Dec. 18.] THE NEW ZEALAND GAZETTE. 2311

than that of the copy, and in the Sixth Standard freehand is extended so as to include drawing from simple models.

In the First Standard the pupils must be able to distinguish vertical, horizontal, and oblique lines, to recognise such lines when they see them, to give the lines the appropriate names, and to draw them with ruler and without ruler at dictation. They must know that when two lines cross one another four angles are presented to view, that the size of the angles is independent of the length of the lines, that one pair of angles may be larger than the other pair, that when there is 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 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 triangles. 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 or two obtuse-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 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: 3 in., 1½ in., or ¾ in. to a foot; ¾ in. to a yard (¼ in. to foot); 1 in. to a mile (⅛ in. 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.