MONS. A. ANGOT proposes a new formula for calculating altitudes from barometric observations, based upon that given originally by Laplace. The existing method of calculation from observed monthly or annual means is found, as Plantataour has shown, to be defective, since its results exhibit an uncertainty that varies with the season, an elevated station appearing to be higher by day and in summer than at night or in winter. As an example, when the height of the Great St. Bernard is measured by comparison of barometer observations between that place and Geneva, it would appear that the height of the Great St. Bernard exhibits a diurnal variation of 17 metres in winter and of more than 47 metres in summer; while the mean of the June observations gives a height of 25 metres higher than that found from the January numbers ! These anomalies M. Angot explains by the facts that the mean temperature between the stations is not exactly equal to the half sum of the two temperatures, and that the weight of the air between the two stations is on the other hand greater when the mean temperature is low. The rather complicated formula proposed by M. Angot gives the difference in altitude by calculating directly the height of each station above an imaginary plane at which the barometric pressure is equal to 760 millims. No empirical coefficients are needed in this case, the standard constants of Regnault and others for air and aqueous vapour being taken. M. Angot has recalculated from his formula a new set of tables, involving all the corrections that must be applied to the older tables of the Bureau des Longitudes.