[Sidenote: Rules for calculating Heights by Means of the Barometer and Thermometers.] Section 348. Rules for calculating the Height of Mountains, when applied to those elevated Stations in the Atmosphere _attainable_ only by Means of the Balloon, will henceforward become more useful, and be more frequently practised: as the Lives of Aironauts _may_ depend on a Knowledge of their _Height_ above the Earth; which, not being determinable by _Sight_, in _all Weathers_, or at all Times, must be referred to the _Barometer_ and _Thermometers_, they carry up with them. De Luc, Horseley, Maskelyne, Shuckburgh, and Roy, have each written +ably+ on the Subject, in the _Transactions_: tho’ few have either Leisure or Inclination to follow them. Sir George Shuckburgh has made successful Attempts to smooth the Way, by Examples and Tables, yet is still too concise for actual Learners, and the Generality of those who will have Spirit enough to go before the Calculators in exploring the Atmosphere; but cannot dedicate sufficient Leisure to overtake them in their Studies. Each may therefore assist the other. 349. Whoever is at the Trouble of comparing the Observations made by Shuckburgh, with the Directions here given, will find that the latter contains the _Essentials_ of the former, with this material Difference, that the Investigation moves here by Steps, which are all pointed out to the Learner; and not by Strides. Each Step is self evident: and, by carrying Conviction to the Mind, is just what the Mind itself woud make use of, in the Attainment of any _distant_ Truth. To do every Justice to Sir George, the Merit of whose Performance wants no Eulogium; his three Precepts are copied; tho’ rather as a Memorandum for those who understand the Methods; than as plain Directions for such as are yet to learn them. It will be found likewise, that the first, second, and fourth Tables are greatly enlarged: being calculated for those _extreme_ Temperatures, and Heights, which the Balloon _only_ can attempt to reach: and the fourth Table, for greater Dispatch in computing the Expansion of the Air. The Foundation and Construction of each Table, is also methodically traced and elucidated. CHAPTER LXX. METHODS TO ASCERTAIN THE TRUE HEIGHT. Section 350. Methods to be pursued on taking and comparing Heights, in order to ascertain the true Height of any Station in the Atmosphere, by the Barometer and Thermometers. For this Purpose it is necessary, 1st, to provide a Barometer, (whose Bulb or Cistern is _large_ enough to contain all the Quicksilver in the Tube;)—into the Frame of which, a Thermometer, on _Farenheit’s_ Scale, is to be fixed or _attached_. The Use of the _attached Thermometer_ is to point out the Temperature of the Barometer. 2d. A second or _detached Thermometer_ is also to be provided.[117]