950

THE NEW ZEALAND GAZETTE.

[No. 46

no such inequality the angles are said to be right angles and
the lines are mutually perpendicular, that in this case any
two segments containing one of the right angles form also a
"square" corner, that a horizontal line is perpendicular with
respect to a vertical line, that the obtuse and the acute
angles are respectively greater and less than the right angle,
and that two lines without mutual inclination are parallel.
Strict scientific definitions will not be demanded, but the
pupils must be able to use and apply the several geometrical
terms required, and to give approximate verbal explanations
of their meaning. They should also know how to draw lines
parallel or perpendicular to one another by means of set-
square and flat ruler. Proceeding to simple geometrical
figures, which should be illustrated by models in cardboard
or wood as well as by drawing, they should know the square
and the oblong as square-cornered figures of four sides, all the
sides being equal in the square, while in the oblong there
are two long sides equal and two short ones equal. The pupils
should draw these figures with sides of prescribed length.
The meaning of diagonal must be known, as also of triangle,
equilateral, isosceles. The two triangles into which a
diagonal divides a square or oblong must be recognised as
right-angled triangles, and in the square as isosceles tri-
angles. So far as is possible without strict geometrical
construction the pupils must be able to draw at dictation,
with ruler or as freehand exercises, the several kinds of
triangles here named, as well as to recognise them. "Base,"
"apex," "altitude," as applied to isosceles triangles, should
be known. The drawing exercises, with and without ruler,
must include combinations of straight lines forming borders
and simple patterns.

In the Second Standard the freehand drawing is to include
forms based on the circle, semicircle, and quadrant. The
knowledge of terms—tested by models, by diagrams, and by
dictation—must include circumference, radius, diameter, arc,
chord, segment, semicircle, and quadrant. The rhombus
and the rhomboid are to be studied: the rhombus as like
the square, except as to its angles, and the rhomboid as
similarly comparable to the oblong; the rhombus as divided
by one diagonal into two obtuse-angled triangles, and by the
other into two acute-angled triangles, all isosceles; and the
rhomboid as divided by one diagonal into two obtuse-angled
triangles, and by the other into two acute-angled triangles,
two at least of the triangles being scalene.

In the Third Standard the new figures for study are the
trapezium and the polygon, especially the regular hexagon
and regular octagon. It is to be known that any regular
polygon may be divided into isosceles triangles (equilateral
in the hexagon), each of which has its apex in the centre of
the figure. The right angle is to be known as an angle of
90 degrees; the sum of the angles round a point as equal to
four right angles or 360 degrees; the sum of the angles of a
triangle as 180 degrees (illustrated by folding a triangular
piece of paper so that the three corners may meet at a point
in one of the sides); and the sum of the angles of any four-
sided figure as 360 degrees (illustrated by tearing off the
four corners of a trapezium and putting them together at a
point). The work of the standard must include ruling,
freehand, dictation, and memory exercises on the geometry
of form, and the freehand from set copies must include
some curves more difficult than such as can be produced by
joining quadrants together.

In the Fourth Standard the freehand drawing is to be
more advanced than that of the Third Standard. Practical
use is to be made of set-squares in the drawing of lines at
angles of 90, 60, 45, 30, 15 degrees, and others depending on
these; and the pupils must be prepared with at least thirty
problems of practical construction. They ought also to be
able to work the problems from given dimensions to one or
other of the following scales: 3in., 1½in., or ¾in. to a foot;
½in. to a yard (¼in. to foot); 1in. to a mile (¼in. to furlong).
The problems required are the following:—

To bisect a given straight line or an arc.

To bisect a given angle.

To draw a perpendicular to a given straight line at a given
point on it.

To draw a perpendicular to a given straight line from a
given point outside it.

To draw a line parallel to a given straight line at a given
distance from it.

To draw a line parallel to a given straight line through a
given point.

To make an angle at a given point in a given line equal to
a given angle.

To divide a given straight line into any number of equal
parts.

To divide a given straight line proportionally to a given
divided line.

To divide a circle into three, six, twelve, four, or eight
equal parts.

To construct a triangle, its three sides being given.

