1837 book on railroad building
A treatise on the Principles and Practice of Leveling
ON THE PRINCIPLES OF LEVELLING.
LEVELLING is the art of tracing a line at the surface of the earth which shall cut the directions of gravity everywhere at right angles. If the earth were an extended plane, all lines representing the direction of gravity at every point on its surface would be parallel to each other; but, in consequence of its figure being that of a sphere or globe (The figure of the earth is not exactly that of a sphere, but of an oblate spheroid flattened at the poles; the length of the equatorial diameter being 7924 miles, and that of the polar diameter 7898 miles. For our present purpose, it is sufficiently correct to consider it as a sphere.), they everywhere converge to a point within the sphere which is equidistant from all parts of its surface; or, in other words, the direction of gravity invariably tends towards the centre of the earth, and may be considered as represented by a plumb-line when hanging freely, and suspended beyond the sphere of attraction of the surrounding objects."
After that he derives the 8 inches per mile squared approximation in a really nice way.
Also gives a good equation approximation for feet!
2D^2/3
So 10 miles would be 200/3 = 66 feet
Book then talks about refraction, provides a practical correction of 1/7th.