Make a form of two-angled figures, being in contact with each other.

Produce figures composed of triangles, of squares, or of ovals, in contact with each other.

Draw figures of any sort of curve lines you fancy. Copy this leaf: any curve-lined ornament on a piece of furniture. (Should some of these ornaments be too complicated, the child limits himself to the principal forms only, by omitting all minutiæ.)

Curve Lines and Circular Figures, considered with respect to Magnitude.

Mother. Draws two, three, four, five circles of equal magnitude. Draw two-arched lines of equal magnitude. Draw two circles of unequal magnitude. Draw two, three, four, &c. concave angles, of equal magnitude in regard to their sides. Draw convex angles of equal magnitude. Draw two, three, four, five, six-angled figures of equal magnitude. Concave and convexangled figures of equal magnitude. Draw

ovals, waved or serpentine lines, spiral lines of equal magnitude: make ovals of unequal magnitude.

APPLICATION TO VARIOUS OBJECTS.

Mother. Find out two curve lines of equal magnitude. Look out, to-day, for concave twoangled figures and triangles. Four and fiveangled figures of equal magnitude. Can you find any object on which the spiral line is visible? (The shell of a snail, &c.)

Relations of Mensuration.

Whatever has been done with the straight lines relative to mensuration, may also be done with circular, curve, and arched lines. For instance; the mo

ther draws the four

lines, a, b, c, d, and

says: the second curve

с

d

a

line, b, is twice as long as the first, a. The fourth, d, is four times as long as the third, c, &c.

Mother. Draw two curve lines, of which the second is five, six, or nine times as long as the first.

This two-angled figure,

in its greatest length, is twice as long as it is broad.

Draw a two-angled figure which is a little longer than it is broad. Draw one which is four times as long as it is broad: twice as long, &c. In the same manner can the three and fourangled figures be treated.

APPLICATION TO OBJECTS.

Mother. How many times is this oval table as long as it is broad? or how many times is its breadth contained in its length? How many times is this two-angled leaf longer than it is broad? How many times this three, four, five, six-angled leaf, &c.

Combination of straight and curve Lines.

The mother draws a straight and a curve line, and says, these two lines are not parallel.

She draws the angles 1 and 2, saying, these are angles of mixed lines, or mixed

lined angles. The first is a mixed

1

line acute concave angle : the second, a mixed-lined acute convex angle.

2

Figures of four, five, or more sides, may be treated in the same manner.

The application and the drawing exercises of these mixed-line figures, are the same as

with the straight and curve-lined figures. Every child who has comprehended the preceding exercises, will, with very little assistance, go through these. A few hints, therefore, as to the application, will suffice. For instance:

Mother. Find out any object near you resembling a mixed-lined, two-angled figure. Compose a pretty form of mixed-lined triangles. The relations of mensuration are also treated in the same manner as straight and curve lines. For instance: Draw a mixed-angled oblong, which is twice as long as broad: another, three times as long as broad.

Produce a figure of separate mixed-lined two-angled figures. Can you find out any object which represents a mixed-lined foursided figure?

Of Planes or Superficies.

Mother. The floor of this room and its ceiling are parallel planes.

The wall of this room is not parallel with its floor. With what is this floor parallel? With what is it not parallel?