774

THE NEW ZEALAND GAZETTE.

No. 15

to the chord; conversely, the perpendicular to a chord
from the centre bisects the chord.
There is one circle, and one only, which passes through
three given points not in a straight line.
In equal circles (or in the same circle), (i) if two arcs
subtend equal angles at the centres, they are equal;
(ii) conversely, if two arcs are equal, they subtend equal
angles at the centre.
In equal circles (or in the same circle), (i) if two
chords are equal, they cut off equal arcs; (ii) conversely,
if two arcs are equal, the chords of the arcs are equal.
Equal chords of a circle are equidistant from the
centre; and the converse.
The tangent at any point of a circle and the radius
through the point are perpendicular to one another.
If two circles touch, the point of contact lies on the
straight line through the centres.
The angle which an arc of a circle subtends at the
centre is double that which it subtends at any point on
the remaining part of the circumference.
Angles in the same segment of a circle are equal;
and, if the line joining two points subtends equal angles
at two other points on the same side of it, the four points
lie on a circle.
The angle in a semicircle is a right angle; the angle
in a segment greater than a semicircle is less than a right
angle, and the angle in a segment less than a semicircle
is greater than a right angle.
The opposite angles of any quadrilateral inscribed in
a circle are supplementary; and the converse.
If a straight line touch a circle, and from the point
of contact a chord be drawn, the angles which this chord
makes with the tangent are equal to the angles in the
alternate segments.
If two chords of a circle intersect either inside or out-
side the circle, the rectangle contained by the parts of the
one is equal to the rectangle contained by the parts of the
other.

Group II.

(5.) Geography.—The requirements will be based on the pro-
gramme of work prescribed for geography in the regula-
tions governing the course of instruction in public
elementary schools, but will be more advanced in
character. Special stress will be laid on physical geo-
graphy. Special attention should also be given to the
geography of New Zealand and of the British Empire
generally with reference to salient facts of their physical
and social geography, or in illustration of geographical
principles.

(6.) History and Civics.—The requirements will be based on the
work prescribed for history and civic instruction in the
regulations governing the courses of instruction in
public elementary schools, but will have special reference
to the history of British Empire extension, the rights and
duties of the citizen, the principal facts of local and
general government in New Zealand, and the principal
social and industrial improvements made since the
accession of Queen Victoria.

(7.) Drawing I.—Free drawing with pencil or brush: The
candidate shall be required to draw on a half imperial
sheet of paper (i) a natural object, or (ii) a fashioned
or artificial object or a group of such objects placed
before him either above or below the line of sight. In
the case of (i) the candidate may also be required to show
that he is able to adapt the form of the object placed
before him to decorative purposes. The object or ob-
jects are to be represented as seen from the point of view
at which the candidate may be seated. The candidate
may use the pencil or brush to estimate the apparent
relative sizes of the objects or parts of the objects to be
drawn, but only by holding it between the eye and the
objects. No other form of measuring and no ruling or
other mechanical means of execution are allowed. The
drawing, which should be as complete as possible, may be