If the Earth is a Globe, 25,000 miles in cir-circumference, any portion of itsn surface is an arc of a circle; From the centre of which there will be a fall of 8 inches in the first mile. In every succeeding mile the fall will increase as the square of the distance: as explained by the following diagram:-
Let an arc of the Earth's circumference be represented by A. B. Then, if from C. (the centre), to fig. 4 be one mile, the lino 1-4, will be 8 inches: but if from C. to fig. 5, be 1000 miles, the line 2-5, will be 32 inches; or the square of 2 (the distance) multiplied by 8 (the fall in the first mile): as
22 x 8 = 32.
Again, if from C, to fig. 6 be three miles, the line 3-6, will be 72 inches; as
32 X 8 = 72.
Remembering that the first mile would curvate 8 inches, and every succeeding mile as the square of the distance, we may readily ascertain whether any convexity exists or not, by the following:-