There was a major epidemic of the foot-and-mouth-disease virus among cattle herds in the UK in 1967-68 which showed a very rapid early spread, a much slower later spread, and eventually infected 12% of herds in the core epidemic area. A simple discrete-time version of a susceptible-latent-infectious-removed epidemiological model is used to generate a set of estimates of the transmission rate. This parameter has high values over the first few days, then the values are lower and they subsequently decline. The early high values are consistent with the view that unusual meteorological conditions produced exceptionally good conditions for wind-borne spread of the virus over the first few days. The corresponding basic reproduction number, Rzero, is estimated as 38.4. Subsequent low values of the transmission rate correspond to a value of Rzero of 2.0; this is within the range of estimates made from the observed ratio of secondary to primary outbreaks for 25 other epidemics. Prophylactic control measures, such as vaccination, would have to be extremely effective to prevent epidemics with the higher Rzero value.