A High Pressure Automated Lag Time Apparatus (HP-ALTA) was used to measure the nucleation curves of Structure I (sI) - forming methane hydrate. The instrument applied a large number of constant cooling ramps to a quiescent water sample contained in a glass sample cell under isobaric conditions and recorded maximum achievable subcooling distributions. Survival curves were constructed from the measured data and nucleation curves were derived from the survival curves using the model-independent method we had recently devised. The convergence of nucleation rates with the number of experimental runs was observed after approximately 400 runs which suggests that sampling of 400 nucleation events is sufficient for the unambiguous determination of the nucleation curves. The impact of the experimental cooling rates and the approximations used in the derivation of the nucleation curves was also assessed in details. Importantly, the derived nucleation curves continuously covered over a range of 15 K. The obtained nucleation curves were then compared to the nucleation rates of methane hydrate measured at several subcoolings by Makogon and analyzed by Kashchiev and Firoozabadi. Our nucleation curves yielded nucleation rates that were broadly similar to but somewhat lower than those of Makogon and Kashchiev and Firoozabadi at the relevant subcoolings.