Note 100 — Chapter LVI
Reading edition
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.