with basic lead. Acetic acid, and probably many other weak organic acids, change the rotation of invert sugar in a positive direction.

(g) ROTATION OF SUGAR MIXTURES AND THE EVALUATION OF m

It has been shown above that the rotatory power of pure invert sugar increases in a negative sense with increase in concentration, and that for the analysis of pure sucrose the Clerget divisor must be increased by the quantity 0.0794 (m-13), in which m is the number of grams of sucrose taken in the sample for the invert polarization. The question now arises as to what the value of m is if the original sample contains invert sugar, organic nonsugars, or inorganic salts in admixture with sucrose. In general, sugar-cane products contain all four of these constituents, while beet products usually contain all except invert sugar.

Consider first the analysis of a mixture of sucrose and invert sugar. The essential condition of the Clerget method is that the rotation of the invert sugar in the direct polarization be the same as in the invert polarization. Jackson and Gillis [3, 9] showed that a given quantity of invert sugar in the presence of sucrose had a slightly lower negative rotation than it would have if all of the sucrose were inverted. However, since its rotation approached constancy more closely if the concentration of total sugar were unaltered than if the relatively large effects of dilution were introduced, they recommended that both direct and invert polarizations have the same concentration of the sample. This expedient was admitted by the authors to be a first approximation "since the problem of the rotation of mixtures. was too large a one for a complete solution at that time." If now the plausible assumption is made that the rotatory power of sucrose is unaltered by admixture with invert sugar, its change of rotation upon hydrolysis would be from the positive rotation of sucrose itself to the negative rotation of invert sugar at the concentration of total invert sugar, which is the sum of the invert sugar formed by hydrolysis and the invert sugar originally present. Since the variations in the Clerget divisor are caused only by the variations of the specific rotation of invert sugar with concentration, the quantity m should represent the grams of total sugar in 100 ml of solution rather than the grams of sucrose."

Vosburgh [19] in a more general study measured the rotations of mixtures of sucrose, dextrose, and levulose and stated his results in an article which has been widely quoted and very frequently misquoted. Vosburgh summarized his conclusions as follows:

1. The specific rotations of glucose and fructose when mixed in equal proportions (invert sugar) are those which the sugars would have if each were present alone at a concentration equal to the total invertsugar concentration.

2. In mixtures of glucose and sucrose the specific rotations of the two are those which the sugars would have if each were present alone at a concentration equal to the total sugar concentration.

3. The relationship is only approximate for mixtures of fructose and sucrose, in which case the rotation is a little smaller (or larger numerically if negative) than that calculated upon its assumption.

This is a reversal of the recommendation of Jackson and Gillis, who substituted for m the grams of sucrose alone.

4. The polariscopic determination of the percentage of sucrose replaced by invert sugar gives slightly high results.

It should be noted that the statement in conclusion 1, which was confined to pure invert sugar and was not even applied to all dextroselevulose mixtures, has frequently in subsequent literature been extended to apply not only to all sugar mixtures but to all sugar-nonsugar mixtures. Conclusion 4, which concerns the Clerget analysis specifically, implies that conclusion 1 does not apply exactly to sucroseinvert sugar mixtures, the deviation amounting to about 0.4 percent, an error quite appreciable in Clerget analysis. This conclusion is in harmony with the previously described experiment of Jackson and Gillis, although the precision of analysis by the invertase method and by the compensation methods described in later paragraphs is closer than 0.4 percent. It should be recognized that the expedients suggested in this paragraph are recommended as approximations and are subject to alteration as knowledge of the rotations of sugar mixtures advances.

Zerban [20] in an extensive study of the analyses of complex sugar mixtures showed that satisfactory agreement of calculated and determined values of sucrose was obtained if "in these calculations the divisor corresponding to the total sugar concentration, and not that for the sucrose concentration, is used." In other words, m represents the number of grams of total sugars taken for inversion and made up to 100 ml after inversion.

In a further study Zerban prepared samples simulating cane molasses by combining accurately known quantities of its constituents, and here he found it necessary to assign to m the total weight of dry substance taken for inversion.

