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Hence the following interpolation-formulæ for determining from the observed angle of rotation a the concentration c and percentage p of solutions have been derived by the method of least squares :

c= 0.75063 a + 0.0000766 a”,
p= 0.74730 a

0:001723 a?.
From these equations the annexed table has been prepared :1

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1 The value p is for solutions of pure sugar. In beet-root solutions where other substances are present, the sugar-percentages must be determined from the values for and the observed specific gravity of the solutioņs.

C,

Grammes

Observed

Rotation with 2-decimetre Tube.

Grammes of Sugar in 100 cub. cents.

Solution.

Observed

Rotation with 2-decimetre Tube.

of Sugar in 100 grammes

Solution.

a.

c.

a.

p.

Differ

ence for

Difference
for 0.1°

of
Rotation.

0.1° of

Rotation.

3.693

3.755 4:507

4.422

5.259

0.073 0.073 0.072 0.072 0.072

6•010

6.762

10°

7.514

10°

0.071

5.147 5.868 6:586 7.301 8:011 8.719 9.424 10.124

11°

8.266

11°

0.071

12°

9:019

12°

13°

9.771

13°

0.071 0:070 0.070 0.070

14°

10.524

14°

0.075

15°

11.277

15°

10.821

16°

12.030

16°

11:516

0.069

17°

12:783

17°

12:206

0.069

18°

13.536

18°

12.893

0.068

19°

14.290

19°

13.576

0.068

20°

15.044

20°

0.068

14.257
14.933

21°

15.797

21°

0.067

22°

16.551

22°

15.606

0.067

23°

17.306

23°

0.067

24°

18.059

24°

0.066

25°

18.814

25°

0.066

26°

19.568

26°

16.277
16.943
17.605
18.265
18.921
19.573
20.223

0.066

20.323

27°

0.065

21.078

28°

0.065

29°

27° 28° 29° 30° 31° 32°

21.833
22:588

0:065
0.06+

30°

20.868

23.343

31°

21:510

0.064

0.076

24.098

32°

22.149

0.064

33°

24.853

33°

22.784

0.063

34°

25.611

34°

23.416

0.063

35°

26.366

35°

0.068

36°

27.122

36°

0.068

24.044
24.670
25.291
25.909

27.878

37°

0.062

37° 38°

28.635

38°

0.062

39°

29.392

39°

26.523

0.061

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For example, suppose an angle of 16:4° has been observed, we see that 16° = 12:030 and 0.4° = 4 x 0.075, hence the solution contains in 100 cubic centimetres 12:330 grammes of sugar. (The constant 0.752 given in $ 90 would show a concentration of 12:333, and its approximate value 0.75, a concentration of 12300.) Again, 100 parts by weight of the same solution, since 16° = 11.516 and 0.4° = 4 x 0.069, contain 11.792 parts by weight of sugar.

As regards the influence of temperature, the researches of Tuchschmid and the calculations of Mategczek (885) show that when the concentration amounts to about 25 grammes of sugar in 100 cubic centimetres, and observations are taken between 150 and 25° Cent. in glass tubes 2 decimetres long, a rise of 1° Cent. causes a decrease of 0.011o angular measure. Thus, when the temperature of observation differs from 20° Cent., the foregoing value may be used to correct the angle of rotation observed. For example, suppose the temperature of the solution were 17° Cent., the amount 3 x 0·011 must be subtracted, or if the temperature were 23o Cent., the same amount must be added to the angle observed. For sugar-solutions of less concentration, the amount of this correction is less, and when the temperature is not far removed from 20° Cent. it may be neglected altogether,

.

183

(e.) Preparation of Solutions for the Saccharimeter.

$ 92. In saccharimetry, measuring flasks of 50 and 100 cubic centimetres are employed which are usually provided with an additional mark, indicating capacities of 55 and 110 cubic centimetres respectively. These marks are fixed by weighing into the flasks water at some determinate mean temperature, usually 17° Cent. (631° Fahr., 14° Reaum.). As will be seen from the table given in $ 73, page 146, the following weights of water must be introduced in order to fix the levels of the several marks :

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For the 50 cubic centimetre mark, 49.938 grammes.
55

54.932
100

99.875 110

109.863

The correction for weight in vacuo is here disregarded.

The solutions necessary for the different forms of saccharimeter, taking observations in each case with 200 millimetre tubes, are as given below : 50 cubic centimetres will generally be found sufficient.

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For weighing the samples, Scheibler recommends basins with a lip made of German silver, a material not readily wetted by aqueous liquids.

1 Reduced to vacuo, the weights required, according to $ 69, are for the 50 cubic oentimetre mark, 49.888 grammes, and for the 100 cubic centimetre mark, 99.775 grammes of water at a temperature of 174° Cent.

2 Scheibler: Zeitsch. des Vereins für Rübenzuckerindustrie, 1870, 614.

The weighed substance should be dissolved directly in the basin, the contents poured into the flask, and the basin itself then carefully washed with a stream of water into the flask, care being taken that the latter does not get more than three-quarters filled.

$ 93. Decoloration of Solutions.-If the solution so prepared, as is usually the case with natural sugars, beet-juice, and the like, is more or less coloured and turbid, the addition of some clarifying substance becomes necessary.

The substance most commonly employed for the purpose is basic acetate of lead, in quantities of one or more cubic centimetres, according to the impurity of the sugar and the concentration of the solution. This usually throws down a heavy precipitate, by which various non-saccharine substances, as malic acid, aspartic acid, etc., are removed as lead salts, carrying down with them the particles which produce the turbidity. If the precipitate formed is small, it is convenient to add besides a few drops of solution of alum, so as to produce a precipitate of sulphate of lead. Too great excess of the basic acetate must be avoided, otherwise the filtered liquid will, in contact with the air, again become cloudy by the formation of carbonate of lead. This turbidity may, however, be dispelled by the addition of a drop of acetic acid. The basic acetate of lead is prepared by putting a finely powdered mixture of 3 parts ordinary acetate of lead and 1 part litharge along with 10 parts water in a closed flask, and allowing the mixture to remain until, aided by frequent shaking, only a small white residue remains undissolved. The filtered liquid should then have a specific gravity of from 1.23 to 1.24.

Aluminium hydrate, as recommended by Scheibler, can also be employed as a decolorant. This can be prepared by precipitating a solution of sulphate of aluminium or of alum by means of ammonia, and washing the precipitate by decantation until the wash-water no longer gives a blue colour to red litmus paper. The voluminous pulpy mass so obtained is to be preserved in a closed flask, from which, by means of a pipette with wide stem, quantities may be removed as required. For the clarification of 13.024 grammes of a sugar dissolved in a 50 cubic centimetre flask, from 3 to 5 cubic centimetres are generally required. The alumina is especially adapted for the removal of turbidity; but less so for the removal of colouring matters; and there

1 Scheibler: Zeitsch. des Vereins für Rübenzuckerindustrie, 1870, 223.

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