Or, again, the quantity of some substances may be measured by the colour
of their solutions, on the principle that, other things being equal, the
colour of a solution depends upon the quantity of colouring matter
present. So that if two solutions of the same substance are equally
coloured they are of equal strength. In this way an unknown may be
compared with a known strength, and a fairly accurate determination may
be made. These three illustrations serve as types of the three chief
classes of volumetric assays--titrometric, gasometric, and colorimetric.

~Titrometric Assays.~--Within the limits of the error of experiment, a
definite volume of a solution or gas represents a certain weight of
metal or other substance, hence the exact weight may be determined by
experiment. The error of experiment may be reduced to insignificant
dimensions by repeating the experiment, and taking the mean of three or
four determinations. This will at the same time show the amount of
variation. Thus, if 0.5 gram of iron were dissolved and found to require
50.3 cubic centimetres of the solution of permanganate of potash, and if
on repeating, 50.4, 50.2, and 50.3 c.c. were required, the experimenter
would be justified in saying that 50.3 c.c. of the permanganate solution
represent 0.5 gram of iron, and that his results were good within 0.2
c.c. of the permanganate solution. So that if in an unknown solution of
iron, 50.5 c.c. of the permanganate solution were used up, he could
state with confidence that it contained a little more than 0.5 gram of
iron. With a larger experience the confidence would increase, and with
practice the experimental error will diminish.

But supposing that the unknown solution required, say, 100.5 instead of
50.5 c.c., he would not be justified in saying that, since 50.3 c.c. are
equivalent to 0.5 gram, 100.6 c.c. are equivalent to twice that amount;