Part 10

144.3 P = -----------. 144.3 - d

In this formula P is the density and d the degree of the scale. In former times the baumé instruments were graduated with a solution of common salt and a different formula was employed for calculating specific gravity, but these older instruments are no longer in common use.

The following table shows the specific gravities of solutions corresponding to baumé degrees from 1° to 75° consecutively:

Degree Specific Degree Specific Degree Specific Degree Specific baumé gravity baumé gravity baumé gravity baumé gravity 0 1.0000 19 1.1516 38 1.3574 57 1.6527 1 1.0069 20 1.1608 39 1.3703 58 1.6719 2 1.0140 21 1.1702 40 1.3834 59 1.6915 3 1.0212 22 1.1798 41 1.3968 60 1.7115 4 1.0285 23 1.1895 42 1.4104 61 1.7321 5 1.0358 24 1.1994 43 1.4244 62 1.7531 6 1.0433 25 1.2095 44 1.4386 63 1.7748 7 1.0509 26 1.2197 45 1.4530 64 1.7968 8 1.0586 27 1.2301 46 1.4678 65 1.8194 9 1.0665 28 1.2407 47 1.4829 66 1.8427 10 1.0744 29 1.2514 48 1.4983 67 1.8665 11 1.0825 30 1.2624 49 1.5140 68 1.8909 12 1.0906 31 1.2735 50 1.5301 69 1.9161 13 1.0989 32 1.2849 51 1.5465 70 1.9418 14 1.1074 33 1.2964 52 1.5632 71 1.9683 15 1.1159 34 1.3081 53 1.5802 72 1.9955 16 1.1246 35 1.3201 54 1.5978 73 2.0235 17 1.1335 36 1.3323 55 1.6157 74 2.0523 18 1.1424 37 1.3447 56 1.6340 75 2.0819

=55. Correction for Temperature.=—The baumé hydrometer should be used at the temperature for which it is graduated, usually 15°. In this country the mean temperature of our working rooms is above 15°. The liquid in the hydrometer flask should therefore be cooled to a trifle below 15°, or kept in a bath exactly at 15° while the observation is made. When this is not convenient, the observation may be made at any temperature, and the reading corrected as follows: When the temperature is above 15° multiply the difference between the observed temperature and fifteen, by 0.0471 and add the product to the observed reading of the baumé hydrometer; when the temperature on the other hand, is below fifteen, the corresponding product is subtracted.

=56. The Balling or Brix Hydrometer.=—The object of the balling or brix instrument is to give in direct percentages the solid matter in solution. It is evident that for this purpose the instrument must be graduated for a particular kind of material, since ten per cent of sugar in solution, might have a very different specific gravity from a similar quantity of another body. Instruments of this kind graduated for pure sugar, find a large use in technical sugar analysis. To attain a greater accuracy and avoid an instrument with too long a stem, the brix hydrometers are made in sets. A convenient arrangement is to have a set of three graduated as follows; one from 0° to 30°, one from 25° to 50°, and one from 45° to 85°. When the percentage of solid matter dissolved is over seventy the readings of the scale are not very reliable.

=57. Correction for Temperature.=—The brix as the baumé scale is graduated at a fixed temperature. This temperature is usually 17°.5. The following table shows the corrections to be applied to the scale reading when made at any other temperature:

PER CENT OF SUGAR IN SOLUTION.

0. 5. 10. 15. 20. 25. 30. 35. 40. 50. 60. 70. 75. Temp. To be subtracted from the degree read. 0° 0.17 0.30 0.41 0.52 0.62 0.72 0.82 0.92 0.98 1.11 1.22 1.25 1.29 5° 0.23 0.30 0.37 0.44 0.52 0.59 0.65 0.72 0.75 0.80 0.88 0.91 0.94 10° 0.20 0.26 0.29 0.33 0.36 0.39 0.42 0.45 0.48 0.50 0.54 0.58 0.61 11° 0.18 0.23 0.26 0.28 0.31 0.34 0.36 0.39 0.41 0.43 0.47 0.50 0.53 12° 0.16 0.20 0.22 0.24 0.26 0.29 0.31 0.33 0.34 0.36 0.40 0.42 0.46 13° 0.14 0.18 0.19 0.21 0.22 0.24 0.26 0.27 0.28 0.29 0.33 0.35 0.39 14° 0.12 0.15 0.16 0.17 0.18 0.19 0.21 0.22 0.22 0.23 0.26 0.28 0.32 15° 0.09 0.11 0.12 0.14 0.14 0.15 0.16 0.16 0.17 0.17 0.19 0.21 0.25 16° 0.06 0.07 0.08 0.09 0.10 0.10 0.11 0.12 0.12 0.12 0.14 0.16 0.18 17° 0.02 0.02 0.03 0.03 0.03 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.06

