=94. Calculation of Results.=—The percentage of sucrose in a solution which has been polarized before and after inversion is calculated by an appropriate formula from the data obtained or is taken directly from tables. These tables are too long to insert here, and in point of fact the calculation can be made from the formula almost as quickly as the result can be taken from a table. Two factors are commonly used in the calculations, one based on the supposition that a sugar solution polarizing 100° to the right will, after inversion, give a reading of 44° to the left, at zero temperature. In the second formula in common use the polarization to the left in the circumstances mentioned above is assumed to be 42.4, a number reached by Landolt after a long series of experiments.[56] The principle of the calculation of the percentage of sucrose is based upon the original observation of Clerget to the effect that the algebraic difference of the two readings, divided by 144, less half of the temperature, will give the percentage of sucrose desired. The formula by which this is obtained is _a_ - _b_ _S_ = -----------. _K_ - _t_ ---- 2 In this formula _a_ is the polarization on the sugar scale before inversion, _b_ the polarization after inversion, _K_ the constant representing the algebraic difference of the two polarizations of pure sugar at 0° and _t_ the temperature of the observation. To _K_ may be assigned the values 144 or 142.4, the one in more common use. In case the polarization, after inversion, is to the left, which is more commonly the case, the sum of the two readings is taken for _a_ - (-_b_) = _a_ + _b_; when both polarizations are to the right or left the difference is taken. S is the percentage of sucrose desired. _Example.—_Let the polarization before inversion be +95 and after inversion -26 and the temperature 20° 95 + 26 Then _S_= -------- = 121 ÷ 134 = 90.6. 144 - 10 Substituting the value 142.4 for _K_, the result of the calculation is 91.4. In high grade sugars, therefore, the difference in the results secured by taking the two values of _K_ amounts to about 1 per cent of sucrose. For a further discussion of the theory and practice of inversion the reader is referred to the articles of Herles, Herzfeld, and Wohl.[57] =95. Method Of Lindet.=—Courtonne recommends the method of Lindet for securing the inversion instead of the method of Clerget.[58] Modified by Courtonne, the method is as follows: Make two or three times the normal weight of sugar dissolved in water to a volume of 200 or 300 cubic centimeters, as the case may be. After thoroughly mixing proceed as follows: