The non interacting magnetic system

LagrangeEuler

[tex]\mathcal{H}=-g\mu_B\sum^N_{i=1}\textbf{S}_i\cdot\textbf{H}[/tex]
- The hamiltonian for a system of [tex]N[/tex] non-interacting magnetic moments in a an external magnetic field [tex]\textbf{H}[/tex].

Why product [tex]\textbf{S}_i\cdot\textbf{H}[/tex] may only assume the values [tex]m_iH[/tex] where
[tex]m_i=-S,-S+1,...,0,...,S-1,S[/tex]?
[tex]g[/tex] - Lande factor
[tex]\mu_B=\frac{e\hbar}{2mc}[/tex] - Bohr magneton