| (1)S = | C - 0.493A |
| 0.827 |
| (2) R = | A - S | = 1.017A - | 6 |
| 1.57 | 1.298 |
In these formulas S and R are the respective per cents of sucrose and raffinose desired, A the polarization in sugar degrees before inversion, B the polarization after inversion read at 20°, and C is the algebraic difference between A and B. It must be understood that these formulas are applicable only to a solution containing no other optically active substances, save sucrose and raffinose.
101. Specific Rotatory Power.—In order to compare among themselves the rotations produced on a plane of polarized light by different optically active bodies in solution, it is convenient to refer them all to an assumed standard. The degree of rotation which the body would show in this condition, is found by calculation, since, in reality, the conditions assumed are never found in practice. In the case of sugars and other optically active bodies, the standard of comparison is called the specific rotatory power. This factor in any given case, is the angular rotation which would be produced by any given substance in a pure anhydrous state if it were one decimeter in length and of a specific gravity equal to water. These are conditions which evidently do not exist in the case of sugars, since crystalline sugar particles have no polarizing power, and it would be impossible to pass a ray of light through an amorphous sugar column of the length specified. The specific rotatory power is therefore to be regarded as a purely theoretical factor, calculated from the actual data obtained by the examination of the solution of any given substance. If the length of the observation tube in decimeters be represented by l, the percentage of the polarizing body in 100 grams by p, and the specific gravity of the solution by d, and the observed angle of rotation by a, then the factor is calculated from the formula:
| [a]Dj = | a. 100 | . |
| p. d. l. |
The symbols Dj refer to the character of light employed, D indicating the monochromatic sodium flame, and j the transition tint from white light.
If the weight of the polarizing body c be given or known for 100 cubic centimeters of the solution the formula becomes
| [a]Dj = | a. 100 | . |
| c. l. |
The latter formula is the one easier of application since it is only necessary in applying it to dissolve a given weight of the active body in an appropriate solvent and to complete the volume of the solution exactly to 100 cubic centimeters. It is therefore unnecessary in this case to determine the specific gravity.
102. Formulas for Calculating Specific Rotatory Power.—In order to determine the specific rotatory power (gyrodynat[64]) of a given substance it is necessary to know the specific gravity and percentage composition or concentration of its solution, and to examine it with monochromatic polarized light in an instrument by which the angular rotation can be measured. The gyrodynat of any body changes with its degree of concentration, in some cases with the temperature, and always with the color of the light. With the red rays the gyrodynat is least and itprogressively increases as the violet end of the spectrum is approached. In practice the yellow ray of the spectrum has been found most convenient for use, and in the case of sugars the gyrodynat is always expressed either in terms of this ray or if made with color compensating instruments in terms of the sensitive or transition tint. In the one case the symbol used is (a)D and in the other (a)j. From this statement it follows that (a)D is always numerically less than (a)j. Unless otherwise specified the gyrodynat of a body is to be considered as determined by yellow monochromatic light, and therefore corresponds to aD.[65]