Note Note [18 — Literal and other Errors proper to be examined, and corrected with the Pen, before the Book is read.
Reading edition
[18]
PROBLEM.
To find the circular Boundary of the celestial Prospect over the Tops of the superior Clouds, from the Balloon at the Height of near a Mile and half above the Surface of the Earth, viz. 2332 Yards. The Height from the Earth to the upper Surface or Floor of Clouds being 1000 Yards; and the Height above the Floor to the Balloon being 1332 Yards.
On the Curvature of the Earth and Clouds, and Elevation of the Eye above their circular Horizon.
Rule. To the Earth’s Diameter, equal to 7940 geographical Miles, add the Height of the Eye above its Surface: multiply the Sum by that Height: then the square Root of the Product gives the Distance at which an Object on the Surface of the Earth can be seen by an Eye so elevated. Note the Diameter of the Earth, in Feet, is 41798117, according to Newton. (See Practical Navigator, by J. Moore, 7th Ed. Page 251.)
FIRST.
Double 1000 Yards, the Height from the Earth to the Clouds for an Addition to the Diameter of the Earth, whose Surface is now considered, as extended to the concentric Floor of Cloud.
1000 1000 —— 2000
SECOND.
13932702(1⁄3) Diameter of the Earth in Yards.
2000 Addition to the Diameter.
————
13934702 Sum, to which add
1332 the Height of the Eye or of the
———— Balloon above the Floor of Cloud.
13936034 Sum, which multiply into
1332 the Height of the Eye above the
———— Floor.
27872068
41808102
41808102
13936034
——————
Extract the . . . . . 1760) Yards in a Mile.
Square Root 18562797288 (136245 (77 Miles.
1 12320
— ———
23) 85 13045
69 12320
—— ———
266) 1662 Yards 440) 725 (1 Quarter of a Mile.
1596 440
—— ——
2722) 6679 285 Yards.
5444
——— Ans. 77 Miles, 1 Qu. 285 Yards.
27244) 123572
108976
———
272485) 1459688
1362425
————
97263
Circular Boundary of the terrestrial Prospect from the Balloon on a clear Day.
PROBLEM.
To find the circular Boundary of the terrestrial Prospect, on a clear Day, from the Balloon at the Height of near a Mile and half, viz. 2332 Yards: the Earth’s Diameter being
equal to 139327052⁄3 Yards,
add 2332 the Height of the Eye or Balloon.
————
13935037 he Sum, multiply into
2332 the Height of the Eye, &c.
————
27870074
41805111
41805111
27870074
——————
Extract the . . . . . 1760) Yards in a Mile.
square Root 32496506284 (180267(102,
1 1760 say 1021⁄2 Miles, Ans.
— ——
28)224 4267
224 3520
—— ——
3602) 9650 747 Yards, Remainder.
7204
———
36046) 244662
216276
————
360527) 2838684
2523689
————
314995 Remainder.