three dimensions which define a solid, and thus eight
smaller cubes are produced.

2. We pass from the undivided to the divided unit, emphasizing the
fact that unity still exists, though divisibility enters as a new
factor.

3. The most important characteristics of the gift are contrasts of
size resulting in the abstraction of form from size; increase of
material as a whole, decrease of size in parts; increase of facilities
in illustrating form and number.

The new experience to be found in this first divided body is the idea
of relativity; of the whole in its relation to the parts (each an
embryo whole), and of the parts in relation to the whole.

The form of the parts is like the form of the whole, but, in shape
alike, the dissimilarity is in size; the fact becoming more apparent
by a variety of combinations of a different number of parts: thus the
relations of numbers are introduced to the observation of the child
together with those of form and magnitude.

4. The third gift was intended by Froebel to meet the necessities of
the child at a period when, no longer satisfied with the external
appearances of things, he strives to penetrate their internal
conditions, and begins to realize the many different possibilities of
the same element.

5. The geometrical forms illustrated in this gift are:--

{Cube.
Solids. {Square Prism.
{Rectangular Parallelopiped.

Planes. {Square.
{Oblong.

6. Froebel intends the building exercise to be carried on in a certain
way with a view of establishing a law to regulate the child's
activity. The upper and lower parts of the figure--the contrasts--are
first brought into position, and the balance is established by the
intermediates--right and left.

The cube itself is divided according to the law of Mediation of
Contrasts. The contrasts of exterior and interior, whole and parts,
analysis and synthesis, are also brought into relation with each
other.

* * * * *

Hailmann on Third Gift.

Mr. W. N. Hailmann says that the third gift marks an important step in
the mental life of the child. Heretofore, he has had to do with
playthings indivisible, whole, complete in themselves. Every
impression, or, rather, every fact, came to him as a unit, a one, an
indivisible whole.

The analyses and syntheses that are presented to him in the first and
second gifts come ready-made as it were, so t