DEC. 15.] THE NEW ZEALAND GAZETTE. 3839

SPECIMEN SET OF EXAMINATION PAPERS FOR EXTRA MASTER.

MATHMATICS.

Paper 1 (3 hours).

1. A glass tumbler is partly filled with mercury (Sp. G. 13·6) in which
   is floating a 1 in. diameter sphere of alloy (Sp. G. 7·3). The
   remaining space is filled with fresh water, when it is found that
   the mercury occupies half the depth of the tumbler. If the
   inside diameters, top, and bottom of the tumbler are 3 and 2 in.
   respectively and the inside depth is 5 in., find the weight of its
   contents.

2. Two points of land are in transit bearing N. 40° W. from a steamer.
   On a westerly course the horizontal angle became maximum
   at 22° at the steamer after making 9·5 miles.
   If the two points are 4 miles apart, find the course made
   good by the steamer.

3. Assuming the identities involving the Sine and Cosine of the half
   angles, deduce the formula for the solution of a spherical triangle.
   Sin a Sin b Sin c
   Sin A = Sin B = Sin C

4. Find the correct G.M.T. when the two stars α Ursa Majoris (Dubhe)
   and ε Ursa Majoris (Alioth) are at the same altitude at a
   position Lat. 60° N. Long. 30° W. on 25th June, 1929.

5. A steamer finds that by increasing her normal speed by 1 knot
   she can make a 2,640 mile passage in one day less. What is
   her normal speed ?

GENERAL SCIENCE.

Paper 2 (3 hours).

(Only 8 of these Questions to be answered.)

1. A crank 15 in. long is driven by a piston and makes 140 revolutions
   per minute. Find the acceleration of the piston when it is
   3½ in. from the end of its stroke, taking the motion as simple
   harmonic motion.

2. What do you understand by the term Pressure, and in what units
   is it measured ?
   If a diver's tank has a volume of 2 cubic feet and contains
   air under a pressure of 30 atmospheres, to what extent will the
   air expand when it is released at a depth of 17 fathoms of water ?

3. A load of 8 tons is lifted by a hydraulic press when an effort of
   15 lb. is applied on the end of a 14 to 1 lever. Assuming an
   efficiency of 90 per cent., find the proportion between the
   diameter of the ram and the plunger.

4. Explain what is meant by the conservation of energy and
   momentum.
   Two equal masses are attached to a rope passing over a
   light frictionless pulley. One mass is supported by means of
   a table and the other is raised 30 in. and then allowed to fall
   freely through that distance.
   Find the velocity of the two masses after the rope has
   become tight.

5. A force of 14 lb. weight is applied at the end of a lever 3 ft. long
   in order to tighten up a nut on a screw bolt, 1 in. in diameter
   and with 8 threads to the inch. If the breaking tension of the
   material of the bolt is 14·4 tons per square inch, show that
   the bolt will just break.

6. Define the term Centre of Pressure.
   Part of the side of a reservoir is a door A, B, C, D. The
   lower side C, D is horizontal, while the side A, B is hinged so
   that the door can turn freely. If the lengths of A, B and C,
   D are 2 ft. and 12 ft. respectively, what force must be exerted
   at the mid point of C, D in order to keep the door shut when
   the level of the water is at A, B ?

7. A piece of wood weighing 40 lb. and specific gravity 0·75 is tied
   by a rope to the bottom of a tank of water so as to be totally
   immersed. What is the tension on the rope ?

8. What is the meaning of Dew Point?
   Describe some method of determining the Dew Point and
   show how to obtain the other quantities which are required
   in order to calculate the humidity of the air.

H