# University of Edinburgh Natural Philosophy Examinations 1882-83

We give the papers for the M.A. Pass degree in Natural Philosophy at the University of Edinburgh.

We give two Natural Philosophy papers, one from October 1882 and the other from April 1883. The first contains 25 questions with 6 additional questions only for those competing for the Neil-Arnott Prize for whom they are compulsory. The second paper contains 24 questions.

### NATURAL PHILOSOPHY PAPER October 1882.

Thursday, 19th October 1882. - 1 to 4 o'clock.

Examiners- Professor TAIT and Dr MACFARLANE.

Not more than eighteen questions to be answered, of which six, must be taken from questions 1 to 8 inclusive.
1. Define Velocity, and Acceleration. What is the relation of Acceleration to Force?

A lift ascends under a uniform acceleration during the former part of its course, and with a uniform velocity during the latter part of its course, and is stopped suddenly at the end; describe the sensations of a passenger with respect to weight.
2. Enunciate Newton's Second Law of Motion, and show how to derive from it the Resultant of two forces acting on a particle.
3. Write down the expressions for the momentum and the kinetic energy of a body in terms of its mass and velocity.

Calculate the Momentum and the Kinetic Energy of a hammer of one ton weight let fall half a foot, expressing the results in terms of the pound, foot, and second.
4. Assuming 32.2 as the foot-second measure of the acceleration produced by gravity, express the same quantity numerically in yard-minute, and in mile-hour, units.
5. State in kinematical terms the nature of the motion of a boat propelled by a couple of oars; (a) when worked simultaneously; (b) when worked alternately.
6. A balloon is 400 feet from the ground, and ascending at the rate of 10 feet per second. What time would a sand-bag take to fall to the ground from it?
7. Define Work and Horse-Power.

Calculate the amount of work done against gravity in drawing a car of 2.5 tons weight, laden with 30 passengers averaging 9 stones each in weight, up an incline the ends of which differ 120 feet in level.

Find the horse-power sufficient to do that work in half an hour.
8. Show that when a ladder, resting against a wall, is about to slip, a man standing on one of the lower steps will make it more secure; but that, if he mounts higher than its centre of gravity, he will bring it down.
9. Describe the nature of Contour Lines.

Show how the following will be indicated:-

(1) A plateau; (2) A gorge; (3) A mountain with crater.
10. What is meant by Elasticity? Show how to distinguish by its aid solids from fluids. Point out the common error in the use of the term "perfectly elastic."
11. Enunciate the laws which go by the names of Pascal, Boyle, and Hooke, respectively.
12. Point out the nature of the process by which Sound is propagated; and show why its velocity in the air depends on the height of the thermometer but not on that of the barometer.

Can you assign any reason for a connection between the intensity of a sound and its velocity?
13. Explain the contrast indicated in the terms Sensible Heat and Latent Heat.

Show how the principle of Latent Heat may be applied to construct a Calorimeter.

The Latent Heat of fusion of ice is 79.25 thermal units centigrade. Express this constant in terms of thermal units Fahrenheit.
14. Upon what physical fact does the possibility of constructing a Compensation Pendulum depend? Show the application to a measuring rod, whose length is to be independent of temperature changes.
15. Define the notion of Temperature.

The temperature of a fluid is ascertained by means of the hand to be the same as that of a mixture of 3 pounds of water taken at 0°C with 7 pounds of water taken at 100°C. What is the temperature of the fluid?
16. Enunciate, and explain, the Second Law of Thermodynamics.

Show how, by means of this law, temperature can be defined absolutely. How is the truth of the law established?
17. What is meant by arranging electric conductors "in series," and "in multiple arc"?

A number of incandescent electric lamps are to be put on one circuit; what advantage has the latter arrangement over the former?
18. Define the terms Quantity, Capacity, and Potential, as applied to a charged conductor. What is the nature of the relation among them, and how can the Energy of the charge be expressed in terms of any two of them?
19. State the principle of the induction of currents by a current.

Show how this phenomenon is apt to produce interference with a telephone circuit.
20. State the physical fact on which the construction of a Galvanometer depends. How can a galvanometer be constructed so as to be capable of measuring, at will, either, strong or feeble currents?
21. State the fundamental laws of Geometrical Optics.

Three equal luminous points are arranged at the corners of an equilateral triangle, and an opaque circular disc is placed symmetrically with respect to them; show the nature of the shadows produced.
22. Explain the nature of the refraction through a Prism; and point out the fundamental precautions necessary for the formation of a Pure Spectrum.
23. Describe one of the methods of photometry. What special difficulty is there in comparing lights produced from different kinds of sources?

