_Polarization._—The proper weight of milk is placed in a sugar flask, diluted with water, clarified with the mercuric salt, the volume completed to the mark, and the contents shaken and poured on a filter. The filtrate is polarized in tubes of convenient length. The observed rotation may be expressed either in degrees of angular measurement or of the sugar scale. The weight of milk used may be two or three times that of the normal weight calculated for the instrument employed. Instead of weighing the milk a corresponding volume determined by its specific gravity may be delivered from a burette-pipette (p. 231). For the laurent polariscope three times, and for the half-shadow instruments for lamplight, twice the normal weight of milk should be used. For approximately sixty cubic centimeters of milk the flask should be marked at 105 cubic centimeters in compensation for the volume of precipitated solids or the reading obtained from a 100 cubic centimeter flask, decreased by one-twentieth. For the laurent instrument the normal weight of lactose is determined by the following proportions: Gyrodynat of sucrose, 66.5: lactose: 52.5 = _x_: 16.19. Whence _x_ = 20.51, that is, the number of grams of pure lactose in 100 cubic centimeters required to read 100 divisions of the sugar scale of the instrument. For the ventzke scale the normal quantity of lactose required to read 100 divisions is found from the following equation: 66.4: 52.5 = _x_: 26.048 Whence _x_ = 32.74. In the one case three times the normal weight of milk is 61.53 and in the other twice the normal weight, 65.48 grams. =244. Error due to Volume of Precipitate.=—Vieth states that the volume allowed for the precipitated solids in the original process, _viz._, two and four-tenths cubic centimeters, is not sufficiently large.[202] In such cases it is quite difficult to decide on any arbitrary correction based on the supposed quantities of fat and albuminoids present. A better method than to try to compensate for any arbitrary volume is to remove entirely the disturbing cause or eliminate it by indirect means. To wash the precipitate free of sugar without increasing the bulk of the filtrate unduly would be extremely difficult and tend, moreover, to bring some of the precipitated matters again into solution. It is better, therefore, to eliminate the error by double dilution and polarization (=86=). The principle of this method is based on the fact, that, within limits not sensibly affecting the gyrodynat by reason of different densities, the polarizations of two solutions of the same substance are inversely proportional to their volumes. For convenience, it is recommended that the volumes of the samples in each instance be 100 and 200 cubic centimeters, respectively, in which case the true reading is obtained by the simple formula given in the latter part of =86=. In this laboratory the double dilution method of determining the volume of the precipitate is conducted as follows:[203]