Mar. 27.] THE NEW ZEALAND GAZETTE. 1055

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 containing the angle, and likewise the external bisector externally.

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.

(b.) Trigonometry: Degrees and radians; use of protractor 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 oblique triangles by drawing to scale; tracing of trigonometrical functions through the four quadrants; arithmetical 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. Description and use of the vernier, theodolite, prismatic compass, and sextant.

Skill in the transformation of trigonometrical expressions or in the manipulation of formulae will not be required except in so far as it is implied in the above syllabus.

(12.) 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 (10) Arithmetic and Algebra, and subject (11) Geometry and Trigonometry.

(13.) 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 (10) Arithmetic and Algebra, and subject (11) Geometry and Trigonometry.

Heat: Sources and nature of heat; methods of measuring energy; different kinds of energy; transformation of energy of visible motion into heat; mechanical equivalent of heat; distinction between temperature and heat; effects of heat. Thermometry; construction