This is a theoretical study of an isolated plume in still air. Previous work, based on similarity concepts to give the mixing rates, is shown to be inadequate, and a new hypothesis is proposed which appears to lead to better agreement with present measurements made in the atmosphere. In particular, the similarity theory does not allow realistic initial conditions to be taken at the bottom of the plume. When the new theory is adjusted to these conditions a substantial change (in the direction needed to fit the observations) is seen in the shape of the new plume as compared to the previous similarity model. Abstract This is a theoretical study of an isolated plume in still air. Previous work, based on similarity concepts to give the mixing rates, is shown to be inadequate, and a new hypothesis is proposed which appears to lead to better agreement with present measurements made in the atmosphere. In particular, the similarity theory does not allow realistic initial conditions to be taken at the bottom of the plume. When the new theory is adjusted to these conditions a substantial change (in the direction needed to fit the observations) is seen in the shape of the new plume as compared to the previous similarity model.