To be added to the degree read. 18° 0.02 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.02 19° 0.06 0.08 0.08 0.09 0.09 0.10 0.10 0.10 0.10 0.10 0.10 0.08 0.06 20° 0.11 0.14 0.15 0.17 0.17 0.18 0.18 0.18 0.19 0.19 0.18 0.15 0.11 21° 0.16 0.20 0.22 0.24 0.24 0.25 0.25 0.25 0.26 0.26 0.25 0.22 0.18 22° 0.21 0.26 0.28 0.31 0.31 0.32 0.32 0.32 0.33 0.34 0.32 0.29 0.25 23° 0.27 0.32 0.35 0.37 0.38 0.39 0.39 0.39 0.40 0.42 0.39 0.36 0.33 24° 0.32 0.38 0.41 0.43 0.44 0.46 0.46 0.47 0.47 0.50 0.46 0.43 0.40 25° 0.37 0.44 0.47 0.49 0.51 0.53 0.54 0.55 0.55 0.58 0.54 0.51 0.48 26° 0.43 0.50 0.54 0.56 0.58 0.60 0.61 0.62 0.62 0.66 0.62 0.58 0.55 27° 0.49 0.57 0.61 0.63 0.65 0.68 0.68 0.69 0.70 0.74 0.70 0.65 0.62 28° 0.56 0.64 0.68 0.70 0.72 0.76 0.76 0.78 0.78 0.82 0.78 0.72 0.70 29° 0.63 0.71 0.75 0.78 0.79 0.84 0.84 0.86 0.86 0.90 0.88 0.80 0.78 30° 0.70 0.78 0.82 0.87 0.87 0.92 0.92 0.94 0.94 0.98 0.94 0.88 0.86 35° 1.10 1.17 1.22 1.24 1.30 1.32 1.33 1.35 1.36 1.39 1.34 1.27 1.25 40° 1.50 1.61 1.67 1.71 1.73 1.79 1.79 1.80 1.82 1.83 1.78 1.69 1.65 50° ---- 2.65 2.71 2.74 2.78 2.80 2.80 2.80 2.80 2.79 2.70 2.56 2.51 60° ---- 3.87 3.88 3.88 3.88 3.88 3.88 3.88 3.90 3.82 3.70 3.43 3.41 70° ---- ---- 5.18 5.20 5.14 5.13 5.10 5.08 5.06 4.90 4.72 4.47 4.35 80° ---- ---- 6.62 6.59 6.54 6.16 6.38 6.30 6.26 6.06 5.82 5.50 5.33

According to observations of Gerlach, the correction for temperature varies with the concentration of the solution and the range of temperature as shown in the table.

=58. Comparison of Brix and Baumé Degrees.=—The following table shows the degree baumé and the specific gravity of a sugar solution for each degree brix (per cent of sugar in solution) from zero to ninety-five:

