Abstract. An hypothesis is presented which ascribes the general increase in vessel size and decrease in vessel density from leaves to roots to a gradient of decreasing auxin concentration from leaves to roots. Application of auxin in a lanolin paste to decapitated bean stems produced a very sharp basipetal gradient of decreasing vessel number and increasing vessel size. The high auxin concentration at the point of application resulted in numerous vessels that remain small because of their rapid differentiation. The low auxin concentration further down resulted in slow differentiation and therefore fewer and larger vessels.