To construct an equilateral triangle on a given side.

To construct an isosceles triangle, the base and the angle
at the apex being given.

To construct a square, the side being given.

To construct a square, the diagonal being given.

To construct a rectangle, the sides being given.

To construct a rectangle, the diagonal and one side being
given.

For the Fifth Standard pupils must be able to make their
own freehand sketches of some common object as a preli-
minary to scale-drawing, to measure the object and note the
measurements on the sketch, and then to draw the object to
scale. Progress in freehand must be shown, and the simplest
exercises of the year must be drawn either larger or smaller
than the copy set. The problems required in practical geo-
metry are the following:—

To construct a rhombus, the diagonal and side being given.

To construct a rhomboid, the sides and one of the angles
being given.

To construct a trapezium equal to a given trapezium.

To construct a triangle on a given base and similar to a
given triangle.

To construct a rectangle on a given side and similar to a
given rectangle.

To enlarge or reduce any given figure by a system of
squares.

To divide a circle into any number of equal parts (by
construction).

To construct any regular polygon on a given line.

To construct an ellipse by pins and string.

To describe a circle through three given points.

To inscribe a circle within a given triangle.

To describe a circle with a given radius to touch two
converging lines.

To describe a circle with a given radius to touch a given
straight line and a given circle.

In the Sixth Standard all copies made from the flat must
be enlarged or reduced. The models for model drawing are
the same simple solids as are prescribed for the geometrical
drawing of this standard, and combinations of the same as
found in simple common objects, such as tables, boxes,
books, bottles, buckets, &c. The model drawing and the
method of teaching it are fully illustrated in the first-grade
model drawing in the Colonial Drawing-book, issued by
authority of the Minister of Education. The work in prac-
tical solid geometry is as follows: Plans and elevations of the
sphere and cube, the cone and pyramid, the cylinder and
prism, and slabs. Pupils must be able to give correct defi-
nitions of these solids, and to draw plans and elevations of
them, and of simple objects based on them, on three planes
of projection, and also (in the largest schools) to draw sections
of them in any plane perpendicular to the horizontal or to
the vertical plane.

Teachers may claim exemption for girls from examination
in geometrical drawing.

20. The instruction in elementary science for Standards
    IV., V., and VI. shall be based on a programme, which shall
    be prepared by the head-teacher, to show the distribution of
    the subject over a three years' course of lessons. The pro-
    gramme must include such elementary knowledge of physics,
    and such a conception of chemical action, as may be im-
    parted by a proper use of Professor Bickerton's "Materials
    for Lessons in Elementary Science," and must also include
    instruction in elementary mechanics, or in elementary laws
    of health, or in ambulance work, and modes of resuscitation,
    or in botany, or some other subject recognised by the In-
    spector as equivalent to one of these; provided, however, that,
    if the elements of agricultural knowledge be efficiently taught,
    no other elementary science shall be required for these
    standards.

21. The programme of the elements of agricultural know-
    ledge which may be substituted for the programme of "ele-
    mentary science" is as follows:—

Standard IV.—(a.) The parts of plants, stems, leaves,
roots, flowers, and fruit (with special reference to fruit-trees
and agricultural plants).

(b.) Fertilisation of flowers and formation of seed. Storage
of food in seeds; roots, &c. Germination.

(c.) Composition of plants. The meaning of the terms
organic and inorganic. Elements and compounds. Outlines
of chemistry of air and water.

(d.) How plants obtain their food. Function of the leaf.
Decomposition of carbonic acid. Leaf-green. Importance
of water to the plant. Absorption of food by the roots.
Action of root-hairs.

(e.) The soil. How soils are formed. Decay of rocks.
Chemical constituents of soil. Subsoil. Humus. The soil
as a source of plant-food.

Standard V.—(f.) Brief outline of the chemistry of the
elements essential to the growth of plants. Influence of
light, warmth, and moisture on plant-growth. Bacteria as
the cause of decay and fermentation.

(g.) Mechanical analysis of soils. Classification of soils.
Good and bad qualities of soils. Influence of mechanical
condition of soils on their fertility. Plant-food in the soil,
available and dormant.