POLARIMETRY,

SACCHARIMETRY,

AND THE SUGARS

By FREDERICK J. BATES AND ASSOCIATES

ABSTRACT

For the purposes of this treatise, the subject matter presented has been divided into five parts. The first of these covers a mathematical treatment of the physical phenomena and a description and discussion of the physical equipment, such as polarimeters, saccharimeters, and accessory apparatus utilized in the study and applications of polarized light.

The development of polarimetric equipment is discussed from the historical standpoint, but emphasis has been placed upon recent developments. This phase of the subject is followed by a general discussion and evaluation of the numerous methods for the analysis and study of raw and refined sugars and sugar products. Special emphasis has been made upon recent contributions and applications of physical science to chemical analysis, including electrical conductivity, colorimetry, refractometry, densimetry, hydrogen-ion concentration, turbidity and viscosity. The latter subject includes the Bureau's recent contributions and important new data on the subject.

The methods of preparation and properties of the sugars and their derivatives are given in considerable detail. In this connection a detailed study of the literature has been made and the most dependable methods of preparation of the more important sugars and their derivatives are given.

A section of general information relating to such subjects as special tests by the Bureau, issuing of standard samples, certificates and statements, test fees, etc., is included.

One hundred and fifty numerical tables are given, which provide a working basis for experimental and analytical purposes. The data given in certain of these tables have not heretofore been available. In table 148, "Optical Rotation and Melting Point of Certain Sugars and Their Derivatives,' the data given are the result of a careful examination of a vast literature. There are also included the United States Customs Regulations and a digest of the Proceedings of the International Commission for Uniform Methods of Sugar Analysis.

PART 1. POLARIZED LIGHT, POLARIMETERS, SACCHARIMETERS, AND ACCESSORY APPARATUS

I. INTRODUCTION

Since the organization of the National Bureau of Standards in 1901 there has been submitted for test a great variety of polariscopic apparatus typifying the designs and methods of construction adopted by American and European manufacturers. The Bureau is equipped with examples of the standard apparatus of the leading polariscope builders, as well as special apparatus for work requiring the highest attainable precision. For most of the apparatus sent to the Bureau for test no intimation is given as to the degree of accuracy to be certified. In these cases it is the practice to report the tests to such precision as the Bureau's previous experience with the type of appa

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ratus involved has shown it to merit. On the other hand, a precision is frequently requested which is greater than the apparatus justifies. In general, two grades or standards of accuracy have been found adequate in standardizing polariscopic apparatus. The first grade is for work requiring the highest commercial accuracy. The second grade is for all scientific work except special research in which the precision of the supplementary data entering into the ultimate results justifies a still higher accuracy in the polarimetric data. In the latter case the Bureau will cooperate with investigators in providing not only for tests of the highest precision but also, on request, in furnishing any information at its disposal in reference to methods of measurement and the design and construction of special apparatus. It also is the desire of the Bureau to cooperate with manufacturers, scientists, and others in bringing about more satisfactory conditions relative to the weights, measures, measuring instruments, and physical constants used in polariscopic work, and to place at the disposal of those interested such information relative to these subjects as may be in the Bureau's possession.

II. POLARIZED LIGHT

1. NATURE OF POLARIZED LIGHT

According to the modern wave theory, light is an electromagnetic disturbance that travels as trains of waves oscillating transversely to the direction of propagation. The associated electric and magnetic forces are, therefore, not only perpendicular to each other but also to the direction of advance. Moreover, the oscillations consist, in general, not only of very nearly periodic variations in the magnitudes of the forces but also of more or less periodic changes in the directions of the force vectors about the propagational axis. The variations in magnitude for the two associated forces are generally so simply related that, although they are 90° out of phase, it is customary in most problems related to polarimetry to consider only the variations in one force. Since the electric force is commonly identified with the light vector, its variations are those usually discussed in such problems.

Although the variations in magnitude and direction of this vector are oscillatory in character, they would undoubtedly seem to possess only the slightest indication of their intrinsic periodicity if it were possible actually to see them as they occur in any beam of polychromatic light. Moreover, the amplitude and period continually vary even if the light is practically monochromatic; also even if the component in any direction perpendicular to the propagational axis is segregated in order to eliminate the directional variation in the unresolved oscillation. In comparison to the rapidity of the primary oscillation, however, the variations in amplitude and period develop slowly. For the sake of simplicity, it is customary, therefore, to consider that both amplitude and period are constant for time intervals that are very great compared to the period. In many cases, this makes it possible to treat the complex oscillations of light as very simple forms of periodic motion.

Of the possible oscillatory forms of periodic motion in a wave-like disturbance such as light, the simplest to visualize and the easiest to analyze are the rectilinear, circular, and elliptical. Obviously, the last of these is the most general of the three, since in a broad sense it

includes the others as limiting cases. Whenever the magnitude and direction of the light vector appear to vary continually in accordance with any one of these simple periodic motions, the light is said to be plane, circularly, or elliptically polarized, respectively. If its oscillation appears to conform only partially or not at all to any of these forms, the light is accordingly said to be partially polarized or unpolarized. Under natural conditions light as emitted by an extended source is never completely polarized. Presumably, however, its oscillation is always either approximately plane, circular, or elliptical for very small intervals of time. In that case, the lack of detectable polarization by the use of ordinary polarimetric tests must be the result of the very rapid changes from one form of oscillation to another, and the changes must develop in such a way that all effects of the light are symmetrical about the propagational axis [1, p. 254].1

