and molasses, the optical method for sucrose, requiring hydrolysis by acid, gives erroneous results.) Direct reading.-Proceed as directed under "Direct reading," page 157. Invert reading.-Pipette a 50-ml portion of the lead-free filtrate into a 100-ml flask and add 25 ml of water. Then add, little by little, while rotating the flask, 10 ml of hydrochloric acid (sp. gr. 1.1029 at 20°/4° or 24.85° Brix at 20°C). Heat a water bath to 70°C and regulate the burner so that the temperature of the bath remains approximately at that point. Place the flask in the water bath, insert a thermometer, and heat with constant agitation until the thermometer in the flask indicates 67°C. (This preliminary heating period should require from 2% to 24 minutes). From the moment the thermometer in the flask indicates 67°C, leave the flask in the bath for exactly 5 minutes longer, during which time the temperature should gradually rise to about 69.5°C. Plunge the flask at once into water at 20°C. When the contents have cooled to about 35°C, remove the thermometer from the flask, rinse it, and fill almost to the mark. Leave the flask in the bath at 20°C for at least 30 minutes longer and finally make up exactly to volume. Mix well and polarize the solution in a 200-mm tube provided with a lateral branch and a water jacket, maintaining a temperature of 20°C. This reading must. also be multiplied by 2 to obtain the invert reading. If it is necessary to work at a temperature other than 20°C, which is permissible within narrow limits, the volumes must be completed, and both direct and invert polarizations must be made at exactly the same temperature. Calculate sucrose by the following formula: in which S= 100(P-I) S percentage of sucrose, P=direct reading, normal solution, I invert reading, normal solution, t=temperature at which readings are made, m=grams of total solids from original sample in 100 ml of the invert solution. Determine with the refractometer the total solids as percentage by weight, as directed on page 258, and multiply this figure by the density at 20°C, as obtained from table 113, page 626. Inversion at room temperature. The inversion may also be accomplished as follows: (1) To 50 ml of the clarified solution, freed from lead, add 10 ml of hydrochloric acid (sp. gr 1.1029 at 20°/4° or 24.85° Brix at 20°C) and set aside for 24 hours at a temperature not below 20°C; or, (2) if the temperature is above 25°C, set aside for 10 hours. Make up to 100 ml at 20°C and polarize. Under these conditions, the formula must be changed to the following: (2) DETERMINATION OF SUCROSE AND RAFFINOSE BY POLARIZATION BEFORE AND AFTER INVERSION WITH HYDROCHLORIC ACID. (Of value chiefly in the analysis of beet products.) If the direct reading is more than 1° higher than the percentage of sucrose, as calculated by the formulas given on p. 156, raffinose is probably present. Calculate sucrose and raffinose by the following formulas: When the polarizations are made at 20° C, P=direct reading, normal solution, I=invert reading, normal solution, R=percentage of anhydrous raffinose. The following formulas are applicable at all temperatures: P(0.478+0.0018t2)-I(1.006-0.000311) (0.908-0.0032t1⁄2) (1.006-0.0003t1) in which R: P(0.43-0.005t2)+I(1.006-0.00031) = (1.681-0.005912) (1.006-0.000311) = P direct reading, normal solution, R= percentage of anhydrous raffinose, See also discussion of Creydt's raffinose formula on page 143. (d) INVERTASE METHODS OF THE ASSOCIATION OF OFFICIAL AGRICULTURAL CHEMISTS (1) DETERMINATION OF SUCROSE. Direct reading. Dissolve the double-normal weight of the substance (52 g), or a fraction thereof, in water in a 200-ml volumetric flask; add the necessary clarifying agent, avoiding any excess; shake, dilute to the mark with water, mix well, and filter, keeping the funnel covered with a watch glass. Reject the first 25 ml of the filtrate. If a lead clarifying agent was used, remove the excess lead from the solution when sufficient filtrate has collected, by adding anhydrous sodium carbonate a little at a time, avoiding any excess; mix well and filter again, rejecting the first 25 ml of the filtrate. (Instead of weighing 52 g into a 200-ml flask, two 26-g portions may be diluted to 100 ml each and treated exactly as described. Depending on the color of the product, multiples or fractions of the normal weight may be used and the results reduced by calculation to the basis of 26 g in 100 ml.) Pipette one 50-ml portion of the lead-free filtrate into a 100-ml flask, dilute with water to the mark, mix well, and polarize in a 200-mm tube. The result, multiplied by 2, is the direct reading (P of formula given below), or polarization before inversion. (If a 400-mm tube is used the reading equals P.) If there is a possibility of mutarotation, allow sufficient time for its completion. Invert reading.