com- 
pounded with a vertical translation which is the same for all 
particles in the layer. 
The following are the chief results : — 
(a) Since the pressure is constant throughout, we have 
P n 
2h ' 
so that njh is constant. 
( b ) Since the motion is steady, no matter passes (on the whole) 
across any horizontal plane. This gives for the speed of translation 
of the layer at x, 
(c) Equal amounts of energy are (on the whole) transferred across 
unit area of each horizontal plane, per unit of time. The value is 
E= - If nvv i(Xl n+ rJ v )l e - 5a / v ) ■ 
By the above value of p, and its consequence as to the ratio n/h , 
these expressions become 
P /5 
a ~ elx 6^ 2 \2 ] 
.5 p\ 
V 
0*06, 
(Ill , — s P l 25 r , r \ (Th 7 — & 
V --U h W(T °i- 5C 3 + C a) = ^ VAO-45. 
Since E is constant, by the conditions, we see that a also must 
be constant. Hence as hr (where r is absolute temperature) is 
constant, we have 
i (It 
t 8 - t constant, or 
dx 
t% = A + Bx* , 