Since the oscillation in plane polarized light is rectilinear, the electric vector in a beam of such light is perpendicular to a fixed plane that lies parallel to the axis pf propagation. This plane is parallel to the magnetic vector and is called the plane of polarization. The angular position of this plane with respect to some chosen reference planealso parallel to the propagational axis-is the azimuth (YP) of the plane of polarization. For example, if a plane polarized beam of parallel light rays is being propagated in the positive Z-direction, and yp=0 with respect to the YZ-plane, the light vector and its oscillations are parallel to the XZ-plane. The oscillation caused by the passage of the wave trains of light at any point, zo, in such a beam may be visualized as rectilinear oscillations of that point about its rest position (for instance, x=0, y=0). While the point is thus representing the supposedly continuous, rectilinear, and periodic variation of the light vector, its displacement from rest position at any time, t, may be expressed by the relation

If the light is polarized so that Yp=7/2, the oscillation is parallel to the YZ-plane, and the displacement of the point at any time, t, will be

These are the equations of the rectilinear oscillations obtained by resolving the oscillation either of an unpolarized or of a polarized beam into rectangular rectilinear components.

If the light is practically monochromatic, the amplitudes, a and b, will be approximately constant over time intervals that are great compared to the oscillation period, although in general both actually vary many thousands of times a second between zero and successive maxima of different magnitudes. The angular frequencies, wx and w, likewise approach constancy over similar comparatively large time intervals, although they actually vary between limits within the spectral range of the "monochromatic" light. Moreover, these frequencies when observed simultaneously are, in general, different even at common points in beams which are components of a single beam.

The numbers in brackets correspond to the numbered literature references given throughout this Circular.

Angular velocities, w, are related to the period, T, and frequency, v, by the identities.

where c and X' are the velocity and wave length of the light in vacuum. The "phase angle" constants, a and B, merely signify that at the time, t=0, the displacements may not have had their maximum positive values, a and b. As written, they are equivalent, when positive, to lags or retardations.

The phase difference between the wave trains of the two beams, 1a and 1, is ẞ-a-do at zo (when t=0), and a positive value for this difference indicates that the y-train lags behind the x-train. If w1 = wy at all times, this lag obviously remains constant; but in general this is not the case, even when the components come from a common and practically monochromatic source. Consequently, after a time, t, the lag at zo becomes

However, under the above conditions relative to the source, 8, (w,wr)t never increases with time indefinitely (as it would if the frequencies or the components were so different that w wr was large and always had the same sign); but it may nevertheless vary uncertainly between positive and negative values of uncertain magnitude, because the difference in frequencies, although small, is subject to erratic variations and changes in sign. Only when w-w, becomes almost vanishingly small at all times will 8, remain approximately

zero.

In polarimetric measurements, the differences in phase between two component trains may be required for other common points (or pairs of related points) along the paths traversed. The expression for the change in the phase difference between two such points is immediately obvious when the equations expressing the displacements for both component beams in terms of both t and z are considered. These equations are

From these the expression for the difference in phase between the oscillations at zy and z, (points in y- and x-beam, respectively) is at the time, t,

The first terms, d, and do, have been discussed and means of making them approach zero will be considered later. A portion, d=2π(2y—Zx)/λy, of the term in parentheses expresses the phase difference caused when the path lengths, D, and D2, traversed by the beams are differ

ent. Such differences appear, for example, when light passes through doubly refracting plates and the component beams diverge. (In that case d-D1-D2). The second portion in the parentheses expresses the phase difference caused by a difference in the wave lengths of the two beams which have traversed equal paths (D=D1=D2). If 2=2y, and 20=0, then 8=0, and the whole term in parentheses becomes simply dь=2πz(1/λ, — 1/λx).

If the difference in wave length is entirely the result of a difference between the refractive indices, μ, and μ, of the medium for the two beams, this phase difference becomes

since == if the component beams have the same wave length in vacuum. That is, d is the phase difference introduced between the two component beams after traversing paths of equal length in a doubly refracting medium. This relation is used in computing the order of thin doubly refracting plates [2, p. 554].

2. INHOMOGENEITY OF LIGHT AND INCOHERENCY
OF LIGHT BEAMS

In the foregoing paragraphs it has been stated that the amplitude and frequency of the oscillations, even in so-called monochromatic light, are never constant. Moreover, the variations in these oscillation characteristics are always unlike in any two plane polarized component beams obtained directly from an unpolarized beam. Under these conditions, the component beams are said to be incoherent. That is, in strictly coherent beams, the ratio of the amplitudes of the oscillations at corresponding points in the beam paths must remain constant and the frequencies must remain equal indefinitely. To say the least, the variability of amplitude and frequency in light oscillations is closely related to the inhomogeneity of the light. Two views of this relation may be taken, either inhomogeneity is the cause of the variability or the reverse of this.

That light as perceived is always inhomogeneous is obvious when it is considered that even the narrowest spectral line obtainable actually represents an infinitude of slightly different frequencies, and that inhomogeneity is related to variability of amplitude is suggested by the composition of rectilinear oscillations in the same azimuth which have constant amplitudes and constant but slightly different frequencies, although, as far as light is concerned, such constancy is purely a convenient assumption. If the displacements contributing to the resultant at zo and time, t, are

the resultant (assuming that the displacements are additive) will be by simple trigonometric operations

x=x1+x2=A1 cos (wt-a')-A2 sin (wt-a')=a cos (wt-a).

(4)

Chiefly as aids in the performance of these operations and in the interpretation of the results, the following identities may be written