-First determine the quantity of acetic acid necessary to render 50 ml of the lead-free filtrate distinctly acid to methyl 323414°-42- -12 red indicator, pH 4.4; then to another 50 ml of the lead-free solution. in a 100-ml volumetric flask, add the requisite quantity of acid and 5 ml of the invertase preparation, fill the flask with water nearly to 100 ml, and let stand overnight (preferably at a temperature not less than 20° C). Cool, and dilute to 100 ml at 20° C. Mix well and polarize at 20° C in a 200-mm tube. If there is doubt as to the completion of the hydrolysis, allow a portion of the solution to remain for several hours and again polarize. If there is no change from the previous reading, the inversion is complete. Carefully note the reading and temperature of the solution. If it is necessary to work at a temperature other than 20° C, which is permissible within narrow limits, complete the volumes and make both direct and invert readings at the same temperature. Correct the polarization for the optical activity of the invertase solution and multiply by 2. Calculate the percentage of sucrose by the formula in which S= 100 (P-I) 142.1+0.073 (m-13)-t/2' S percentage of sucrose, P=direct reading, normal solution, I invert reading, normal solution, t=temperature at which readings are made, m=g of total solids from original sample in 100 ml of the invert solution. Determine with the refractometer the total solids as a percentage by weight, as directed on page 258, and multiply this figure by the density at 20° C, as obtained from table 113, p. 626. Rapid inversion at 55° to 60° C.-If more rapid inversion is desired, proceed as follows: Prepare the sample as directed under "direct reading," p. 157, and to 50 ml of the lead-free filtrate in a 100 ml volumetric flask add glacial acetic acid in sufficient quantity to render the solution distinctly acid to methyl red, pH 4.4. The quantity of acetic acid required should be determined before pipetting the 50-ml portion, as described in the preceding paragraph. Then add 10 ml of invertase solution, mix thoroughly, place the flask in a water bath at 55° to 60° C, and allow to stand at that temperature for 15 minutes with occasional shaking. Cool, add sodium carbonate until distinctly alkaline to litmus paper, dilute to 100 ml at 20° C, mix well, and determine the polarization at 20° C in a 200-mm tube. Allow the solution to remain in the tube for 10 minutes and again determine the polarization. If there is no change from the previous reading, the mutarotation is complete. Carefully note the reading and the temperature of the solution. Correct the polarization for the optical activity of the invertase solution and multiply by 2. Calculate the percentage of sucrose by the formula given above. If the solution has been rendered so alkaline as to cause destruction of sugar, the polarization, if negative, will in general decrease, since the decomposition of fructose ordinarily is more rapid than that of the other sugars present. If the solution has not been made sufficiently alkaline to complete mutarotation quickly, the polarization, if negative, will in general increase. As the analyst gains experience he may omit the polarization after 10 minutes, if he has satisfied himself that he is adding sodium carbonate in sufficient amount to complete mutarotation at once without causing any destruction of sugar during the period intervening before polarization. (2) SUCROSE AND RAFFINOSE BY POLARIZATION BEFORE AND AFTER TREATMENT WITH TWO ENZYME PREPARATIONS. Invertase solution (top-yeast extract).-Prepare as directed on page 147. This solution should be free from the enzyme melibiase. Its invertase activity should be at least as great as that used for the determination of sucrose in the absence of raffinose. Invertase-melibiase solution (bottom-yeast extract).