=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_. 100 [_a_]_{Dj} = ---------------. _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_. 100 [_a_]_{Dj} = ----------. _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.