where f(v_x) is called the distribution function for x -component of velocity.
Similarly,

(4.67)

and  

(4.68)

(4.69)

Some of the molecules of have y -component velocities lying between v_y and v_y + dv_y and let this be represented by . A differential of second order  has been used, since this is a small fraction of an already small fraction, but still large enough to contain many molecules. Since the number of molecules is large, the following relation holds good.

(4.70)

(4.71)

Similarly, represent the number of molecules whose velocity components would lie between v_x and v_x + dv_x, v_y and v_y + dv_y and v_z and v_z + dv_z. Therefore,

(4.72)

The number of representative points per unit volume, or the density of point in velocity space, represented by ρ, is

(4.73)

Since the velocity distribution is isotropic, the density is the same in any volume element so that

(4.74)