d to the intensity
of the affinity between atoms. Judging by the heat liberated in their
union, oxygen has a far stronger affinity for hydrogen than does
nitrogen, but an atom of oxygen can combine with two atoms only of
hydrogen, while an atom of nitrogen can combine with three.

~Measure of valence.~ In expressing the valence of an element we must
select some standard for comparison, just as in the measurement of any
other numerical quantity. It has been found that an atom of hydrogen is
never able to hold in combination more than one atom of any other
element. Hydrogen is therefore taken as the standard, and other elements
are compared with it in determining their valence. A number of other
elements are like hydrogen in being able to combine with at most one
atom of other elements, and such elements are called _univalent_. Among
these are chlorine, iodine, and sodium. Elements such as oxygen,
calcium, and zinc, which can combine with two atoms of hydrogen or other
univalent elements, are said to be _divalent_. Similarly, we have
_trivalent, tetravalent, pentavalent_ elements. None have a valence of
more than 8.

~Indirect measure of valence.~ Many elements, especially among the metals,
do not readily form compounds with hydrogen, and their valence is not
easy to determine by direct comparison with the standard element. These
elements, however, combine with other univalent elements, such as
chlorine, and their valence can be determined from the compounds so
formed.

~Variable valence.~ Many elements are able to exert different valences
under differing circumstances. Thus we have the compounds Cu_{2}O and
CuO, CO and CO_{2}, FeCl_{2} and FeCl_{3}. It is not always possible to
assign a fixed valence to an element. Nevertheless each element tends to
exert some normal valence, and the compounds in which it has a valence
different from this are apt to be unstable and easily changed into
compounds in which the valence of the element is normal. The valences of
the various elements will become familiar as the elements are studied in
detail.

~Valence and combining ratios.~ When elements combine to form compounds,
the ratio in which they combine will be determined by their valences. In
those compounds which consist of two elements directly combined, the
union is between such numbers of the two atoms as have equal valences.
Elements of the same valence will therefore combine atom for atom.
Designating the valence of the at