THEORY AND GENERAL PRINCIPLES 7
this weight, or 3.943 gm may be weighed to only the third deci-
mal place, the same number of significant figures being determined
in the two cases. This sample may be weighed much more rapidly
than the first. One solution of sample thus serves for several
different titrations.
The principle of aliquot parts is of service also in the analysis
of materials that are not homogeneous and that cannot be mixed
readily, the larger quantity being more nearly representative
than the smaller one and the mixing being accomplished after
the weighed sample has been dissolved.
Normal System.—In case it is possible to apply a given stand-
ard solution to the titration of a number of different substances
(as a standard acid for various bases or a standard base for various
acids), there is a certain convenience to be derived from adjusting
the concentration of the standard so as to make FB equal to one-
thousandth of the equivalent weight of the substance determined,
or to some other simple fraction of the equivalent weight, as
0.002, 0.0001, 0.0005, etc.
The " equivalent weight77 of any element or group of elements
is the number of weight units of this entity that is chemically
equivalent to eight weight units of oxygen. In the case of elements
this is the combining weight. In all cases the equivalent weights
compose a series of relative weights of the various chemical
entities, chemically equivalent to each other in reacting power.
From this definition it is obvious that if FB is to be made
equal in grams to one-thousandth of the equivalent weight of
the substance determined (or 1 milligram-equivalent), 1 cc of
the standard solution must contain 1 milligram-equivalent of the
active constituent. A solution of this concentration is a normal
solution and the following relations are consequences of the defini-
tions discussed above:
(a) One cubic centimeter of any normal solution is equivalent
to 1 milligram-equivalent of any substance.
(6) One cubic centimeter of any normal solution is equivalent
to 1 cc of any other normal solution.
Normal solutions are too concentrated to allow a very high
degree of accuracy in analytical work and it is more often desir-
able to use half-, fifth-, tenth- or even hundredth-normal solu-
tions for accurate work. The relations existing between solutions