atoms of the individual elements. If we accept these two propositions,
it follows that hydrogen can be replaced atom for atom by other elements
not only by the hydrogens but by alkali metals, etc. Hydrogen is, it may
here be remarked, an element of unique character; not only can it be
replaced by the elements of the widely different classes represented by
chlorine and sodium, but it is the terminal of the series of paraffins,
C_{n}H_{2n}; C_{3}H_{6}, C_{2}H_{4}, H_{2}. The third proposition which
must be taken for granted is, that the groups of elements, C_{2}H_{5},
CH_{3}, behave as elements, and that these radicals, ethyl, methyl,
etc., do not suffer decomposition in many chemical reactions.

Now as to valency or atomicity, accepting the received atomic weights of
the elements, it is certain that there are at least four distinct types
of hydrogen compounds represented by ClH, OH_{2}, NH_{3}, CH_{4}. The
recognition of these types, and their relations to each other as
types, was one of the most important and best assured advances made in
theoretical chemistry. When we compare the formula of water with that of
hydrochloric acid, we find that there is twice as much hydrogen combined
with one atom of oxygen as there is combined with one atom of chlorine;
and in a great many other instances, we find that we can replace two
atoms of chlorine by one atom of oxygen, so that we get an idea of the
exchangeable value of these elements, and we say that one atom of oxygen
is worth two of chlorine, or is bivalent; similarly, nitrogen is said to
be trivalent. The meaning attached to the word "valency," is simply one
of interchangeability, just as we say a penny is worth two halfpennies
or four farthings. The question next arises, is the valency of an
element fixed or variable? If the word be defined as above, it is
absolutely certain that the valency varies. Thus, tin may be trivalent,
SnCl_{2}, or tetravalent, SnCl_{4}. Accordingly elements have been
classed as monads, dyads, triads, etc. The lecturer objected most