-Prepare as directed on page 147, using bottom fermenting yeast (brewers' yeast) instead of bakers' yeast. The invertase activity should be at least as great as that from the top-yeast extract. Test the melibiase activity of the solution as follows. Add 2 ml of the solution to be tested to 20 ml of a weakly acid melibiose solution polarizing 20.0° S and allow to stand 30 minutes at about 20° C. Then add sufficient sodium carbonate to render the solution slightly alkaline to litmus paper. A preparation suitable for the overnight hydrolysis of solutions containing not more than 0.2 g of raffinose in 100 ml should hydrolyze 35 percent of the melibiose present under the conditions mentioned; a preparation suitable for the overnight hydrolysis of solutions containing not more than 0.65 g of raffinose in 100 ml should produce 50-percent hydrolysis of melibiose; and a preparation suitable for the overnight hydrolysis of solutions containing 0.65 to 1.3 g of raffinose in 100 ml should hydrolyze at least 70 percent of the melibiose present under the above condition. The polarizations that correspond to 35-, 50-, and 70-percent hydrolysis of a melibiose solution polarizing, before hydrolysis, +20° are +16.4°, +14.9°, and +12.9° S, respectively. Determination. In the analysis of sugar-beet products, weigh the quantity of material specified in table 19, transfer to a 300-ml volumetric flask, add the quantity of basic lead acetate solution indicated in the table, and dilute to volume at 20° C. Mix thoroughly and filter through fluted paper in a closely covered funnel, rejecting the first 25 ml of filtrate. When sufficient filtrate has collected, remove the lead from the solution by adding ammonium acid phosphate in as small excess as possible (see table 19). This condition is readily determined, after a little practice, by the appearance of the lead phosphate precipitate, which usually flocculates and settles rapidly in the presence of a slight excess of the salt. Mix well and filter, again rejecting at least the first 25 ml of the filtrate. Make a direct polarization in a 200-mm tube at 20° C, unless the solution contains an appreciable quantity of invert sugar, in which case pipette a 50-ml portion of the lead-free filtrate into a 100-ml flask, dilute with water to the mark, mix well, and polarize at 20° C, preferably in a 400-mm tube. This reading, calculated to the normal weight of 26 g in 100 ml and 200-mm tube length, is the direct reading (P) of the formula given in table 19. for polarization before inversion. Transfer two 50-ml portions of the lead-free filtrate to 100-ml flasks. To one add 5 ml of invertase solution (top-yeast extract), page 147, and to the other add 5 ml of invertase-melibiase solution (bottom-yeast extract), page 147, let stand overnight at atmospheric temperature (preferably not below 20° C), dilute to volume, mix well, and polarize at 20° C, preferably in a 400-mm jacketed tube. If a TABLE 19.-Quantity of sample and reagents required for clarification and deleading of beet sugar-house products 3 Neutralize with acetic acid before adding basic lead acetate. Lime in solution will be precipitated partly by the phosphate, and it is necessary to add sufficient phosphate to complete the precipitation of both the lead and lime salts; hence no definite quantity can be specified. rapid hydrolysis is desired, add 10 ml of each of the enzyme solutions to the 50-ml portions of deleaded filtrate in 100-ml flasks, and place in a water bath at 50° to 55° C for 40 minutes. Then add sodium carbonate until the solution is slightly alkaline to litmus paper, dilute to volume at 20° C, mix well, and polarize at 20° C, preferably in a 400-mm tube. Correct the invert readings for the optical activity of the enzyme solution, and calculate the polarization to that of a normal-weight solution of 26 g in 100 ml; also calculate the reading to a 200-mm tube length, if necessary. Calculate the percentages of anhydrous raffinose and sucrose from the formula R=1.354 (A—B), S= in which (P-2.202A+1.202B) 100 132.12-0.00718[132.12 — (P−2.202A+1.202B)]' R=percentage of raffinose, S percentage of sucrose, P=direct polarization, normal solution, A corrected polarization after top-yeast hydrolysis, normal solution, B=corrected polarization after bottom-yeast hydrolysis, normal solution. A and B are treated algebraically. (e) DOUBLE-ACID METHOD OF OSBORN AND ZISCH Osborn and Zisch [31], finding the double-enzyme method reliable in the analysis of beet products, but impracticable because of the expense of the enzymes and the difficulty of obtaining satisfactory preparations, sought to modify the methods of acid hydrolysis in such manner as to make them suitable for routine analysis. They pointed out that the direct polarization is the resultant rotation of sucrose, |