59. Error Due to Impurities.—The fact that equal per cents of solid bodies in solution affect the specific gravity in different degrees has already been noted. The specific gravities of the solutions of the common sugars, however, are so nearly the same for equal per cents of solid matter in solution as to render the use of a brix hydrometer quite general for technical purpose. For the mineral salts which often occur in sugar solutions the case is quite different. A twenty per cent solution of cane sugar at 17°.5 has a specific gravity 1.08329 and of dextrose 1.08310, practically identical. But a solution of calcium acetate of similar strength has a specific gravity of 1.0874; of sodium sulfate 1.0807, and of potassium nitrate 1.1359. This latter number would correspond to a sugar content of nearly twenty-seven per cent. The brix scale can, therefore, be regarded as giving only approximately the percentage of solid matter in sugar solutions and, while useful in technical work, should never be relied upon for exact analytical data.
THE DETERMINATION OF SUGAR
WITH POLARIZED LIGHT.
60. Optical Properties of Natural Sugars.—The solutions of all natural sugars have the property of deflecting the plane of polarized light and the degree of deflection corresponds to the quantity of sugar in solution. By measuring the amplitude of the rotation produced the percentage of sugar in the solution can be determined. In order to secure accuracy in the determinations it is necessary that only one kind of sugar be present, or, if more than one, that the quantities of all but one be determined by other means, and the disturbances produced thereby in the total rotation be properly arranged. In point of fact the process in practice is applied chiefly to cane and milk sugars, both of which occur in nature in an approximately pure state. The process is also useful in determining cane sugar when mixed with other kinds, by reason of the fact that this sugar after hydrolysis by treatment with a weak acid for a long or a strong acid for a short time, definitely changes its rotating power. Since, by the same treatment, the rotating power of other sugars which may be present is only slightly altered, the total disturbance produced is approximately due to the inversion of the cane sugar.
Dextrose and maltose arising from the hydrolysis of starch may also be determined with a fair degree of accuracy by their deportment with polarized light. When a solution of natural sugars shows negative results when examined with polarized light, it is due to an admixture of two or more sugars of opposite polarizing powers in such proportions as to produce neutrality. This condition often occurs in the examination of honeys or in submitting artificial sugars to polarimetric observations. In the latter case the neutrality is caused by the tendency manifested by artificially produced sugars to form twin compounds of optically opposite qualities.
The instrument used for measuring the degree of deflection produced in a plane of polarized light is called a polariscope, polarimeter, or optical saccharimeter. For a theoretical discussion of the principles of polarization and the application of these principles in the construction of polariscopes, the reader is referred to the standard works on optics and the construction of optical instruments.[35] For the purposes of this work a description of the instruments commonly employed and the methods of using them will be sufficient.
61. Polarized Light.—When a ray of light has been repeatedly reflected from bright surfaces or when it passes through certain crystalline bodies it acquires peculiar properties and is said to be polarized.
Polarization is therefore a term applied to a phenomenon of light, in which the vibrations of the ether are supposed to be restricted to a particular form of an ellipse whose axes remain fixed in direction. If the ellipse become a straight line it is called plane polarization. This well-known phenomenon is most easily produced by a nicol prism, consisting of a cut crystal of calcium carbonate (Iceland spar). This rhombohedral crystal, the natural ends of which form angles of 71° and 109°, respectively, with the opposite edges of its principal section, is prepared as follows:
The ends of the crystals are ground until the angles just mentioned become 68° and 112°. The crystal is then divided diagonally at right angles with the planes of the ends and with the principal section, and after the new surfaces are polished they are joined again by canada balsam. The principal section of this prism passes through the shorter diagonal of the two rhombic ends. If now a ray of light fall on one of the ends of this prism, parallel with the edge of its longer side, it suffers double refraction, and each ray is plane polarized, the one at right angles with the other. That part of the entering ray of light which is most refracted is called the ordinary and the other the extraordinary ray. The refractive index of the film of balsam being intermediate between those of the rays, permits the total reflection of the ordinary ray, which, passing to the blackened sides of the prism, is absorbed. The extraordinary ray passes the film of balsam without deviation and emerges from the prism in a direction parallel with the incident ray, having, however, only half of its luminous intensity.
Two such prisms, properly mounted, furnish the essential parts of a polarizing apparatus. They are called the polarizer and the analyzer, respectively.