Editing Brix (section)

===Specific gravity===

Formulas derived from the NBS table<ref name="fbates" /> above:

Approximate (R<sup>2</sup>=0.999 98) values can be computed from:
:<math>^{\circ}Bx = 263.663-\frac{263.806}{SG}</math>
where SG is the [[apparent specific gravity]] of the solution at 20&nbsp;°C/20&nbsp;°C.

More accurate (R<sup>2</sup>=0.999 999 994) values are available from the polynomial:

:<math>^{\circ}Bx = 182.46007\,SG^3-775.68212\,SG^2+1262.7794\,SG-669.56218</math>,

RMS disagreement between the polynomial and the NBS table is 0.0009 °Bx.

Another accurate (R<sup>2</sup>=0.999 999 97) and simpler formula is:

:<math>^{\circ}Bx = 28.14203\,SG+202.4427-\frac{230.5870}{SG}</math>

The above formulas should not be used outside the range 1.00000 to 1.17874 SG (0 to 40 °Bx).

The [[Plato scale]] can be approximated with a mean average error of less than 0.02°P with the following equation:<ref name="jbuhl">{{cite web |last1=Buhl |first1=Josh |title=Physical Equations Relating Extract and Relative Density |url=https://osf.io/9wfym/ |website=OSF Preprints |publisher=Center for Open Science |access-date=13 October 2023 |ref=jbuhl |archive-date=19 October 2023 |archive-url=https://web.archive.org/web/20231019134432/https://osf.io/9wfym/ |url-status=live }}</ref>

:<math>^\circ P = 260.4 - \frac{260.4}{SG}</math>

or with even higher accuracy (average error less than 0.00053°P with respect to the ASBC tables) from the best-fit polynomial:<ref name="jbuhl" />

:<math>^{\circ}P = 133.5892\,SG^3 - 622.5576\,SG^2 + 1102.9079\,SG - 613.9427</math>.

The difference between the °Bx and °P as calculated from the respective polynomials is:

:<math>^{\circ}P-^{\circ}Bx = -48.8709\,SG^3+133.1245\,SG^2-159.8715\,SG+55.6195</math>

The difference is generally less than ±0.0005 °Bx or °P with the exception being for weak solutions. As 0 °Bx is approached °P tend toward as much as 0.002 °P higher than the °Bx calculated for the same specific gravity.

Disagreements of this order of magnitude can be expected as the NBS and the ASBC used slightly different values for the density of air and pure water in their calculations for converting to apparent specific gravity. It should be clear from these comments that Plato and Brix are, for all but the most exacting applications, the same.

The ICUMSA polynomials are generally only published in the form where mass fraction is used to derive the density. As a result, they are omitted from this section.