If the relative polarizing power of sugar A is a and that of B is B, then, in the mixture, ar+By-P, in which P is the polarizing power of the mixture of sugars expressed in Ventzke degrees. Hence Relative polarizing power (a and 8) is defined as the ratio of specific rotation of the sugar in question to that of sucrose. The values of a and ẞ for 20° C and a concentration of 10 percent are given in table 29. For levulose and galactose these values vary considerably with concentration and temperature and must be calculated by the formulas Levulose a=-1.3393-0.00166p+0.0085 (t-20), Galactose B 1.210+0.0012 (p-10)-0.00315(t-20), in which p is the percentage of the sugar in the solution polarized. Table 29.-Constants applicable to the Browne method of analysis of sugar mixtures The constants required for calculation are given in table 29. The list is capable of extension as the constants for other sugars are determined. The values tabulated under a and a refer to the sugar A and those under b and 8 to the sugar B. Example.-A solution containing 4.52 percent of levulose and 4.84 percent of dextrose rotated -2.15° V in a 200-mm tube at 22° C and showed a reducing power equivalent to 9.06 g of dextrose. By the above formula, a==-1.3378. Then x (percentage of levulose) = 0.7939.06 (−2.15) 0.915X0.793-(-1.3378) = 4.524. y (percentage of dextrose) = 9.06-(0.915X4.524)=4.92. (2) MATHEWS FORMULA.-The most commonly occurring mixture of two sugars which can be analyzed by a combination of reducing and polarizing equations is that of dextrose and levulose. Mathews [6, p. 433] has derived a formula which permits a ready calculation of the ratio of levulose to total reducing sugar when the sample has been polarized in a saccharimeter and its reducing power determined by the Lane and Eynon method of titration. The method of calculation is valid under the assumptions that no optically active or reducing substance other than dextrose and levulose is present in the sample, and that the rotation of the mixture is the algebraic sum of the rotations of the constituents whose specific rotations are referred to the concentration of total sugar rather than to the partial concentration of each. While the method of determination strictly applies only to pure mixtures of dextrose and levulose, it may frequently be applied to crude mixtures, such as fruit juices, to yield a proximate analysis. At this Bureau the method has been applied to numerous samples of hydrolyzed juices of the jerusalem artichoke for rapid proximate analysis. The sugar mixture in such products consists of about 70 to 80 percent of levulose, about 20 to 25 percent of dextrose, and a small quantity of dextrorotary difructose anhydrides, which introduces an error of about 2 percent into the analysis. Application of an empirical correction diminished the error considerably. The procedure is simple. If the levulose content is high, prepare a sample containing 15 to 20 percent of sugars, or somewhat more if dextrose is the predominating sugar. Polarize in a 200-mm tube, preferably at 20° C. Dilute a measured aliquot to such volume that the resulting solution contains about 0.5 g of sugar per 100 ml and titrate against 25 ml of mixed standardized Soxhlet solution by the method of Lane and Eynon. If necessary, correct the burette reading to conform to an exactly standardized Soxhlet reagent. The method of calculation is greatly facilitated by use of table 95, p. 601. Example.-Assume that a solution of levulose and dextrose polarized - 43.8°S at 20° C, and that 5 ml of this solution diluted to 100 ml gave a Lane and Eynon titration (25 ml of Soxhlet solution) of 26.18. Then D=100/5=20 and PT 43.8X26.18 = D 20 == - 57.3. By table 95, p. 601, the approximate ratio is 89.8 percent, and the correction factor, f, is -0.80. The correction is and the true ratio is 89.8-0.6-89.2. The concentration of total sugar is calculated in the usual way from the titer (c) TWO SUGARS BY COMBINATION OF TWO REDUCTION EQUATIONS (1) GENERAL. For analysis of two sugars in a mixture, advantage is frequently taken of differences in reducing action which the individual sugars show under different conditions of analysis. In many instances the difference in behavior between the two sugars is so marked that one sugar can be determined selectively. In most cases the accompanying sugar produces minor effects, and corrections are required for accurate analysis. Thus Jackson and Mathews in their modification of the Nyns method found that 12.4 mg of dextrose reduced as much copper as 1 mg of levulose, but that this constant correction could be applied with certainty. The variety of combinations by which this analysis can be conducted is considerable. but quite invariably one process is the de termination of total reducing sugar. The remaining methods of analysis can be chosen from the group of selective methods, but should take advantage of some property which the accompanying sugar lacks. (2) SUCROSE AND LACTOSE IN DAIRY PRODUCTS BY TWO REDUCTION PROCESSES.-An interesting method for the simultaneous determination of sucrose and lactose in sweetened condensed milk and ice cream has been described by White [19]. In outline, the clarified solution is subjected to the Munson and Walker method of lactose. analysis and the copper referred to the appropriate column of lactosesucrose mixtures. The filtrate from the cuprous oxide, which is then free from lactose, is collected quantitatively, acidified, and heated to invert the sucrose, which is then determined in the form of invert sugar by a second reducing-sugar analysis. Inasmuch as a portion of the sucrose is destroyed during the lactose analysis, an empirical correction is applied to the cuprous oxide precipitated by invert sugar. The method is given in the following brief example: Weigh 10 g of condensed milk (20 g of ice cream) into a 250-ml volumetric flask and dissolve in 125 ml of boiling water. Mix for 3 minutes, cool to 20° C and add gradually 10 ml of Soxhlet coppersulfate solution and 6 ml of 0.5 N sodium hydroxide. Make to 1.5 ml over the mark (3.2 ml for ice cream) and filter. Determine lactose in 50 ml of the filtrate by the Munson and Walker method, using the "1 lactose-4 sucrose" column. Collect the filtrate from the cuprous oxide precipitate in a 250-ml flask and wash with 80 ml of hot water. Add 34 ml of 1+1 hydrochloric acid and invert in a boiling-water bath for 5 minutes. Cool and neutralize with 50-percent sodium hydroxide. Determine invert sugar by Munson and Walker method. Add 1.6 mg to the weight of cuprous oxide (1.0 mg for ice cream). Refer both weights of copper to the Munson and Walker table 78, p. 564. 