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]
In each of two flasks marked at 100 and 200 cubic centimeters,
respectively, are placed 65.52 grams of milk, four cubic centimeters
of mercuric nitrate added, the volume completed to the mark and the
contents of the flask well shaken.
After filtering, the polarization is made in a 400 millimeter tube
by means of the triple shadow polariscope described in =75=. From
the reading thus obtained the volume of the precipitate and the
degree of correction to be applied are calculated as in the subjoined
example. The flasks should be filled at near the temperature at which
the polarizations are made and the observation room must be kept at
practically a constant temperature of 20° to avoid the complications
which would be produced by changes in the gyrodynat of lactose and
the value of the quartz plates and wedges of the apparatus by marked
variations in temperature.
_Example._—Weight of milk used in each case 65.52 grams.
Polarimetric reading from the 100 cubic centimeter flask, 20°.84
” ” ” ” 200 ” ” ” 10°.15
Then 10.15 × 2 = 20.30
20.84 - 20.30 = 0.54
0.54 × 2 = 1.08
20.84 - 1.08 = 19.76
19.76 ÷ 4 = 4.94,
which is the corrected reading showing the percentage of lactose in the
sample used.
The volume of the precipitate is calculated as follows:
20.84 ÷ 4 = 5.21, the apparent percentage of lactose present.
Then 5.21: 4.94 = 100: _x_.
Whence _x_ = 94.82. From this number it is seen that the true volume of
the milk solution polarized is 94.82 instead of 100 cubic centimeters,
whence the volume occupied by the precipitate is 100 - 94.82 = 5.18
cubic centimeters. So little time is required to conduct the analysis
by the double dilution method as to render it preferable in all cases
where incontestable data are desired. Where arbitrary corrections are
made the volume allowed for the precipitate may vary from two and a
half cubic centimeters in milks poor in fat, to six for those with a
high cream content.
For milks of average composition sufficient accuracy is secured by
making an arbitrary correction of five cubic centimeters for the volume
of the precipitate.