As it is well known that Objects of the _greatest_ Magnitude appear but as +blue air+ at even a _less_ Distance than 100 Miles; to which add the Difficulty of Journies, and Ascent to the Summit of these astonishing Mounds of Earth; and all this for the Sake, not of a complete +down prospect+, subject to _a perpetual Variety_, but merely an _imperfect Side-View_: the +pleasure+ and +ease+ of attaining still _more_ stupendous Heights at _any_ Place and Time, by Means of the +balloon+, are strikingly in Favor of that Invention. And, notwithstanding the confessed Merit of Dr. Black’s Project with the _Farciminàlis_ of a Calf, and Mr. Cavallo’s Soap Bubbles with inflammable Air; (see his History of Aerostation, Page 34;) if the Emperor had been alive who offered a Reward for the Invention of a _NEW PLEASURE_; the _first_ Prize had been due to the Brothers Montgolfier, and a _second_ to the Brothers Roberts. [46] As therefore it may be supposed that the Peak of St. George, in _receding_ from it, woud _vanish_ at the Distance of 150 Miles; its Height may _easily_ be ascertained geometrically thus: [Illustration] See the Figure annexed. Let M be the Summit of the Mountain: and let the Line M T drawn to the Circumference of the Circle at T, be the _evanescent_ Distance of the Mountain in the Horizon, viz. 150 Miles. Join T C, viz. a Line drawn from the _Tangent_ to the Center of the Circle, which Line will therefore represent the Semidiameter of the _Earth_, viz. 3958 Miles, according to Newton. Draw a Line from C to M, which will pass throu’ some Point of the Circumference as H, the Base of the Mountain. Then, in the Triangle M T C, as the Angle at T is a right Angle (Euclid’s Elements, Book 3, Proposition 18;) and the Sides M T, and T C, containing the right Angle, are _known_; the _third_ Side C M is readily found: (being a Corollary to the 47th Prop. 1st Book Euclid:) viz. having the two Sides of a right Angle Triangle given to find the _third_. Therefore RULE. Multiply the Sides containing the right Angle, each into itself: viz. 150 and 3958: add the Products into one Sum: from which extract the _square Root_; _equal_ to the Length in Miles, of the _third_ Side required. From the _third_ Side, subtract that Part, viz. C H, which is equal to the Semidiameter T C already found: and the Remainder H M is the _Height of the Mountain_.