The path lengths of monochromatic muons emerging in the $pi to mu u_{mu} $ decay were measured by the coordinate method with the view to determine their energy by path length. The dispersion of muon energy measurements by this method was $ sigma_{mu}
= (0.11 pm 0.01)$ MeV, which corresponds to the accuracy of $ sigma approx 2.7%$ of the energy of a charged particle estimated by its path length in nuclear emulsion. The developed method will enable measurements of electron energies in $2beta $ decay ($sim 3$ MeV) to an accuracy of $ sigma approx 5%$.
