70 
MR. CLERK MAXWELL ON THE DYNAMICAL THEORY OE GASES. 
positive direction 
(u-u')u § +? s (60) 
If the plane moves with the velocity u, this expression is reduced to % 2 g , where | 2 repre- 
sents the mean value of f 2 . 
This is the whole momentum in the direction of x of the molecules projected from the 
negative to the positive side of the plane in unit of time. The mechanical action 
between the parts of the medium on opposite sides of the plane consists partly of the 
momentum thus transferred, and partly of the direct attractions or repulsions between 
molecules on opposite sides of the plane. The latter part of the action must be very 
small in gases, so that we may consider the pressure between the parts of the medium 
on opposite sides of the plane as entirely due to the constant bombardment kept up 
between them. There will also be a transference of momentum in the directions of y and 
z across the same plane, 
(u-u')v^- H&jg, (61) 
and 
(u— w')w§+££ ? , . (62) 
where & and represent the mean values of these products. 
If the plane moves with the mean velocity u of the fluid, the total force exerted on the 
medium on the positive side by the projection of molecules into it from the negative side 
will be 
a normal pressure | 2 g in the direction of x, 
a tangential pressure in the direction of y, 
and a tangential pressure in the direction of z. 
If X, Y, Z are the components of the pressure on unit of area of a plane whose 
direction cosines are l, m, n, 
X=/f 2 § -j-m&o | 
mrfq +n'/i%%, i (63) 
When a gas is not in a state of violent motion the pressures in all directions are nearly 
equal, in which case, if we put 
rt+^+r?=3p, (64) 
the quantity^ will represent the mean pressure at a given point, and f 2 g>, tfg, and £ 2 ^ will 
differ from p only by small quantities ; £%, and fyg will then be also small quan- 
tities with respect to p. 
Energy in the Medium — Actual Heat. 
The actual energy of any molecule depends partly on the velocity of its centre of 
gravity, and partly on its rotation or other internal motion with respect to the centre of 
gravity. It may be written 
iM{( M +i) 2 +( v +^) 2 H-(w+^) 2 }+iEM, 
(65) 
