A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2019 Nov 26, 15:24 -0800
It's certainly true that a catenary (hanging chain) displays an exponential function and therefore, if inverted, natural logarithms. The equation that describes the catenary's shape is proportional to the hyperbolic cosine function, cosh(x), given by
cosh(x) = (ex+e-x)/2.
In principle, you can "measure" values of this function from a hanging chain. Whether this was ever done successfully to help generate a table of the exponential function or its inverse, the natural logarithms, I don't know. But even if this was done experimentally at some point, I suspect the value of this was process was quite limited compared to other techniques for calculating exponentials and logarithms by hand.