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Col. 5. 8, the corrected number of grammes of sugar in 100 cubic centimetres of

solution.

c

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8, the difference between the assumed and corrected values of the

7.

or

concentration. N 100.0

the corrected scale-reading.
26.048Q

N
N- the difference between the corrected and uncorrected percentages.

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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

[a].

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:

с

n

Degrees of Saccharimeter

Scale.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

Grammes of Sugar in 100 cub. cent. Solution.

Corrected

per cent.

Uncorrected.

Corrected.

Difference.

1.00

0.261

0.260

0.001

1.99

0.002

2.99

0:521
0.781
1.042

0.002

0.519
0.779
1.039
1.298

3.99

0.003

4.98

1.302

0.004

5.98

1.563

1.558

0.005

6.98

1.823

1.817

0.006

7.98

2.084

2:078

0.006

8.97

2.344

0.007 0.008

9.97

2.605

2:337 2.597 2.857 3:117

10.97

0.008

2.865
3.126

11.97

0.009 0.010

12.96

3.386

3.376 3.637

13.96

3.647

0.010

14.96

3.907

3.896

0.011

15.96

4.168

4:156

0.012

16.95

4.428

4.416

17.95

4.689 4.949

0.012 0.013 0.013

4.676 4.936 5.196

18.95

19.95

5.210

0.014

20.95

5.456

0.014

5.470
5.731

21.94

0.015

22.94

5.991

5.716
5.976
6.236

0.015

23.94

6.252

0.016

24.94

6:512

6.496

0.016

25.94

6.773

6.756

0.017

26.94

0.017

7.033
7.293

27.93

0.017

28.93

7.016 7.276 7.536 7.796 8.056

0.018

29.93

0.018

30.93

0.019

7.554 7.814 8.075 8.335 8.596 8.856

31.93

8.316

0.019 0.019

32.93

33.93

0.019

8.577
8.837
9.097
9.357

34.92

0.020

35.92

9.117 G.377 9.638

0.020

36.92

9.618

0.020

Grammes of Sugar in 100 cub. cent. Solution.

Degrees of Saccharimeter

Scale.

38

39 40

41

42 43

44

45

46

47 48 49

50

51 52

53

54

55

56

57 58 59

60

61

62

63

64

65

66

67 68

69 70

71

72 73

74

Corrected

per cent.

Uncorrected.

Corrected.

Difference.

9.878

0.020

37.92 38.92 39.92

9.898 10.159

10.138

0.021

10.419

10.398
10.659

40.92

10.680

41.92

10.940

10.919

0.021 0.021 · 0·021

0.021 0.021

42.92

11.201

11.180

43.92

11.440

11461
11.722

44.92

11.701
11.961

45.92

11.982

46.92

12-243

47.92

12.503

12.222 12.482 '12-743

0.021 0.021 0-021 0.021 0.021 0.021 0.021 0.021

48.92

12.764

49.92

13.024

13.003

50.92

13.285

13.264

51.92

13.545

13.524

52.92

13.805
14.066

13.784
14.044

53.92

54.92

14:326

14.305
14.566

55.92

14.587

14.847

14.826

56.92
57.92

15.108
15.368

58.92

15.087
15:347
15.608
15.868

59.92

15.629

60.92

15.889

61.92

16.150

16.130

62.92

16.410

16.390

0.021 0.022 0.021 0.021 0.021 0.021 0.021 0.021 0.021 0.020 0.020 0.020 0.019 0.019 0.019 0.019 0.019 0.018 0.018 0.017 0.017 0.017

63.92

16.671

16.651

64.92

16.931

16.912

65.93

17.192

17.173

66.93

17.452

17.433

67.93

17.694
17.954

68.93

69.93

70.93

17.713
17.973
18.234
18.494
18.755
19.015
19.276

71.93

18.216
18.476
18.738
18.998
19.259

72.93

73.94

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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.

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a

a x 100

$ 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]p = 66:541

- 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 = 66.322 we get [a]]

= 34.55o.

That is to say, a 2 x 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 34:55o. Hence, 1° Ventzke's scale (ray j) = 0.3455o 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 ;) = 0.3906° angular measurement (ray ;).

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 21:67o and ray j through 24.5o angular measure. In a subsequent table (S 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 21.67o, 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 21.67o and 24:50 by that number we obtain the value of 1° Ventzke.

Thus :
1° Ventzke (ray ;) 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.

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$ 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

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