The method applied to some of the more important carbohydrates gave the following results:
149. Birotation.—As is well known, dextrose exhibits in fresh solutions the phenomenon of birotation. The authors supposed that this phenomenon might have some relation to the size of the molecule. They, therefore, determined the molecular volume of freshly dissolved dextrose by the method of Raoult and found M = 180. The high rotatory power of recently dissolved dextrose is therefore not due to any variation in the size of its molecule.
The mathematical theory of birotation is given by Müller as follows.[121] In proportion as the unstable modification A is transformed into the stable modification B, the rotation will vary. Let ρ = the specific rotatory power of B and aρ = that of A, both in the anhydrous state. Let now p grams of the substance be dissolved in V cubic centimeters of solvent and observed in a tube l decimeters in length. The time from making the solution is represented by θ. The angle of rotation α is read at the time θ. Let x = the mass of A, and y = that of B, and the equation is derived.
| α = | a ρ xl | + | ρyl |
| V | V |
But x + y = p
| whence α = [(a - 1)x + p] | ρl |
| V |
If now there be introduced into the calculation the final angle of rotation αn, which can be determined with great exactness; we have
| αn = | p ρ l |
| V |
| and consequently α = αn[1 + | (a - 1)x | ]. |
| p |