Though the labours of M. De Luc, and of the excellent observers who followed him, have brought the barometrical measurement of heights to very great exactness, they have not yet given to it the utmost perfection it can attain. Some causes of inaccuracy are still involved in it; of which we ought, at least, to estimate the effects, if we cannot correct them altogether. The allowance made on account of the temperature of the air, implies in it a hypothesis that has not been examined, nor even expressed, and many other circumstances that affect the denfity of the atmosphere, have either been wholly omitted, or improperly introduced. The object of the present paper is to correct, the errors that arise from these causes, or, where that cannot be done, to assign the limits within which those errors are contained.