1 Introduction  

The afterglow of the burst of May 8, 1997, was bright for a relatively long time and produced emission from $\gamma$ rays to radio. This enabled a detailed analysis of its broad-band spectrum, confirming in great detail that in the afterglow we see synchrotron emission, and that the dynamical evolution of the expanding blast wave agrees with predictions if the blast wave dynamics are adiabatic (Galama et al. 1998a,b). In principle, one can derive the blast wave properties from the observed synchrotron spectral features. The problem is that the characteristic synchrotron frequencies and fluxes are taken from simple dimensional analysis in the published literature, so they are not suitable for detailed data analysis. We amend this situation and correct the coefficients in the equations for the break frequencies by up to a factor 10. We then use our theoretical results to infer the physical properties of the afterglow of GRB970508.