The first nucleation theorem is the most widely used method to assess atmospheric new-particle formation mechanisms from particle formation rate measurements. The theorem states that the slope (partial derivative log J)/(partial derivative log C) of the nucleation rate J versus the concentration C of a nucleating compound gives the number of molecules of that species in the critical cluster. In principle, the derivation of the theorem is solid, but it contains very restrictive assumptions, the validity of which is questionable in realistic situations. It applies only for systems where clusters grow by addition of single molecules, and there are no external losses. In addition, application of the theorem to experimental data requires that the nucleation rate can be determined from particle concentration observations. This work presents simulation results on particle formation rates in atmospherically relevant conditions. We show that the slope of the nucleation rate in realistic conditions differs from that in an ideal situation. The slope analysis can easily lead to erroneous conclusions on the critical cluster size, and should therefore not be used to interpret experimental data. (C) 2014 Elsevier Ltd. All rights reserved.