If it is desired to have a solution with a standard exactly 1.0 gram, it
is best first to make one rather stronger than this, and then to
standardise carefully. Divide 1000 by the standard thus obtained and the
result will be the number of c.c. which must be taken and be diluted
with water to 1 litre. For example: suppose the standard is 1.008, then
1000/1.008 gives 992, and if 992 c.c. be taken and diluted with water to
1000 c.c. a solution of the desired strength will be obtained. The
standard of this should be confirmed. A simpler calculation for the same
purpose is to multiply the standard by 1000; this will give the number
of c.c. to which 1 litre of the solution should be diluted. In the above
example a litre should be diluted to 1008 c.c.

It has been assumed in these rules that the titration has yielded
proportional results; but these are not always obtained. There can be no
doubt that in any actual re-action the proportion between any two
re-agents is a fixed one, and that if we double one of these then
exactly twice as much of the other will enter into the re-action; but in
the working it may very well be that no re-action at all will take place
until after a certain excess of one or of both of the re-agents is
present. In titrating lead with a chromate of potash solution, for
example, it is possible that at the end of the titration a small
quantity of the lead may remain unacted on; and it is certain that a
small excess of the chromate is present in the solution. So, too, in
precipitating a solution of silver with a standard solution of common
salt, a point is reached at which a small quantity of each remains in
solution; a further addition either of silver or of salt will cause a
precipitate, and a similar phenomenon has been observed in precipitating
a hydrochloric acid solution of a sulphate with baric chloride. The
excess of one or other of the re-agents may be large or small; or, in
some cases, they may neutralise each other. Considerations like these