Note 17 — Chapter VII

It has been said that the

apparent

Height from the Balloon to the Ground was 7 Miles, viz. 4 to the Summit of the Clouds, and 3 below: and the

barometric

Height was about a Mile and half, viz. 2332 Yards,

a Calculation of which will be given

.

If then we divide that Height or Distance into 2 such Parts, that the greater shall be to the less as 4 to 3; we obtain the Length of each Part; i. e. the barometric Height from the Balloon to the Summit of the Clouds, and thence to the Earth; which is done thus:

Suppose the whole Distance to be any Line, as A. B. to be divided in C. Then, as 7 is the whole Line, and 4 the greater Part; say, as the whole 7 is to the greater Part 4, so is the whole Distance to a fourth Term proportional, which will be equal to the greater Distance sought:

Whole Distance in Yards. Greater Distance in Yards.

Thus 7, : 4 :: 2332 : 1332⁠4⁄7 Ans.

4

———

7)9328

2332 the whole. 1332⁠4⁄7

1332⁠4⁄7 being the greater Distance found; take the greater from the whole, and then will remain the lesser Distance wanted, viz. 999⁠3⁄7: the 1332⁠4⁄7 = the greater Distance, and 999⁠3⁄7 = the lesser Distance: and adding the Fractions 4⁄7 3⁄7 = 1 to the 999; we have 1332 Yards for the greater Distance, or Height of the Balloon above the Summit of the superior Clouds: and 1000 Yards for the less Distance, or Height from the Earth to the Summit of the superior Clouds.

Note. The Line A. B. here selected is the famous Measure of (half) a mathematical Rhinland and Roman Foot, according to Snellius. (See Geographia Generalis of Varenius, published by Newton. Lib. 1. Cap. 2. De variis Mensuris.)