The Gompertz transform of the distribution function for the age at death expresses mortality in a form R = R0ealpha t where R0 is themortality at time zero and α is the rate of increase ofmortality, frequently taken as the rate of ageing. The slope ofthe line α is frequently used as a measure of the rate of ageing.It is argued that it is incorrect to use α in this way. Tosupport this contention, a paradox is produced whereby selectionfor longevity increases α, which could lead to the absurdconclusion that selection for longevity increases the rate ofageing.