at a time until a precipitate is no longer formed, but here 1.5 c.c.
must be deducted for excess, since it is evident that the whole of the
last "c.c." must have been, and a portion of the previous one may have
been, in excess.

~Indirect Titration.~--The action of permanganate of potash upon a
ferrous solution is one of oxidation, hence it is evident that if any
other oxidising agent is present it will count as permanganate. In such
a case the titration can be used (indirectly) to estimate the quantity
of such oxidising agent, by determining how much less of the
permanganate is used. For example, suppose that 1 gram of iron dissolved
in sulphuric acid requires 100 c.c. of standard permanganate to fully
oxidise it, but that the same amount of iron only requires 35.6 c.c. of
the same standard permanganate if it has been previously heated with 0.5
gram of black oxide of manganese. Here it is evident that 0.5 gram of
black oxide does the work of 64.4 c.c.[4] of the permanganate solution,
and that these quantities are equivalent; moreover, if 64.4 c.c.
correspond with 0.5 gram, then 100 c.c. correspond with 0.7764 which is
the standard. On theoretical grounds, and by a method of calculation
which will be explained further on (under the heading "Calculations from
FormulÊ"), it can be found that if the standard for iron is 1 gram, that
for the black oxide will be 0.7764 gram.

The principles of these indirect titrations become clearer when
expressed in a condensed form. Thus, in the example selected, and using
the formulÊ Fe = Iron, KMnO_{4} = permanganate of potash, and MnO_{2} =
oxide of manganese, we have:--

(1) 1 gram Fe = 100 c.c. KMnO_{4}