${\displaystyle \text{d}N=2N\cdot \frac{m^3}{h^3}\cdot \frac{\text{d}u\cdot \text{d }v\cdot \text{d}w}{1+\text{exp}{\displaystyle \left(\frac{E-E_{\text{M}}}{kT}\right)}}}$

where
N is the total number of particles
m is the mass of the particle
T is the thermodynamic temperature
k is the Boltzmann constant
h is the Planck constant
E is the kinetic energy of a particle,

${\displaystyle E=\frac{m}{2}\left(u^2+v^2+w^2\right)}$

E_M is the inner work function
dN/N represents the probability that a particle has its components within the intervals considered.