the corrected number of grammes of sugar in 100 cubic centimetres of

solution.

c

the difference between the assumed and corrected values of the

concentration.

-

N

Q'

the corrected scale-reading.

the difference between the corrected and uncorrected percentages.

As the 0 and 100 marks of the saccharimeter scale, indicating 0 gramme and 26.048 grammes concentration respectively, are given as fixed, the difference between the corrected and the uncorrected readings will be greater the further their distance from these points, and greatest midway between them. This is shown in cols. 6 and 8.

The fact that the formula above given for the calculation of specific rotation refers to ray D, whereas observations with the SoleilScheibler saccharimeter are taken with the transition tint, has no

effect upon the results, the ratio [ale being the same for all rays.

[a]n

The differences between the corrected and uncorrected values are thus seen to be not inconsiderable for solutions of medium concentration. The corrections required have been calculated by Schmitz for each degree of the saccharimeter scale and embodied in the accompanying table:—

As will be seen by comparing cols. 1 and 2, the corrected percentages at points between 17 and 84 on the scale, differ from the actual readings by amounts ranging from 0.05 to 0-08. Within these limits, therefore, and reckoning percentages to tenths only, it will suffice to deduct 0.1 per cent. from the actual readings. With rotations of less than 16 or more than 85 scale degrees, such as occur in the analysis of natural sugars and their refined products, the correction is superfluous.

$83. To convert the degrees on Ventzke's scale into true rotationdegrees, as is necessary when the specific rotation of a substance is to be determined with this instrument, the formula [a] = 66541 -0.0084153 c, given in § 82, can be used. With concentration c = 26·048, [a]D = 66.322, and determining the angle of rotation given by such solution, in a tube 2 decimetres long, from the equation a × 100 = 66-322 we get [a]D 34.55°. That is to say, a

=

2 × 26.048 solution of 26-048 grammes of sugar in 100 cubic centimetres, which rotates mean yellow ray j to the amount of 100 divisions on the Ventzke scale, would record on instruments having angular graduation a rotation of the sodium ray D through an angle of 34·55°. Hence,

1° Ventzke's scale (ray j) = 0·3455° angular measurement (ray D).

And further assuming the dispersive power of the substance to be equal to that of quartz, in which, as we have seen (§ 18), the rotations for rays D and j are to one another as 1 to 1·1306, we obtain :1° Ventzke's scale (ray j) = 0·3906° angular measurement (ray j).

Another mode of arriving at these relations is afforded by the observed fact (see § 18) that a quartz plate 1 millimetre thick rotates ray D through 21·67° and ray j through 24.5° angular measure. In a subsequent table (§ 91) the angles of rotation of ray D for sugar solutions of various degrees of concentration, in 2 decimetre tubes are given, from which, by interpolating for the decimal figures, it appears that to give an angle of rotation of 21.67°, a solution must contain 16.302 grammes of sugar in 100 cubic centimetres. This concentration, it will be seen from the table already given, § 82, corresponds with a reading of 62-662 divisions on Ventzke's scale. It is evident, therefore, that by dividing the angular values 21.67° and 24.5° by that number we obtain the value of 1° Ventzke. Thus :

1° Ventzke (ray j) = 0.3458 angular degrees (ray D), 1° Ventzke (ray j) = 0·3910 angular degrees (ray j), values which agree almost exactly with those previously obtained.

§ 84. Correction of Errors due to Imperfect Construction.In using a new instrument, it is necessary previously to test the correctness of the scale. When the zero-point of the instrument has been carefully fixed, and brought, by means of the adjust