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:

From these equations the annexed table has been prepared :1

substances are present, the sugar-percentages must be determined from the values

For example, suppose an angle of 164° has been observed, we see that 16° = 12·030 and 0·4° = 4 × 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 12-300.) Again, 100 parts by weight of the same solution, since 16° 11.516 and 0.4° = 4 × 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 (§ 85) show that when the concentration amounts to about 25 grammes of sugar in 100 cubic centimetres, and observations are taken between 15° and 25° Cent. in glass tubes 2 decimetres long, a rise of 1° Cent. causes a decrease of 0·011° 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 × 0.011 must be subtracted, or if the temperature were 23° 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.

(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 1710 Cent. (6310 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:

For the 50 cubic centimetre mark, 49.938 grammes.

The correction for weight in vacuo is here disregarded.1

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.

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 centimetre mark, 49.888 grammes, and for the 100 cubic centimetre mark, 99.775 grammes of water at a temperature of 1730 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,1 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 there1 Scheibler: Zeitsch. des Vereins für Rübenzuckerindustrie, 1870, 223.