MATHEMATICAL PHYSICS.

Examiner-PROFESSOR ANDERSON, M.A.

1. Show that any system of forces in a plane is equivalent to three forces acting along the sides of a given triangle ABC in the plane. If these forces be P, Q, R, find the line of action of the resultant of the system.

2. A force P acting up a rough inclined plane just sustains a weight W resting on the plane, and a force Q acting up the plane is just sufficient to drag the same weight up; find the co-efficient of friction.

3. A particle is acted on by finite forces; prove that the increase in the kinetic energy is equal to the work done on it.

A particle moves along a circular tube under the action of a force varying as the distance towards a point A in the circumference, the initial position being at B, the other end of the diameter through A; prove that the velocity at any point P is proportional to PB.

4. A fly-wheel whose mass is 9000 lbs. is rotating at a rate of 20 revolutions per minute. Its size and shape are such that its mass may be supposed concentrated on the circumference of a circle whose radius is 10 feet; find how many revolutions it will make, steam being shut off, and a friction of 400 lbs. weight applied to its axle 1 foot in diameter.

5. Find by a geometrical construction the maximum range along an inclined plane through the point of projection, of a particle projected with a given velocity.

6. Show how to find the resultant thrust exerted by a uniform liquid at rest under gravity on a plane area exposed to it.

Find the centre of pressure of a circular area immersed in a liquid in any manner.

7. A solid whose volume is is pushed below the surface of a liquid of density p, show that the potential energy of the liquid is increased by gp V%, z being the depth to which the centroid of the volume is immersed below the surface, the level of which is supposed not to be appreciably altered.

8. Prove that the illumination at any point of a plane area due to a uniformly bright surface is proportional to the projection on the plane of part of the surface of a certain sphere.

The ceiling of a room whose breadth is b and height h is uniformly bright. Show that if the room is infinitely long the illumination at a point on the floor, whose distance from a side-wall is x, is proportional to

x/(x2 + h2)2 + (b − x)/( (b − x)2 + h2)}

9. A small pencil of rays diverging from a point passes directly through a glass plate of given thickness; find the distance between the foci.

10. Describe and explain the apparent path of Venus in the heavens during a complete synodic period.

CHEMISTRY-LABORATORY WORK.
PROFESSOR SENTER, PH.D.

Give results at which you arrive, together with full experimental proof. Marks will be given for excellence in manipulation.]

1. A solution-search for one basic and one acid radical. [Potassium iodide.]

[Basic lead chromate.]
[Red oxide of lead.]
Search for one basic and

2. A red powder: identify it. 3. A red powder: identify it. 4. A white crystalline powder. one acid radical. [Sodium biborate.]

ENGINEERING.

Examiner-PROFESSOR TOWNSEND, M.A.

1. In a dumpy level, in order to adjust the line of collimation parallel to the bubble-tube, the following observations are made:-A level is set up midway between two staffs A and B, 200 feet apart, the reading on A is 3.41 feet, and on B, 6.05; the level is then moved to a point between the staffs at distance of 40 feet from A, and the readings are, on A 4.55, on B 7.30.

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From the above show how to adjust the line of collimation. 2. Bidder's tabular numbers, corresponding to two given heights, are-red = 39.1, black 62.9; find Macneill's multiple and additive tabular numbers, II. series, the ratio of slopes being 1 to 1, and calculate the number of square yards in the slopes, the length of the cutting being 200 feet.

3. The radius of a railway curve is 4 furlongs 2 chains,

the angle between the extreme tangents 138° 20′. Calculate
the length of the tangent, the distance to middle point of
curve from intersection of the tangents, and the length of the
curve in chains.

4. Calculate the area of the cross-section of a cutting, with
an uniform sidelong slope in terms of H, bo, r, s, where H
central depth, bo, half breadth of base, r, ratio of slope of
sidelong ground, S ratio of slope of cutting.

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5. In the following taken from a Level-Book fill in the
columns, Reduced Level, and Height of Collimation, the
starting-point being 40.23 feet over datum; and show how
to check the accuracy of your work by two methods.

6. Explain the adjustments of the instrument set before

you.

7. Read the Verniers set before you.

8. Calculate the discharge in gallons per minute from a pipe 8 inches in diameter, the fall per mile being 2.67 feet.

9. When slates are nailed near the centre, make a sectional sketch showing the margin, lap, and batten, and figure on dimensions of the above for a Duchess slate.

10. Assuming the Lowell or Francis' formula for the flow of water in a rectangular weir, prove the formula for the flow of water in cubic feet per minute in a V-notch, and state the peculiar merits of the latter.

QUEEN'S COLLEGE, GALWAY, STUDENTS' LITERARY AND DEBATING SOCIETY.

This Society meets in the Physiological Laboratory on Friday evenings throughout the Session, at 7.30 p.m.