The viscosities of the vapours of ethane, n-hexane, cyclohexane, benzene, methyl chloride, ethyl chloride, methyl alcohol, diethyl ether, acetaldehyde, acetone and acetonitrile have been measured at temperatures 35, 50, 65 and 78 degrees C and pressures between 1 and 3 cm. Measurements were made by observing the damping of a pendulum swinging in the vapour. A linear relation between coefficient of viscosity and temperature was found in all cases. The ratios of thermal conductivity to viscosity were calculated, using thermal conductivity values obtained recently in the same temperature range. The observed values of the Eucken factor for non-polar vapours show systematic positive deviations from the theoretical values; strongly polar vapours show systematic negative deviations; weakly polar vapours show intermediate behaviour. The theoretical implications of these phenomena are discussed.