Zetetic Astronomy, by 'Parallax' (pseud. Samuel Birley Rowbotham), [1881], at sacredtexts.com
IF the earth is a globe, and is 25,000 English statute miles in circumference, the surface of all standing water must have a certain degree of convexityevery part must be an arc of a circle. From the summit of any such arc there will exist a curvature or declination of 8 inches in the first statute mile. In the second mile the fall will be 32 inches; in the third mile, 72 inches, or 6 feet, as shown in the following diagram:
Let the distance from T to figure 1 represent 1 mile, and the fall from 1 to A, 8 inches; then the fall from 2 to B will be 32 inches, and from 3 to C, 72 inches. In every
mile after the first, the curvature downwards from the point T increases as the square of the distance multiplied by 8 inches. The rule, however, requires to be modified after the first thousand miles. 1 The following table will show at a glance the amount of curvature, in round numbers, in different distances up to 100 miles.
Curvature 
in 
1 
statute 
mile 
8 
inches. 
" 
" 
2 
" 
" 
32 
" 
" 
" 
3 
" 
" 
6 
feet. 
" 
" 
4 
" 
" 
10 
" 
" 
" 
5 
" 
" 
16 
" 
" 
" 
6 
" 
" 
24 
" 
" 
" 
7 
" 
" 
32 
" 
" 
" 
8 
" 
" 
42 
" 
" 
" 
9 
" 
" 
54 
" 
" 
" 
10 
" 
" 
66 
" 
" 
" 
20 
" 
" 
266 
" 
" 
" 
30 
" 
" 
600 
" 
" 
" 
40 
" 
" 
1066 
" 
" 
" 
50 
" 
" 
1666 
" 
" 
" 
60 
" 
" 
2400 
" 
" 
" 
70 
" 
" 
3266 
" 
" 
" 
80 
" 
" 
4266 
" 
" 
" 
90 
" 
" 
5400 
" 
" 
" 
100 
" 
" 
6666 

" 
" 
120 
" 
" 
9600 
" 2 
It will be seen by this table that after the first few miles the curvature would be so great that no difficulty could exist in detecting either its actual existence or its proportion. Experiments made on the sea shore have been objected to on account of the constantly changing altitude of the surface of the water, and of the existence of banks and channels which produce a "crowding" of the waters, as well as currents and other irregularities. Standing water has therefore been selected, and many important experiments have been made, the most simple of which are the following:
In the county of Cambridge there is an artificial river or canal, called the "Old Bedford." It is upwards of twenty miles in length, and (except at the part referred to at page 16) passes in a straight line through that part of the Fens called the "Bedford Level." The water is nearly stationaryoften completely so, and throughout its entire length has no interruption from locks or watergates of any kind; so that it is, in every respect, well adapted for ascertaining whether any or what amount of convexity really exists.
10:1 Any work on geometry or geodesy will furnish proofs of this declination.
10:2 To find the curvature in any number of miles not given in the table, simply square the number, multiply that by 8, and divide by 12. The quotient is the curvation required.