4. DETERMINATION OF THREE SUGARS IN A MIXTURE (a) GENERAL The analysis of mixtures containing three sugars requires the application of analytical processes which yield three equations. Special methods in great variety have been brought into use for the analysis of these complex products. The combinations of methods which have proved most successful are those which include at least one process which is selective for one of the constituent sugars. The number and nature of the possible combinations of methods is large, but for the present purpose it will suffice to illustrate the principles by a few examples given in detail. In a very few instances one equation can be evaluated for total sugar in a mixture by using a physical method. Such a mixture can consist solely of pure sugars, but it is of such infrequent occurrence that the methods of analysis will not be described here. They can be found in Browne's Handbook of Sugar Analysis [3]. (b) THREE SUGARS BY COMBINATION OF POLARIMETRIC AND REDUCTION METHODS AND ONE SELECTIVE METHOD Wherever this combination can be applied, it is the simplest method of analysis of a complex mixture, involving as it does but three stand ard operations. Thus for the analysis of a mixture of sucrose, dextrose, and levulose, a direct and invert polarization and a reducing-sugar analysis suffice for the completed determination. The method is illustrated in the determination of the Browne polarizing constants [2]. It would seem preferable to call them 'quotients" rather than "constants," since the value of the quotient is not constant but varies with the ratio of dextrose to levulose. The Browne polarizing constants are defined by the expression (S-P)/R, in which S and R are the percentages of sucrose and reducing sugar, respectively, and P is the direct polarization. Assume a normal solution of a mixture of 99 percent of sucrose and 1 percent, or 0.26 g, of invert sugar. The invert sugar will rotate -1.19×0.26= -0.309. The value of the quotient is then 99-(99-0.309)/1=0.309. Similarly, if the reducing sugar were 1 percent levulose, the quotient would be 1.404, and if 1 percent dextrose, -0.806. At the ratio of dextrose to levulose of about 64 to 36, the quotient becomes 0. To calculate the percentages of dextrose and levulose, Browne used the equations 2+ky R cx+c1y+S=P, in which x and y are the percentages of dextrose and levulose, respectively; k, the reducing ratio of levulose to dextrose; c, the polarizing ratio of dextrose to sucrose at 20° C; c1, the polarizing ratio of levulose to sucrose; and R, the percentage of total reducing sugar, expressed as dextrose (Allihn method). Solving the equations for x and y, y=percentage of levulose CR+S-P r percentage of dextrose R-ky. Sucrose is estimated selectively by the Clerget method. The numerical value of c is 52.74:66.5=0.793; that of c1, -92.88:66.5=-1.397. For k an average value of 0.915 is employed. The method yields reliable results if the reducing-sugar content is not too low. If S approaches closely to P, small errors in either become large errors in their difference. It was, however, the only practicable method previous to the introduction of the selective method for levulose. Zerban has shown the fair agreement of results obtained by this method with those obtained by two selective analyses. The comparative results are shown in table 30. The method of two selective analyses, combined with the determination of total reducing sugar, must be considered the more reliable procedure. (c) THREE SUGARS BY COMBINATION OF TOTAL REDUCING POWER AND TWO SELECTIVE METHODS Mixtures of sucrose, dextrose, and levulose can be analyzed by a selective determination of sucrose by the Clerget method, a selective determination of levulose by the Nyns method, and a determination of total reducing sugar. Alternatively, a selective determination of dextrose by the iodine-alkali reaction can be used to replace the levulose analysis, provided that adequate correction is applied for the action of iodine on the nonaldose sugars. TABLE 30.-Zerban analyses of dextrose and levulose in raw cane sugar Method II. Total reducing sugar and selective levulose analysis (1) SUCROSE, DEXTROSE, AND LEVULOSE IN RAW SUGAR.-Zerban and Wiley [20] have applied the method of two selective analyses to the determination of sucrose, dextrose, and levulose in raw cane sugar, using for levulose the modification of Jackson and Mathews and for sucrose the invertase Clerget analysis. For the determination of total reducing sugar they used the Lane and Eynon volumetric method, but since the original tables listed titers for dextrose, levulose, and invert sugar only, they prepared interpolated tables for varying ratios of these sugars in the presence of 10 and 25 g of sucrose, respectively. In abbreviated form, these data are reproduced in tables 90 and 91, p. 596. Zerban and Wiley found slightly higher factors for invert sugar than Lane and Eynon and recommend that the analyst verify the published factors or establish his own. A similar recom mendation was made with respect to the Jackson-Mathews method. They found that in order to obtain the same copper equivalents as tabulated by these authors, they must conduct the reduction at 55.2° C instead of 55.0° C, as specified. They determined the reduced copper by ferric sulfate-permanganate titration. The reducing power of dextrose (12.4 mg of dextrose=1 mg of levulose) determined by Jackson and Mathews was confirmed. Four grams of sucrose reduced 8.5 mg of copper; 5 g, 9.0 mg; and 2 g, 5.7 mg. Procedure. Transfer a sample of raw sugar containing 62.5 g of sucrose (determined by direct polarization) to a 250-ml flask, clarify with neutral lead acetate, make to volume, and filter. Delead with dry potassium oxalate. Determine (preferably in duplicate) apparent |