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After reading this answer and writing this comment, I decided to ask this question: When and where was the earliest known use of a log-log plot to demonstrate power-law behavior?

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Napier introduced the logarithms in 1614, and Gunter invented the slide rule somewhere in 1620s. One might think that log log plots came soon after, but no. According to The Age of Graphical Computing: "In 1844 Leon Lalanne succeeded in linearizing the curves $y=x^p$ by plotting the first log-log plot in history, thereby creating his Universal Calculator, chock-full of lines for common engineering calculations and capable of graphically computing formulas in powers or roots of x ( or of trigonometric functions in x) with ease... Lalanne envisioned copies of his Universal Calculator posted in public squares and business meeting places for popular use". Lallane's successor, d'Ocagne, also credits him with the invention of logarithmic graph paper. The first link has a nice image of Lalanne's Universal Calculator, which looks like a fanciful version of it.

Lalanne's approach was not specific to logarithms, he came up with a general idea of transforming curved graphs into straight line ones by modifying the scales on the axes, which he called "geometrical anamorphosis". d'Ocagne developed Lalanne's ideas after 1880 under the name of nomography, and nomograms remained a popular computing tool, especially among engineers, until the onset of pocket calculators. Smith's Source Book in Mathematics has large excerpts from d'Ocagne's Treatise on Nomography (1899), which describes his and Lalanne's methods of graphical computing. The slide rule, logarithmic paper and nomograms, those nostalgic pieces of the old lore of scientific and technical computing wiped out by the advent of electronic calculators and computers...

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    $\begingroup$ Wow, thank you for your thorough answer! I'm quite surprised by the 200+ year gap. I have fond memories of nomograms, some were quite complex and beautiful. A lot of work went into them. I wonder if anything like "The Beauty of Nomograms" or "Nomogram Hall of Fame" exists. $\endgroup$ – uhoh Mar 27 '16 at 1:56

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