is a very strong
base-forming element, with pronounced metallic properties. Beryllium,
following lithium, is less strongly base-forming, while boron has some
base-forming and some acid-forming properties. In carbon all
base-forming properties have disappeared, and the acid-forming
properties are more marked than in boron. These become still more
emphasized as we pass through nitrogen and oxygen, until on reaching
fluorine we have one of the strongest acid-forming elements. The
properties of these seven elements therefore vary regularly with their
atomic weights, or, in mathematical language, are regular functions of
them.

~Periodic law.~ The properties of the first seven elements vary
_continuously_--that is steadily--away from base-forming and toward
acid-forming properties. If lithium had the smallest atomic weight of
any of the elements, and fluorine the greatest, so that in passing from
one to the other we had included all the elements, we could say that the
properties of elements are continuous functions of their atomic weights.
But fluorine is an element of small atomic weight, and the one following
it, sodium, breaks the regular order, for in it reappear all the
characteristic properties of lithium. Magnesium, following sodium, bears
much the same relation to beryllium that sodium does to lithium, and
the properties of the elements in the second row vary much as they do in
the first row until potassium is reached, when another repetition
begins. The properties of the elements do not vary continuously,
therefore, with atomic weights, but at regular intervals there is a
repetition, or _period_. This generalization is known as the _periodic
law_, and may be stated thus: _The properties of elements are periodic
functions of their atomic weights._

~The two families in a group.~ While all the elements in a given vertical
column bear a general resemblance to each other, it has been noticed
that those belonging to periods having even numbers are very strikingly
similar to each other. They are placed at the left side of the group
columns. In like manner, the elements belonging to the odd periods are
very similar and are arranged at the right side of the group columns.
Thus calcium, strontium, and barium are very much alike; so, too, are
magnesium, zinc, and cadmium. The resemblance between calcium and
magnesium, or strontium and zinc, is much less marked. This method of
arrangement therefore divides each group into tw