3. Shew that the stress at a point of an elastic solid can be specified by means of six elements, and obtain formulæ for the stress across any plane at the point.

The stress in a bar being a simple longitudinal tension of intensity T, find the intensities of the normal and shearing stresses across a plane making an angle with the axis of the bar, and shew that the shearing stress is a maximum when the angle is 45°.

B.

4. Describe how to determine the torsion modulus of a wire, and give the theory of the method.

5. Give a general explanation of the effect of pressure-change on the temperatures at which changes of state occur.

How would you determine the relation between the boiling point of water and the external pressure?

6. Explain the terms Isothermal, Adiabatic, Indicator Diagram; and show how an indicator diagram is used to investigate the working of a heat engine.

7. Describe how to determine the magnetic dip, and explain the reason for each step in the process. 8. Describe fully how you would test the accuracy of the graduations of a station ammeter.

9. Describe how to measure the insulation resistance of an installation.

10. Describe the construction and give the elementary theory of some good form of three phase gene

rator.

DEDUCTIVE LOGIC.

Professor Laurie.

TO BE USED AS PASS PAPER, AND ALSO AS HONOUR PAPER No. 1.

1. What do you understand by the extension and intension of names? And how are these quantities related to each other? Illustrate by a short series of general names ordinated in

extension.

2. Find, where possible, the converse, the contrapositive, and the inverse of the following propositions:-Virtue alone is happiness below.Every wealthy person is not to be envied.—When a plant has more than one seed-lobe, it is an exogen. A few terms are free from ambiguity. Where the inference required is impossible, give the reason for this.

3. What arguments may be used for, and against, the adoption of the propositions U and Y in addition to the traditional forms of categorical proposition ?

4. Mention the peculiarities and uses of each of the four figures of the categorical syllogism. Show that Baroco can be reduced, both directly and indirectly, to the first figure.

5. What are the distinctive marks of the hypothetical proposition, as distinguished by Keynes from the conditional? Show how, in hypothetico-categorical syllogisms, the modus ponens may be reduced to the modus tollens, and vice versâ.

6. What distinction has been drawn between Perfect and Imperfect Induction? Mention any peculiarity, or peculiarities, of the Inductive Syllogism, as compared with other recognised moods of categorical argument.

7. Mention different kinds of the fallacy of Accident. In what does the fallacy of Ignoratio elenchi consist? Should this fallacy be ranked among formal or among material fallacies, and why?

8. State the following in syllogistic form, and point out fallacies, if any :—

(a) All true discoveries have been attacked at first; and, therefore, as the theory now before us

has been attacked, it is more likely to be true than otherwise.

(b) It seems paradoxical to say that even teetotallers should be taxed to encourage the industry of wine-making, or that those who do not smoke should contribute towards bonuses on tobacco-growing; but how do you escape these conclusions if you admit that every industry should be encouraged?

(c) Planets move in ellipses, but, since comets are not planets, our premisses leave us in doubt whether comets move in ellipses or not.

(d) Either every war is unjust, or the present war is justifiable; either the majority are wrong, or some wars are not unjust; therefore, if the majority be right, the present war is justifiable.

9. A scientific association is composed of ordinary and honorary members. Members are divided into three sections, botanical, zoological, and geological, but no ordinary member belongs to more than two of these sections. Honorary members, as it happens, are either botanical or geological, but not both. Every member of the zoological section is also a member of the geological. How would you characterise (1) the botanical, and (2) the geological members? Work out this question by Jevons' Method of Indirect Inference.

INDUCTIVE LOGIC.

Professor Laurie.

TO BE USED AS PASS PAPER, AND ALSO AS HONOUR
PAPER No. 1.

1. How does Mill arrive at his classification of Propositions, according to their import? Are his classes mutually exclusive?

2. It is remarked by Mill that it is extremely important "to place before our minds, in its full extent, the whole of what our evidence must prove if it proves anything." Explain his position here.

3. Compare the so-called Perfect Induction with the induction of a scientific generalisation. What, from a material point of view, is the value of the former?

F

4. On what grounds has the Law of Causation been alleged to be the main pillar of inductive science? Are our statements of uniformities of co-existence wholly free from the influence of this law?

5. If A be introduced into a set of definitely known circumstances B, C, D, and if x, which was absent, at once makes its appearance, what are you entitled to infer, and under what Method? 6. Show the value, qualitative and quantitative, of the Method of Concomitant Variations.

7. Explain Mill's statement that the experimental method cannot be directly applied, with safety, to the phenomena of politics and history.

8. Mention different meanings which have been attached to Analogy. Show the connection between Analogy, as treated by Mill, and hypothesis.

MENTAL PHILOSOPHY.

Professor Laurie.

To be used as Pass Paper and Honour Paper No. 1 for Second Year Students, and as Pass Paper No. 1 for Third Year Students.

1. Show the connection of the philosophy of Descartes with the movement of the Renascence.

2. Indicate the historical influence of the accounts of Substance given by Descartes and Locke respectively.