If then at the Height of one Yard, the Balloon has acquired (suppose) the Levity of 1 Pound; then, if this Levity encreases in geometrical Progression; (as twice 1 is 2,) it will, at the Height of 2 Yards, have encreased to 2 Pounds: and, as twice 2 is 4;) it will, at the Height of 3 Yards, have encreased to 4 Pounds: and, as (as twice 4 is 8;) it will, at the Height of 4 Yards, have encreased to 8 Pounds: and, (as twice 8 is 16;) it will, at the Height of 5 Yards, have encreased to 16: and, (as twice 16 is 32;) the Levity will, at the Height of 6 Yards, have encreased to 32 Pounds; and so on, _doubling_ the preceding Number; at the Height of each Yard, Fathom, Rood, Mile, &c. &c. [101] _Whiston’s_ Tacquet’s Euclid, Book XI. Definition of a _right_ Cylinder, Art. 3, Page 166. [102] Archimedes’s Theorems. Proposition 33, 34; at the End of _Whiston’s_ Euclid, Page 42. [103] Inferred in the Chester Chronicle, Sept. 30, 1785. [104] The Writer not having yet been able to procure it from the London Booksellers. [105] See Chambers’s Dictionary under the Article +resistence+. [106] See his “Navires des Anciens.” [107] See “Gordon’s Principles of Naval Architecture.” Also the Balzaes and Guaraes, in Ullòa’s Voyage to America, Book 4, Chapter 9, Vol. 1, Page 183. [108] Mons. Carra proposed to ascend with two Balloons. One, a seventh Part less than the other, is to be connected by a Rope, throu’ a Pulley fixed in the equatorial Hoop of the great Balloon, to a Reel in the Center of the Car: in descending, the Reel is to be unwound: the great Balloon and Car will therefore descend, while the small Balloon remains in the Air. The Scheme is certainly practicable. See the Cut in the London Magazine for June, 1784. [109] See “Lewis’s Commerce of the Arts.” [110] See Priestley’s numerous Experiments: and that Library of _curious Investigation_, the Philosophical Transactions. [111] And _Magnitude_ of distant Objects. Bacon says that Objects are more _visible_ in an East Wind, and Sounds more _audible_ in a West Wind; being heard at a _greater_ Distance. “Historia Ventorum, P. 37, Art. 31.” [112] See Le Roi’s Uses of the airostatic Globe _at Sea_, in his “Navires des Anciens, Page 225.” [113] The _natural Figure_ of the _Dìodon-Globe-Fish_, a coloured Print of which is given in “Martyn’s new and elegant Dictionary of natural History:” where it is described as follows: “The Form of the Body is usually oblong: but when the Creature is alarmed, it possesses the Power of _inflating_ its Belly to a globular Shape of great Size;”—seems to furnish a Hint for the proper Figure of a Balloon, when the Art is more improved. The Balloon, as far as it is meant to resemble the upper Part of the Fish, is to be made stiff, with Pasteboard or _Papier-mâchè_ varnished; for, being strong, and in a permanent Form, it is more capable of continuing Air-tight: the lower Parts being _flaccid_, will be inflated, as the Balloon rises, and deflated during the Descent.