Degree Degree Specific Degree Degree Specific brix. baumé. gravity. brix. baumé. gravity. 1.0 0.6 1.00388 37.0 20.7 1.16413 2.0 1.1 1.00779 38.0 21.2 1.16920 3.0 1.7 1.01173 39.0 21.8 1.17430 4.0 2.3 1.01570 40.0 22.3 1.17943 5.0 2.8 1.01970 41.0 22.9 1.18460 6.0 3.4 1.02373 42.0 23.4 1.18981 7.0 4.0 1.02779 43.0 24.0 1.19505 8.0 4.5 1.03187 44.0 24.5 1.20033 9.0 5.1 1.03599 45.0 25.0 1.20565 10.0 5.7 1.04014 46.0 25.6 1.21100 11.0 6.2 1.04431 47.0 26.1 1.21639 12.0 6.8 1.04852 48.0 26.6 1.22182 13.0 7.4 1.05276 49.0 27.2 1.22128 14.0 7.9 1.05703 50.0 27.7 1.23278 15.0 8.5 1.06133 51.0 28.2 1.23832 16.0 9.0 1.06566 52.0 28.8 1.24390 17.0 9.6 1.07002 53.0 29.3 1.24951 18.0 10.1 1.07441 54.0 29.8 1.25517 19.0 10.7 1.07884 55.0 30.4 1.26086 20.0 11.3 1.08329 56.0 30.9 1.26658 21.0 11.8 1.08778 57.0 31.4 1.27235 22.0 12.4 1.09231 58.0 31.9 1.27816 23.0 13.0 1.09686 59.0 32.5 1.28400 24.0 13.5 1.10145 60.0 33.0 1.28989 25.0 14.1 1.10607 61.0 33.5 1.29581 26.0 14.6 1.11072 62.0 34.0 1.30177 27.0 15.2 1.11541 63.0 34.5 1.30177 28.0 15.7 1.12013 64.0 35.1 1.31381 29.0 16.3 1.12488 65.0 35.6 1.31989 30.0 16.8 1.12967 66.0 36.1 1.32601 31.0 17.4 1.13449 67.0 36.6 1.33217 32.0 18.0 1.13934 68.0 37.1 1.33836 33.0 18.5 1.14423 69.0 37.6 1.34460 34.0 19.1 1.14915 70.0 38.1 1.35088 35.0 19.6 1.15411 71.0 38.6 1.35720 36.0 20.1 1.15911 72.0 39.1 1.36355 73.0 39.6 1.36995 85.0 45.5 1.44986 74.0 40.1 1.37639 86.0 46.0 1.45678 75.0 40.6 1.38287 87.0 46.5 1.46374 76.0 41.1 1.38939 88.0 47.0 1.47074 77.0 41.6 1.39595 89.0 47.5 1.47778 78.0 42.1 1.40254 90.0 49.9 1.48486 79.0 42.6 1.40918 91.0 48.4 1.49199 80.0 43.1 1.41586 92.0 48.9 1.49915 81.0 43.6 1.42258 93.0 49.3 1.50635 82.0 44.1 1.42934 94.0 49.8 1.51359 83.0 44.6 1.43614 95.0 50.3 1.52087 84.0 45.1 1.44298

=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. 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.

If now the plane of vibration in each prism be regarded as coincident with its principal section, the following phenomena are observed: If the prisms are so placed that the principal sections lie in the prolongation of the same plane, then the extraordinary polarized ray from the polarizer passes into the analyzer, which practically may be regarded in this position as a continuation of the same prism. It happens, therefore, that the extraordinary polarized ray passes through the analyzer exactly as it did through the polarizer, and is not reflected by the film of balsam, but emerges from the analyzer in seemingly the same condition as from the polarizer. If now the analyzer be rotated 180°, bringing the principal section again in the same plane, the same phenomenon is observed. But if the rotation be in either direction only 90°, then the polarized ray from the first prism, incident on the second, deports itself exactly as the ordinary ray, and on meeting the film of balsam is totally reflected. The field of vision, therefore, is perfectly dark.

In all other inclinations of the planes of the principal sections of the two prisms the ray incident in the analyzer is separated into two, an ordinary and extraordinary, varying in luminous intensity in proportion to the square of the cosine of the angle of the two planes.

Thus, by gradually turning the analyzer, the field of vision passes slowly from maximum luminosity to complete obscurity. The expression crossed nicols refers to the latter condition of the field of vision.

=62. Description of the Prism.=—In a nicol made as described above, Fig. 31, suppose a ray of light parallel with the longer side of the prism be incident to the end a b at m. By the double refracting power of the spar the ray is divided into two, which traverse the first half of the prism. The two rays are polarized at right angles to one another. The less refracted ray when it strikes the film of Canada balsam passes through it without interference. The more refracted ray strikes the balsam at o at such an angle as to be totally reflected and made to pass out of the prism in the direction o r. If the prism be blackened at the surface the ray will be entirely absorbed. The other ray passes on through the other half of the prism and emerges in the direction of qs. It is evident that the emergent light from a nicol has only half the illuminating power possessed by the immergent rays.

The polarized plane of light from the nicol just described may be regarded as passing also into a second nicol of essentially the same construction as the first.

This second nicol, called the analyzer, is so constructed as to revolve freely about its longitudinal axis, and is attached to a graduated circle in such a way that the degree of rotation can be accurately read. If the planes of polarization of the two nicols are coincident when prolonged, the ray of light passing from the first nicol will pass through the second practically unchanged in character or intensity. If, however, the analyzing nicol be turned until the plane of polarization is at right angles to that of the polarizer the immergent ray will suffer refraction in such a manner as to be totally reflected when reaching the film of balsam and will be thus entirely lost. In making a complete revolution of the analyzer, therefore, two positions of maximum intensity of light and two of darkness will be observed. In intermediate positions the ray immergent to the analyzer will be separated as in the first instance into two rays g p varying intensities, one of which will be always totally reflected.