310. To compute the Height and Distance of the Balloon, by Means of a white Flag, or other visible Object, suspended from the Car, at a certain Distance below it.
Let the Observer take the Altitude of the Car with a Quadrant: and also the Altitude of the Object or Flag.
Then by a Case in plain Trigonometry; if the Altitude of the Car be by the Quadrant 59° = HAC, the Altitude of the Object 55° = HAO, and the Length of the Line veered out be 200 Yards, or otherwise = CO.
Then the Complement of HAO = AOH = 35°; and the Complement of the Angle HAC = ACH = 31°; and the Supplement of OAC + ACO = AOC = 145°.
Then, CAO 4° : CO 200 :: AOC 145° : AC; and Radius : AC :: CAH 59° : CH 1409 Yards, the Height of the Balloon taken at the Time.
Next, Radius : AC :: ACH 31° : AH 846 Yards, which is the horizontal Distance of the Place on the Earth from the Observer, over which the Balloon was then suspended.
This Method finds the Height truer than the Barometer, and with fewer Circumstances of Confusion.
And if the Balloon Art coud be perfected, so as to make them stationary at any Height; this Circumstance woud afford excellent Opportunities of proving the Heights by the Barometer: besides which, the Distance also has been obtained: a Point not before attempted.[103]
