Degrees Plato, `{::}^oP`, defines the sugar content of an aqueous solution. One degree The Plato scale defines the amount  sucrose in volume of solution and represents the strength of the solution as percentage by weight (% w/w). The Plato scale has been used since 1843 and is closely related to the Brix scale.

This equation is an approximation because the solution typically contains dissolved solids other than sucrose, so the `{::}^oP` only approximates the dissolved solid content.

Another related scale, the oldest related scale, identifies sugar content in degrees Balling.

Input:

• S is the apparent specific gravity of the solution 20C/20C.

Notes

An example of computing the degrees Brix:

A sucrose solution with an apparent specific gravity of 1.05 (20/20C) would be 12.38703 `{::}^oBx` or 12.38765 P.   Because the differences between the reported values in these different systems are very small (typically less than the precision of the instruments used to measure the sugar content), the most current  devices calculate mass fraction using ICUMSA official formulas but still report the result as `{::}^oBx`.

When a refractometer is used, the Brix value can be obtained from the polynomial fit to the ICUMSA table: Bx = (((((11758.74*nD -88885.21)*nD + 270177.93)*nD - 413145.80)*nD + 318417.95)*nD -99127.4536) where nD is the refractive index, measured at the wavelength of the sodium D line (589.3 nm) at 20 C.

The Plato tables is maintained by the American Society of Brewing Chemists (ASBC) . The current version of the Brix table is maintained by NIST and can be found on their website. The ICUMSA tables report in mass fraction (m.f.).

Both NBS and ASBC converted to apparent specific gravity at 20C/20C. The ICUMSA tables are based on more recent measurements on sucrose, fructose, glucose and invert sugar and tabulate true density and weight in air at 20 C against mass fraction.

Sugars dissolved in water change both the solution's specific gravity and its optical properties.  The refractive index of a sugar solution and its rotation of the plane of linearly polarized light are both affected. The refractive index, nD, for sucrose solutions of various concentrations by weight has been measured provide as tables of nD vs. `{::}^oBx`. NIR (Near Infra Red) and FT-IR (Fourier Transform Infrared Spectrometry) techniques are also used to measure infrared absorption to identify sugar content.

Not the notation for specific gravity is given with the appended notation of (`T_s`/`T_r`), where `T_s` is the temperature of the sample and the `T_r` is the temperature of the reference density (of water).