Radius of the $\pi$-meson and the proton and analytic properties of the form factor

On the basis of the analytic properties of the electromagnetic form factor, upper and lower limits for the mean square radius of elementary particies are established by different methods. The first method uses only the experimental distribution of the modulus of the form factor in the annihilation channel; the second uses also the experimental value of the form factor at a certain space-like point. Both methods lead to within the limits of the experimental errors to the same value for the $\pi$-meson radius: $r_\pi=0.7\pm0.15\,F$. Lower and upper bounds are also obtained for the proton radius: $0.7\pm0.12\,F\leqslant r_p\le1.05\pm0.06\,F$.