(b) INFLUENCE OF REAGENTS ON THE ROTATION OF SUCROSE

Sugar sirups of commercial importance frequently contain appreciable quantities of inorganic salts. Cane and beet molasses are essentially sirups in which, by removal of sugar, the salts have accumulated to such an extent that no further crystallization of sugar is possible. The presence of salts causes an alteration of the rotatory power of sucrose and, therefore, not only is the direct polarization of plant juices rendered uncertain, but both the direct and invert polarizations of the Clerget method are affected and the analytical results are made uncertain unless the change in the direct is the same as in the invert polarization.

In general, dissolved inorganic salts diminish the rotatory power of sucrose. For a few salts, Jackson and Gillis measured this depression and found it linear with respect to concentrations of salt ranging between 0 and about 4 g in 100 ml. They established the relations shown in table 16.

In the early literature [21] efforts were made to find some regularity between the depression and the molecular weight of the salt, and indeed the "molecular depression," that is, the depression caused by 1 g multiplied by the molecular weight, approached constancy for a few closely related salts, such as the chlorides of barium, strontium, and calcium. But molecular depression failed of constancy if applied more generally. Evidently in the relations listed above no constant molecular depression can be observed.

The depression caused by a given quantity of salt is, in dilute solution, a constant percentage of the rotation of pure sucrose quite regardless of the concentration of the latter. Thus Jackson and Gillis [22] showed by their own measurements and by calculation of the careful measurements of Browne [23] that 3.392 g of ammonium chloride produced the same relative depression on the rotation of sucrose, even when the concentration of the latter was varied between 5 and 52 g in 100 ml. When all rotations were calculated to 26 g of sucrose, the depressions were found to be the constant quantity 0.56° S. Similarly, 2.315 g of sodium chloride in 100 ml of a sucrose solution caused depressions of rotation which, when calculated to 26 g of sucrose, amounted to 0.62° S, quite regardless of the concentration of sugar.

Brown [24] extended these studies to very low concentrations of sugar and various salts, expressing this relation by the formula

Percentage of sugar=P+KPM,

in which P is the polarization, M the weight in grams of the salt present in 100 ml of the solution polarized, and K a constant which is characteristic for cach salt. The following values of K were found mainly by measurement in very dilute solution, and with inevitable multiplication of error:

Brown thus agreed with Jackson and Gillis that the depressive effect of salt was the same relative fraction of the total polarization regardless of concentration. Hence the values of K can be determined at high concentrations where the errors are small and applied to the low concentrations of thin juice and other dilute sirups.

(i) METHODS OF COMPENSATION

The direct application of the Clerget method in unmodified form to low-grade cane and beet products frequently leads to the introduction of analytical errors which are due to the effects of impurities in such samples. Cane products usually contain, in addition to sucrose, invert sugar which in the case of molasses may amount to 30 percent or more of the total sugar. It is necessary that the rotation of this invert sugar remain unaltered in both the direct and invert polarizations. Mention has already been made of the necessity of observing both polarizations in the same concentration of substance in order to avoid the change in rotation caused by dilution. An additional source of error is introduced in the acid methods of inversion as a result of the

fact that the invert sugar which is present as an impurity has its rotation increased negatively in the invert reading in the presence of the hydrochloric acid. Browne [25] has shown by applying the simple acid Clerget method to pure synthetic mixtures of invert sugar and sucrose that gross inaccuracies can be caused by the changed rotation of the added invert sugar in the two polarizations.

TABLE 17.-Errors of analysis of sucrose caused by invert sugar

Jackson and Gillis sought to avoid this source of error by adding to the solution for direct polarization a neutral salt in such quantity that its effect on the invert sugar just equalled that of hydrochloric acid. The effects of added reagents on the rotation of invert sugar have been described on page 137. It was shown that 10 ml of 6.34 N hydrochloric acid in 100 ml increased negatively the rotation of the negative constituent of the divisor by 1.25° S. From the list of neutral salts it can be computed that 2.312 g of sodium chloride in 100 ml produces the same change of rotation. If, therefore, this weight of salt is added to the solution for direct polarization, the invert sugar present as an impurity will have the same rotatory power in both polarizations. But the addition of salt has now diminished the rotatory power of the normal sucrose solution from 100° to 99.38° S. The total change in rotation of sucrose is then from 99.38 to -33.18, and the Clerget divisor becomes 132.56 at 20° C. This is the basis of the Jackson and Gillis method IV described on page 155.

