In view of the practical significance in dynamical meteorology of the problem of evaporation from areas of finite lateral extent, it is a matter of fundamental importance to test as fully as possible the applicability of the hypothetical three-dimensional model of turbulence which was introduced by the author in 1947. The present paper describes in detail the manner in which the two-dimensional system developed by O. G. Sutton, K. L. Calder and E. L. Deacon for flow over aerodynamically smooth and rough surfaces may be extended to three-dimensional diffusion of vapour over an evaporating area. The agreement obtained between theory and experiment is good at points over the area. This agreement indicates that the assumed law, introduced by the author to give the variation of the coefficient of lateral diffusivity with height above the surface, may be used satisfactorily in evaporation problems as long as attention is confined to points not too far outside the boundaries of the area. The complicated mathematical relationship previously obtained for the vapour distribution vertically above the down-wind edge of a parabolic strip is reduced to a much simpler one. This serves to bring out explicitly the relationship between the effects of the two- and three-dimensional theoretical systems of turbulent transfer at points on the central axis of the area.