  We present a dispersion relation in the pion-mass squared, which static
quantities (nucleon mass, magnetic moment, etc.) obey under the assumption of
analyticity in the entire complex $m_\pi^2$ plane modulo a cut at negative
$m_\pi^2$ associated with pion production. The relation is verified here in a
number of examples of nucleon and $\Delta$-isobar properties computed in chiral
perturbation theory up to order $p^3$. We outline a method to obtain relations
for other mass-dependencies, and illustrate it on a two-loop example.
