Subtract (3) from (2) _P_ = 53_d_ + 133_m_ + 193_dʹ_ _Pʹ_ = 193_dʹ_ -------------------------------------- _P_ - _Pʹ_ = 53_d_ + 138_m_ (4) Multiply (1) by 53 and subtract from (4) _P_ - _Pʹ_ = 53_d_ + 138_m_ 53_R_ = 53_d_ + 32.86_m_ ------------------------------------------- _P_ - _Pʹ_ - 53_R_ = 105.14_m_ (5) _P_ - _Pʹ_ - 53_R_ Whence _m_ = ------------------ (6) 105.14 _d_ = _R_ - 0.62_m_ (7) _Pʹ_ _dʹ_ = ---- (8) 193 Sidersky assigns the values [_a_]_{D} = 138.3 and [_a_]_{D} = 194.8 to maltose and dextrin respectively in the above formulas.[211] _Illustration_: In the examination of a sample 26.048 grams of midzu ame in 100 cubic centimeters were polarized in a 200 millimeter tube and the following data were obtained: Polarization of sample in angular degrees 69°.06, which is equal to an apparent gyrodynat of 132.6: Total reducing sugar as dextrose 33.33 per cent: Polarization in angular degrees after fermentation 30°.84 = [_a_]_{D} = 59.2. Substituting these values in the several equations gives the following numbers: (1) 0.3333 = _d_ + 0.62_m_ (2) 132.6 = 53_d_ + 138_m_ + 193_dʹ_ (3) 59.2 = 193_dʹ_ (4) 73.4 = 53_d_ + 138_m_ (5) 55.74 = 105.14_m_ (6) _m_ = 0.5301 = 53.01 per cent. (7) _d_ = 3333 - 3286 = 0.0047 = 00.47 per cent. (8) _dʹ_ = 59.2 ÷ 193 = 0.3067 = 30.67 ” ” _Summary_: Sample of midzu ame: Percentage of dextrin 30.67 per cent. ” ” maltose 53.01 ” ” ” ” dextrose 00.47 ” ” ” ” water 14.61 ” ” ” ” ash 00.31 ” ” ----- Sum 99.07 ” ” Undetermined 0.93 ” ” For polarization the lamplight shadow polariscope employed for sugar may be used, and the degrees of the sugar (ventzke) scale converted into angular degrees by multiplying by 0.3467. The process of fermentation is conducted as described in the paragraph given further on, relating to the determination of lactose in the presence of sucrose.