Nitrogenous substances consisting mainly of amino acids and their internally compensated salts occur in both beet and cane molasses. Many of these are optically active but possess one rotatory power in acid solution and quite a different one in neutral or alkaline solution. In order to compensate for this source of error Saillard [26] proposed that the invert solution be neutralized with sodium or potassium hydroxide. The method was elaborated in greater detail by Jackson and Gillis, who proposed that ammonia be used for neutralization because it had less destructive action on invert sugar than the more caustic alkalies. The neutralization of 10 ml of 6.34 N hydrochloric acid with ammonia produces 3.392 g of ammonium chloride; this causes an increased value of the negative constituent of the Clerget divisor, making it -33.84. This method of compensation was designed for beet products which were free from invert sugar. The basic value of the Clerget divisor becomes 133.84 for inversion at 60° C, or 133.94 for room-temperature inversion. This was designated Jackson and Gillis method III.

Many samples of sugar products contain both invert sugar and amino acids. Jackson and Gillis in method II sought to compensate for the altered rotation of these substances by neutralizing the solution

903232 O-50 - 11

for invert polarization with ammonia and adding 3.392 g of ammonium chloride to the solution for direct polarization. This diminishes the rotation of sucrose from 100° to 99.43° S. The basic value of the divisor according to this method is 133.27.

Method III has had such limited use that it will not be described in the present Circular. While it is capable of eliminating the errors which otherwise would be introduced by the altered rotations of aminoacids, it still serves no useful purpose, because quite invariably products which contain aminoacids also contain raffinose. Such products, therefore, contain three unknown quantities and cannot be analyzed accurately by processes which yield but two equations. The method, however, has been utilized by Osborn and Zisch, whose procedure is described in a later paragraph (p. 160).

Saillard [27] has emphasized the fact that molasses contains sodium and potassium salts of organic and inorganic acids which diminish the rotation of sucrose and increase the levorotation of invert sugar. These two effects are incompletely compensated, the effect on invert sugar being the greater. His proposed remedy is to determine the ash content of each sample, and in a control test to determine the Clerget divisor by adding to pure sucrose and to the invert-sugar solution sodium or potassium chloride in amount equivalent to the ash in the sample. Thus for beet molasses no less than four polarizations and an ash analysis are required for a single Clerget test. Saillard's proposal has not been put into extensive practice, primarily because of the prohibitive labor involved. Moreover, the procedure rests on a questionable basis, because the assumption is made that sodium and potassium chlorides produce the same effects as the alkali salts of all other acids, regardless of the nature of the anion. In other words, Saillard unwittingly assumes the constancy of "molecular depression," which numerous previous experiments had shown was lacking. Nevertheless, it is quite possible that Saillard's procedure diminishes the error caused by alkali salts in the sample, and it would be desirable to investigate the effects upon the rotations of sucrose and invert sugar of the particular alkali salts which are known to occur in molasses. The special determination of the divisor for each test recommended by Saillard appears to be an unnecessary complication, for we have complete equations for the effects of sodium chloride upon sucrose and invert sugar and of potassium chloride upon invert sugar. If the procedure should prove of value, these equations could be solved for any desired concentration of salt.

Zerban and Gamble [28] have studied the question by preparing and analyzing known solutions of sucrose mixed with low-purity products of high ash content and observed no noticeable effect on the Clerget divisor, provided the divisor was based on the dry-substance concentration. (See conclusion 10, p. 145).

The ingenious suggestion has been made by R. J. Brown, who pointed out that the data of Jackson and Gillis showed that the effect of a given quantity of salt was approximately twice as great on invert sugar as on sucrose, and that in the absence of invert sugar in the sample, if the concentration of salt in the invert polarization is half as great as in the direct, the effect is completely compensated in the two polarizations. It is then merely necessary to use the normal weight for the direct polarization and the half-normal weight for the invert polarization.