OPTICAL ROTATION 135 the first 15 cc. Polarize at a temperature of exactly 20°, using a 200-min tube unless the solution is still colored enough to make this difficult, other- wise use a 100-mm tube and double the reading. This is the quantity P in the Clerget formula (4) on page 133. Invert Polarization.—Precipitate the lead from the clarified sugar solution by adding either powdered anhydrous sodium carbonate or powdered anhydrous sodium oxalate, very carefully, until a very slight excess is indicated by failure to produce more precipitate. Filter on a dry filter to remove the lead salt. Reject the first 15 cc and save the remainder of the filtrate. Pipette 50 cc of the clear, lead-free filtrate into a 100-cc flask of ordinary form. If sodium carbonate has been used for precipitating lead, carefully neutralize the excess with hydrochloric acid. Invert the sucrose by one of the following methods: (a) Add 25 cc of water and then add from a pipette 5 cc of concentrated hydrochloric acid, dropping the acid slowly and mixing by rotating the flask. Place the flask in a water bath which is kept at 70°. The tempera- ture of the solution should reach 69° in about 3 minutes. After the flask has been in the bath for 10 minutes remove and cool to 20° in running water. Rinse into a 100-cc volumetric flask, dilute to the mark and mix. (6) Add 5 cc of concentrated hydrochloric acid, slowly and mixing well. Set the flask aside for 24 hours at a temperature of 20 to 25°, or for 10 hours at somewhat above 25°. Dilute to 100 cc and mix. On account of the considerable variation of the specific rotation of levti- lose with temperature it is necessary to polarize at a constant, definite temperature. For this purpose a water jacketed tube is used and water at 20° is circulated. Since the dilution of the solution was doubled after the direct polarization, the reading for the invert polarization is multiplied by 2 if a 200-mm tube is used, or by 4 for a 100-mm tube. Calculate the per cent of sucrose in the syrup. For low concentrations of invert sugar the variation of rotation with concentration is such .that formula (4) on page 133 will not apply. The official method specifies the following formula, where the concentration of sugar in the invert solution is less than 12 gm per 100 cc: S = 100(P - /) 142.66 - ~ - 0.0065[l42.66 - ^ - (P - /)] This might be further simplified to 100(P - I) S = 141.73 - 0.4967 t + 0.0065(P - I) (5) (6)