A method for correcting the beam hardening artefacts in computerised tomography is introduced. After an initial reconstruction of the object the uncorrected image is used to estimate the amount of bone and tissue along each ray. The bone and tissue lengths obtained from the initial reconstruction are used to add a correction term to each original projection. A second reconstruction using the corrected projection data yields the final beam hardening corrected image. The results are presented showing the application of this formalism to a mathematical phantom. The instability of the correction method with respect to various possible sources of error is examined.