How may the illuminating power of the Moon be compared with that of a street lamp?
24. What is meant by Polarized Light, and what information do we obtain from the mere fact that light can be polarized?
25. State briefly what you know about periodic comets.
Candidates for the Neil-Arnott Prize will answer the following questions along with not more than twelve of the preceding questions.

1. State generally how to calculate the rate of flow of a liquid through a tube under given conditions. What peculiarity is shown by capillary tubes?
2. Give the general principles on which you would proceed in selecting suitable spectacles for different cases of defective vision.
3. Explain one method of applying actual cautery by the help of a voltaic battery.
4. Describe the action of the Stethoscope, pointing out the physical principles involved.
5. Explain the Kinematical principles on which the action of the Sphymograph depends.

What is the physical cause of the sensation called Discord?

### NATURAL PHILOSOPHY PAPER April 1883.

Wednesday, 11th April 1883.- 1 to 4 o'clock.
1. Define force and kinetic energy.

What is the amount of kinetic energy in a train of twenty-five tons when moving with a velocity of twenty miles per hour? What force (measured in foot-pound-second units) acting for ten seconds is sufficient to stop the train?
2. Define Simple Harmonic Motion; and show that the resultant of two S.H.M: of the same period, in one line, is another of the same period.

Hence deduce the more obvious phenomena of the Tides.
3. What is erroneous in the term centrifugal force.

A skater describes a circle of radius 10 feet, with a velocity of 18 feet per second; what is his inclination to the ice?
4. A stone is let fall; and another is, at the same instant, projected upwards from a point 500 feet lower in the same vertical. With what speed must it be projected so that the two may meet half-way?
5. Show how to attach three horses abreast to a coach so that they may have equal amounts of work to do.
6. A ladder, resting on the ground, leans over a horizontal rail in a direction at right angles to it. If the length of the ladder be twice the height of the rail above the ground, what is the coefficient of friction if the ladder is just about to slide down when inclined 45° to the vertical?
7. What is the best direction for putting a stone, when the field is horizontal?
8. Show that angular velocities about intersecting axes are to be compounded by the same rule as linear velocities.
9. Define density and specific gravity.

A sphere of cast-iron floats in the liquid metal at nearly the same temperature. The upper segment has a height of 0.7 inch, and a diameter of 3.6 inch. What is the density of the solid relatively to the liquid cast-iron?
10. What is meant by the mean density of the earth? Explain fully one process by which it has been approximately determined.
11. What is meant by Surface Tension?

A strip of paper is floated on the surface of water in a basin. A small piece of camphor is placed upon one end of the strip, but at the side, and so as to touch the water, and a similar piece is placed on the other end, but so as to project on the water on the opposite side. The strip will revolve for a long time. Explain the motion.
12. Compare the extensibilities of two spiral springs, one of which is 3 feet long and is extended by an inch for every pound appended, while the other is 7 feet long and is extended by a foot for each cwt. appended.
13. The climate of Egypt is hot and dry, and the river Nile is remarkable for its low temperature. Show the connection between these two phenomena.
14. Define the Dew-point, and explain fully one method of finding it.
15. Define the ordinary unit of heat, and Specific Heat.

Find the amount of heat which must be given to an iron armour plate 8 feet long, 7 feet wide, and 12 inches thick, in order to heat it from 12°C to 900°C. (The specific heat of iron is 0.12, and its density 0.28 Ibs. per cubic inch.)
16. State, in any one form, the Second Law of Thermodynamics; and point out the nature of the evidence for its truth.
17. What is the difference between an arc electric light and an incandescent electric light? What are their relative advantages and disadvantages?
18. State the fundamental experiments on which Faraday based his discovery of Magneto-electricity.

Explain, generally, the action of what is now absurdly called a "Dynamo."
19. Describe the mode in which sound is propagated.

A shot is fired at a target; find the locus of the positions where 4 spectators will hear the report of the shot and the report of the impact simultaneously.

Why do such positions exist?
20. Explain the action of a convex lens of short focus when employed as a simple microscope.
21. Enumerate the fundamental colour sensations. How are the others produced?
22. Describe, fully, one method of measuring the velocity of light.
23. Find the length of the sidereal second in terms of the mean solar second.
24. Point out the various means we have of obtaining information as to the rigidity, temperature, distribution of density, etc., under the crust of the earth; showing generally the nature and amount of the information we have received or may yet receive from each.
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