For any degree of concentration according to Tollens the gyrodynat may be computed by the following formula: [_a_]_{D} = 66°.386 + 0.015035_p_ - 0.0003986_p_², in which _p_ is the number of grams of sugar in 100 grams of the solution.[67] In the table constructed by Schmitt the data obtained are as follows: In 100 parts by weight Specific Rotation _a_ of solution. gravity Concentration for 100 mm. Sugar _p_. Water _q_. at 20° C. _d_. _c_ = _pd_. at 20° C. [_a_]_{D}. 64.9775 35.0225 1.31650 85.5432 56°.134 65°.620 54.9643 45.0357 1.25732 69.1076 45°.533 65°.919 39.9777 60.0223 1.17664 47.0392 31°.174 66°.272 25.0019 74.9981 1.10367 27.5938 18°.335 66°.441 16.9926 83.0074 1.06777 18.1442 12°.064 66°.488 9.9997 90.0003 1.03820 10.3817 6°.912 66°.574 4.9975 95.0025 1.01787 5.0868 3°.388 66°.609 1.9986 98.0014 1.00607 2.0107 1°.343 66°.802 =105. Bi-Rotation.=—Some sugars in fresh solution show a gyrodynat much higher than the normal, sometimes lower. The former phenomenon is called bi- the latter semi-rotation. Dextrose shows birotation in a marked degree, also maltose and lactose. After standing for a few hours, or immediately on boiling, solutions of these sugars assume their normal state of rotation. The addition of a small quantity of ammonia also causes the birotation to disappear.[68] This phenomenon is doubtless due to a certain molecular taxis, which remains after solution is apparently complete. The groups of molecules thus held in place have a certain rotatory power of their own and this is superadded to that of the normal solution. After a time, under the stress of the action of the solvent, these groups are broken up and the solution then assumes its normal condition. =106. Gyrodynat of Dextrose.=—The gyrodynat of dextrose, as has already been mentioned, increases with the degree of concentration, thus showing a property directly opposite that of sucrose. The general formula for the anhydrous sugar is [_a_]_{D} = 52.°718 + 0.017087_p_ + 0.0004271_p_². In this formula _p_ represents the grams of dextrose in 100 grams of the solution. In a ten per cent solution the gyrodynat of dextrose is therefore nearly exactly [_a_]_{D}20° = 53°. As calculated by Tollens the gyrodynats corresponding to several degrees of concentration are shown in the following table: