Nov. 29.

THE NEW ZEALAND GAZETTE.

Volume of the prism and pyramid.
The generation of the right circular cylinder, right
circular cone, and sphere by revolution.
Development of the right circular cylinder, and right
circular cone; the surface of each.
Volume of the cylinder, cone, and sphere.

SECTION D (THEORETICAL).
If a straight line is drawn parallel to one side of a
triangle, the other sides are divided proportionally; and
the converse.
If two triangles are equiangular, their corresponding
sides are proportional; and the converse.
If two triangles have one angle of the one equal to
one angle of the other, and the sides about their equal
angles proportional, the triangles are similar.
The internal bisector of an angle of a triangle divides
the opposite side internally in the ratio of the sides con-
taining the angle, and likewise the external bisector ex-
ternally.
The ratio of the areas of similar triangles is equal to
the ratio of the squares on corresponding sides.
The ratio of the areas of similar polygons is equal to
the ratio of the squares on corresponding sides.
In equal circles (or in the same circle) the ratio of any
two angles at the centre or of any two sectors is equal to
the ratio of the arcs on which they stand.
(d.) Trigonometry: Degrees and radians; use of pro-
tractor or scale of chords; trigonometrical functions and
their fundamental relations; determinations of their
value by graphical methods and setting-out of angles
when the value of the sine, cosine, or tangent is given.
Approximate solution of right-angled triangles and ob-
lique triangles by drawing to scale; tracing of trigno-
metrical functions through the four quadrants; arith-
metical values of the trigonometrical functions of 30°,
45°, 60°, 75°, 90°, &c. Formulae for finding the sine,
cosine, and tangent of the sum or difference of two angles
(excluding angles greater than two right angles), and easy
derived formulae; the sine rule in triangles, or sin A/sin
B = a/b, and other simple properties of triangles; the
area of a triangle. Use of natural and logarithmic tables
of sines, cosines, and tangents of four or five figures.
Solution of triangles; heights and distances.
Skill in the transformation of trigonometrical ex-
pressions or in the manipulation of formulae will not be
required except in so far as it is implied in the above
syllabus.

Group IV.
(18.) Mechanics and Hydrostatics.—The composition and
resolution of forces acting on a point and on a
rigid body on one plane; the mechanical powers;
friction between two plane surfaces treated simply;
the centre of gravity; the fundamental laws of
motion; the laws of uniform and uniformly accelerated
motion and of falling bodies; projectiles (exclusive of
problems depending on the geometry of the parabola);
impact; circular motion; simple pendulums; the
pressure of liquids and gases; the equilibrium of floating
bodies; specific gravities; the principal instruments and
machines the action of which depends on the properties
of fluids, with simple problems and examples.
Candidates will be expected to show an experimental
as well as a theoretical knowledge of fundamental laws,
but will not be expected to show any further knowledge
of pure mathematics than what is demanded in subject
(17), clause 36, Pure Mathematics.
(19.) Heat and Light.—Candidates will be expected to show an
experimental as well as a theoretical knowledge of the
fundamental laws of heat and light, but will not be
expected to show any further knowledge of pure
mathematics than what is demanded in subject (17),
clause 36.

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