e
sphere and the edge of the cylinder.

3. All the objects hitherto used have, with the exception of the ball
and cylinder, dealt with straight lines and the figures formed by
those lines. We now begin a series of exercises with the curve, and
the variety of symmetrical figures that can be constructed is
immensely increased.

4. Much new knowledge can be conveyed by means of this fresh material,
a complete set of new figures may be produced, and the imitation of
objects passes from that of things constructed by man, which are
mostly rectilinear, to those of nature in which curved lines in every
possible variety prevail.

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

{ Circles.
{ Semicircles.
Planes. { Quadrants.
{ Sectors.
{ Segments.

By the union of straight and curved lines (sticks and rings) the
entire geometry of the circle may be illustrated, and the child
may thus become acquainted with the appearance of the

Diameter.
Radius.
Circumference.
Chord.
Arc.

6. The law of mediation of contrasts is shown as follows: the
semicircles, when placed on the table with ends towards right or left,
connect points of opposite direction up and down, and when placed with
ends pointing upward or downward they connect the right with the left
side.

The circle is of course an unending line traced from a given point
back to itself, according to certain laws, but it is also a union of
two semicircles curving outward in opposite directions. "It is a
representation of the general law, since the periphery and centre
stand in contrast to each other, and are connected by the
radii."--(Froebel.)

* * * * *

The New Gift and its Charms.

Having already analyzed straight lines in the sticks, we will pass
directly to the consideration of the ninth in the series of Froebel's
gifts, the rings, which are whole, half, and quarter circles of bright
silvered wire.

If the sticks were fascinating to the child as the embodied straight
edge or line, and perfect treasure-houses of new possibilities to the
kindergartner, the rings are just a bit more delightful as, with their
glittering surface and curved lines, and their wonderful property of
having neither beginning nor end, they are quite different in
appearance from anything which precedes or follows them. Of course the
child sees at once that here is an entirely new field for