This is the first paper of a promised series on the subject here announced. In the present paper the author endeavours to shew, that in remote epochs the atmosphere was more extensive and heavier than it is now, that it contained a greater absolute quantity of oxygen, and that this quantity has gradually diminished up to our own era, and is probably still undergoing a sensible diminution. His views are founded partly on speculative considerations, of which it is not possible to give a sufficiently circumstantial abridgment, and partly on the evidence of various operations going on at or near the surface of the earth, the tendency of which must, on the whole, apparently be to diminish the quantity and proportion of the oxygen in the atmosphere. In addition to the ordinary and well known causes of deterioration, the author points out a new source of diminution to which his attention has been lately drawn. From experiments made upon the aeriform fluid discharged from the earth during an inundation, and obviously expelled by the water penetrating to a considerable depth, and displacing the gases contained in the soil, he found that this gaseous matter consists of 2.5 per cent, carbonic acid, 12.764 oxygen, and 84.736 nitrogen. Taking this observation in conjunction with many others previously made on the composition of the gaseous discharges in volcanic districts, and the gaseous contents of mineral waters, he infers that a process of oxidation is constantly going on at various depths below the earth's surface, the oxygen for which is in all probability derived by absorption of the atmospheric gases at the surface.