In the complete inversion of the cane sugar the reaction which takes place is represented by the following formula: — + C₁₂H₂₂O₁₁ + H₂0 = C₆H₁₂O₆ + C₆H₁₂O₆. The minus and plus signs indicate that the resulting invert sugar is a mixture of equal parts of levulose (_d_ fructose) and dextrose (_d_ glucose). We are not concerned here with the fact that a complete inversion of cane sugar is a matter of great difficulty nor with the danger which is always experienced of destroying a part of one of the products of inversion. They are matters which may cause a variation in the analytical data afterward, but do not affect the principles on which the process is based. In the inversion of 26.048 grams of cane sugar there are therefore produced 13.71 grams of levulose and 13.71 grams of dextrose or, in all, 27.42 grams of the mixed sugars. The angular rotation which would be produced by 13.71 grams of dextrose in a volume of 100 cubic centimeters and through a column 200 millimeters in length is, with sodium light, 14°.53 equivalent to 41.89 divisions of the cane sugar scale. The specific rotatory power of a dextrose solution of the density given is almost exactly 53, and this number is used in the calculations. In a mixture of the two sugars under the conditions mentioned and at a temperature of 0° the angular rotation observed is -15°.15 equivalent to 43.37 divisions of the cane sugar scale. The + rotation due to the dextrose is 14°.53. Therefore the total negative rotation due to levulose at 0° is 15°.15 + 14°.53 = 29°.68. Hence the gyrodynat of levulose at 0° and in the degree of concentration noted is readily calculated from the formula 29.68 × 100 [α]°_{D} = - ------------ = -108.24. 2 × 13.71 Since at 88° (_circa_) the mixture of levulose and dextrose is neutral to polarized light, it follows that at that temperature the specific rotatory power of levulose is equal to that of dextrose, _viz._, 53°. [α]⁸⁸ °_{D} = - 53°. The total variation in the specific rotatory power of levulose, between zero and 88°, is 55°.24. The variation for each degree of temperature, therefore, of the specific rotatory power of levulose is equal to 55.24 divided by 88, which is equal to 0.628. From these data it is easy to calculate the specific rotatory power of levulose for any given temperature. For instance, let it be required to determine the gyrodynat of levulose at a temperature of 20°. It will be found equal to 108.24 - 0.628 × 20 = 95.68. The required rotatory power is then [_a_]²⁰ °_{D} = -95°.68. In these calculations the influence of the presence of hydrochloric acid upon the rotatory power of the levulose is neglected.