_A Discourse of the Rule of the Decrease of the height of the _Mercury_ in the Barometer, according as Places are elevated above the Surface of the Earth; with an Attempt to discover the true Reason of the Rising and Falling of the _Mercury_, upon Change of Weather. By _Edm. Halley_._ The Elastick Property of the Air has been long since made out, by Experiments before the _Royal Society_, and elsewhere; and the Resistance of its Spring is found to be nearly equal to the Weight or Force that compresses it; as also, that the Spaces the same Air occupies, under differing Pressures, are reciprocally as those Pressures: It has been shewn likewise by undoubted Experiment, that the specifick Gravity of the Air, near the Earth's Surface to that of Water, was once as 1 to 840; again as 1 to 852; and a third time, in a very large Vessel holding 10 Gallons, as 1 to 860; all which, considering the Difficulty of the Experiment, agree well enough, the Mercury standing at all those times about 29 Inches ¾: But by Reason 'twas Summer-weather, and consequently the Air rarified, when all these were tried, we may without sensible Error say in round numbers, that the Barometer standing at 30 Inches, and in a mean State of Heat and Cold, the specifick Gravity of the Air to Water, is as 1 to 800. By the like Trials the weight of Mercury to Water, is as 13½ to 1, or very near it; so that the weight of Mercury to Air, is as 10800 to 1; and a Cylinder of Air of 10800 Inches or 900 Feet, is equal to an Inch of Mercury; and were the Air of an equal density like Water, the whole Atmosphere would be no more than 5,1 Miles high, and in the Ascent of every 900 Feet the Barometer would sink an Inch. But the Expansion of the Air increasing in the same proportion as the incumbent weight of the Atmosphere decreases; that is, as the Mercury in the Barometer sinks; the upper Parts of the Air are much more rarified than the lower, and each Space answering to an Inch of Quicksilver, grows greater and greater; so that the Atmosphere must be extended to a much greater height. Now, upon these Principles, to determine the height of the Mercury at any assigned height in the Air; and _è contra_, having the height of the _Mercury_ given, to find the height of the Place where the Barometer stands, are Problems not more difficult than curious; and which I thus resolve.