The late Palaeocene Thermal Maximum (LPTM) was a brief interval at c. 55 Ma characterized by a −2.5 to −3‰ shift in the δ¹³C of global carbon reservoirs. The geochemical perturbation probably represents a massive input of ¹²C-rich carbon to the exogenic carbon cycle. Largely unresolved issues concerning this carbon injection during the LPTM are the rates of carbon input and removal. Simple expressions are developed here to describe a δ¹³C excursion in the exogenic carbon cycle after carbon input. A change in global δ¹³C (dδ_Ex/dt) can be explained to a first approximation by a set of parameters: the initial mass and isotopic composition of the global carbon cycle (M_Ex(o), δ_Ex(o)), and the fluxes and isotopic compositions of external carbon inputs, outputs and injected carbon (F_In, δ_In, F_Out, δ_Out, F _Add, δ_Add). In general, for a given exogenic carbon cycle, a large F _Add or low δ_Add results in a larger δ¹³C excursion. Likewise, for a given negative δ¹³C excursion, a large M_Ex or low δ_Ex requires a greater input of ¹²C. Differences in F_In, δ_In, F_Out and δ_Out cause changes in the response of δ_Ex over time. For a negative δ¹³C excursion of given magnitude, a greater F_In requires a greater input of ¹²C and lessens the time for δ_Ex to return to initial conditions. A decrease in δ_Out (caused by an increase in the relative output of organic matter and carbonate) has a similar effect. Variable dM_Add/dt produces transients in δ_Ex that are related to the source function but modified by carbon removal. In theory, a well-dated and representative global δ¹³C excursion could be used to derive the carbon inputs and ouputs. Ocean Drilling Program (ODP) Site 1051 has an expanded early Palaeogene section, and recent work at this location has provided a well-dated δ¹³C record across the LPTM. This δ¹³C record contains transient variations of apparently global nature. These observed transients are best explained by a pulsed injection of CH₄ into an exogenic carbon cycle with a greater carbon throughput or enhanced burial of organic matter after carbon addition.