The formula is applicable for temperatures between 0° and 100°. Its values are expressed in degrees of angular measure which can be converted into degrees of the sugar scale by appropriate factors:
Formula.— aᵗ = a°(1 + 0.000146t);
in which a° = polarization in angular degrees at 0°, t the temperature of observation and aᵗ the rotation desired.
Example.—A quartz plate which has an angular rotation of 33° at 0° will have a rotation at 20° of 33°.09834.
aᵗ = 33(1 + 0.000146 × 20) = 33.09834.
Since in instruments using the ventzke scale one degree of the sugar scale is equal to 0.3467 degree angular measure, the sugar value of the quartz plate mentioned is equal to 95.47 percent; 33.09834 ÷ 0.3467 = 95.47.
The sugar value of this plate at 0° is 95.18 per cent; 33 ÷ 0.3467 = 95.18.
80. Tables for Correcting Quartz Plates.—Instead of calculating the variation in quartz plates for each temperature of observation, it is recommended by the Bureau of Internal Revenue of the Treasury, to use control quartz plates the values of which at any given temperature, are found on a card which accompanies each one.[45] The variations given, are from temperatures between 10° and 35°. Three control plates are provided with each instrument used by the Bureau, for polarimetric work in the custom houses, or in ascertaining bounties to be paid on the production of domestic sugars. For example, the case of a sugar which polarizes 80°.5 may be cited. One of the control plates nearest to this number, is found to have at the temperature of observation, a polarization of 91°.4, the reading being made in each case at 25°. On consulting the card which accompanies the control plate, it is seen that its value at the temperature mentioned, is 91°.7. The reading of the instrument is therefore too low by three-tenths of a degree, and this quantity should be added to the observed polarization, making it 80°.8. In this method of correcting the reading for temperature, it is assumed that the compensating wedges of the instrument, are free of error at the points of observation. The plates used for the purpose above, are all standardized in the office of weights and measures of the Coast and Geodetic Survey, before delivery to the analysts.
81. Applicability of Quartz Plates.—Quartz plates which are correctly set for one instrument or kind of light, should be equally accurate for the sugar scales of all instruments, using the same sugar factor. In other words a quartz plate which reads 99° on a scheibler color polariscope, should give the same reading on the sugar scale of a shadow compensating or a monochromatic direct reading apparatus using 26.048 grams of sugar.
The most useful quartz plates for sugar analysis, are those which give the readings at points between 80° and 96°, which cover the limits of ordinary commercial sugars. For molasses the plates should read from 45° to 55°. For sugar juices of the cane and beet, the most convenient graduation would be from 10° to 20°, but plates of this value would be too thin for practical work and are not in use. When quartz plates are to be used for control purposes, they should be purchased from reliable manufacturers, or better, tested directly against pure sugar solutions by the observer.