The Relationship Between the Bulk Modulus of Elasticity of a Complex Tissue and the Mean Modulus of its Cells

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Abstract
A relationship has been derived mathematically between the bulk modulus of elasticity of a leaf, E, measured by the pressure bomb technique, and the individual cellular bulk moduli, e, of the leaf tissue as measured by the pressure probe technique. A number of examples have been worked out that shows that E underestimates the mean value of e by less than 10 per cent in most circumstances. Within 2 per cent, E equals the ‘mean’ value of e weighted according to the water content change of each cell expressed as a fraction of the water content change of the whole leaf when the water potential. ψ, changes by a small amount. An analysis of the sources of error involved in the evaluation of E by the pressure bomb technique reveals that E can be calculated within an error of 10 per cent from values of ψ and water loss, We; this error is about the same as the error in e measured on individual cells by the pressure probe technique.