Static friction may not be proportional to normal reaction

Actually static friction $\left({\text{f}}_{\text{s}}\right)$  depends on a applied force F

i.e. ${\text{f}}_{\text{s}}=\text{F}$  for $\text{F}<{\text{f}}_{\text{ms}}$

So ${\text{f}}_{\text{s}}$  is not proportional to normal reaction N.

We have observed that ${\text{f}}_{\text{s}}=\text{F}$

i.e. ${\text{f}}_{\text{s}}$  adjust its value such that it is equal to applied force therefore ${\text{f}}_{\text{s}}$  is called self adjusting force.