| whence | (a - 1)x | = | α | - 1. |
| p | αn |
This equation gives the quantity x of the unstable matter which is transformed into the stable modification in the time θ.
It must be admitted that the quantity dx which is changed during the infinitely small time dθ is proportional to the mass x which still exists at the moment θ, whence dx = -Cʹxdθ where Cʹ represents a constant positive factor. From this is derived the equation
| dx | = - Cʹdθ. |
| x |
Integrating and calling x the quantity of matter changed to the stable form at the moment θ, corresponding to a rotation α₀, we have
| Cʹ = | 1 | log. nap. | x₀ | , |
| θ - θ₀ | x |
and taking into consideration the equation given above, and substituting common for superior logarithms we get
| C = | 1 | log. | α₀ - αₙ | . |
| θ - θ₀ | α - αₙ |
Experience has shown that such a constant C really exists, and its value can be easily calculated from the data of Parcus and Tollens.[122] The mean value of C from these data is 0.0301 for arabinose; 0.0201 for xylose; 0.0393 for rhamnose; 0.0202 for fucose; 0.00927 for galactose; 0.00405 for lactose; 0.00524 for maltose, and for dextrose, 0.00348 at 11° to 13° and 0.00398 from 13° to 15°. The constant C as is well known, increases as the temperature is raised.
The constant C, at a given temperature, measures the progress of the phenomenon of the change from the unstable to the stable state. It will be noticed that among the sugars possessing multirotation properties the pentoses possess a much higher speed of transformation than the others.