[99]To find the Direction of an upper Current, without the Inconvenience of rising above the Level which the Aironaut has fixed on.
This the Abbé Bertholon has hinted at, by Means of a smaller Balloon.
The Dimensions of which, must however be so large; that, allowing for the Evaporation of Gass, it will just rise with the Weight of a Quantity of Cord, a Mile and half, for Instance, in Length: and have sufficient Room left within, to admit of the Expansion of Gass without Rupture.
The Pioneer-Balloon may be taken up, empty, and filled with Gass necessarily escaping from the mouth of the great Balloon, when stationary: and may be sent up with a Cord, fastened to the Center above the Car of the great Balloon, to reconnoitre the superior Currents: or it may be only filled in Part; and made to descend, and discover the lower Currents.
See “Des Avantages de Ballons, &c. Page 72.”
[100] As the Heights of the Atmosphere encrease in an arithmetical Progression; the Densities are said to encrease in a geometrical Progression: which is a mathematical and pedantic Mode of Expression.
For arithmetical Progression here means no more than the Height of 1, 2, 3, 4, 5, 6, &c. &c. Yards, Fathoms, Roods, or any other equal Interval.
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.