Referee's report by William Hopkins, on a paper 'On the geometrical representation of the expansive action of heat, and the theory of thermo-dynamic engines' by William John Macquorn Rankine Recommended for publication in the 'Philosophical Transactions of the Royal Society'. The author's 'clear and systematic treatment' of the subject outweighs the fact that the results have already appeared elsewhere. The method of arriving at the results appears to be original. Subject: Physics, Mathematics [Published in the Philosophical Transactions of the Royal Society] [1854]