Comment onUse of Single-Well Tracer Dilution Tests to Evaluate LNAPL Flux at Seven Field SitesandMeasurement ofLNAPLFlux Using Single-Well Intermittent Mixing Tracer Dilution Tests

What is it about?

An error in the standard name of the mathematical inverse cosine function has propagated and caused confusion in the literature and in a patent. In mathematical formulas in scientific papers there are two standard notations for the inverse cosine function, namely cos^(-1) (x) and the less common arccos(x). Because the first form is unsuitable for programming, Fortran used the name acos() which was later also used by Matlab and Excel. We commented that the use of the form acos in a mathematical formula was not recognized by the equation editing software, and it was rendered incorrectly as italic "a" followed by a space and then "cos", as if it was a variable named a multiplied by the cosine function. When the same formula was later used in a patent, the error was carried over and made worse as alpha cos because the "a" variable was given as the Greek letter alpha, which was the name of a quite different variable. The original scientific content was correct, but its representation in mathematical formula was not, and caused confusion in later papers and the patent. It is not correct to use the programming name "acos" in mathematical typesetting.

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