3. A uniform heavy string of length 27 and weight w per unit length is suspended from two points a distance 2a apart on the same level, c being the parameter and h the greatest depth of the catenary. Find the centre of mass of the string, and shew that the work required to haul up its middle point vertically to the level of the ends is w (lh + lc ac).

4. Investigate the attraction at any point due to a uniform infinite lamina of gravitating matter.

Apply the result to determine the change of normal force in passing through a thin shell of any form.

5. Determine completely the orbit of a particle which is projected from a given point with given velocity in a given direction and is under a central force varying as the distance.

Shew that under the law of the inverse cube a particle may approach the centre of force at a uniform rate and find the orbit.

6. Investigate the time of oscillation of a simple pendulum correct to the square of the amplitude.

7. If air resistance is as the square of the velocity, shew that a particle projected vertically upwards with the velocity giving a resistance equal to its weight will lose half its kinetic energy before it returns to the point of projection.

8. A pendulum consists of a cylindrical rod of radius a and length 1, which passes centrally through a solid sphere of radius r, the end forming part of the spherical surface. The other end of the rod

is cut off normally, and the axis of suspension is a diameter of this section. Find the time of a small oscillation.

9. Find the coordinates of the initial centre of rotation when a free lamina at rest begins to be acted on by forces such as (X, Y) at (x, y).

10. Two smooth inelastic lamina in the same plane impinge with given linear and angular velocities. Find the motion immediately after impact.

11. A smooth uniform rectangular lamina ABCD of can turn freely about the side AB,

weight
which is horizontal. The lamina is held at an
inclination a to the horizontal with CD above
AB. A particle of weight w is placed at the
middle point of the lamina, which is then released.
Shew that the initial reaction between particle
and lamina is w cos a.

PHYSICAL GEOLOGY AND MINERALOGY.

The Board of Examiners.

1. Explain Darwin's views of the formations of Atolls, and discuss the objections which have been raised to them.

2. About what amount of central heat now reaches the surface of the earth; or about how much ice would it melt in a year?

3. About what rate does the form of an earthquake wave travel at ? What is about the velocity of a particle of rock "in amplitude"? What is

the velocity of the "sound wave" through air? Distinguish between the velocity of transit of a "shock" and of an earthquake wave.

4. Mention some examples of the mechanical transporting effect of fresh-water currents of different ordinary velocities on different sizes and conditions of rock materials. At about what rate do the carrying powers of currents of different velocities vary?

5. Describe some of the more important geological actions of freezing, and of frozen, water.

6. Explain what is meant by "cropping-out," "thinning-out," "false bedding," and "unconformity of strata." Sketch examples of the different formations of valleys recognised by geologists.

7. In monometric minerals what intersections of faces of primary crystalline forms would be indicated by angles of about 54°, 35°, 70°, and 45° respectively?

8. Give some examples of the crystalline forms derived from a cube by (a) truncations of angles, (b) truncations of edges, (c) bevelling, (d) hemihedral developments.

9. What is a "form" in crystallography, and how are primary and secondary forms distinguished?

10. Give some examples of what are understood by "Pseudomorphous minerals" and their general characteristics.

STRATIGRAPHICAL GEOLOGY AND PALÆON. TOLOGY.

The Board of Examiners.

1. Write down as many as you can of the stratified formations in chronological order.

2. What are the great distinguishing Palæontological characteristics of the Tertiary, the Mesozoic, and the Palæozoic Geological Periods?

3. In what Palæontological respects do the modern and newer Tertiary formations differ from those of older date?

4. What are the generic characters and difference of range in time of (a) Mastodon ; (b) Dinotherium; (c) Equus; (d) Machairodus; (e) Diprotodon; and (f) Dinornis?

5. Give the generic characters of as many types of Cephalopodous Mollusca peculiar to the Mesozoic period as you can.

6. What are the ranges in geological time and generic pecularities of the more common Enaliosaurian Reptiles?

7. What are the general characteristics of Trilobites, distinguishing them from other crustacea? What geological formations do they range through? Explain the terms Pygidium, Glabella, Eye-line, Pleuræ, and Facet.

8. Discuss the chief diverse views of the nature of Eozoon, and the existence of Pre-Cambrian fossiliferous strata.

9. What are the chief Paleontological peculiarities of the "Primordial Zone"?

10. What are the characteristics of the Oligocene formations?

DEDUCTIVE LOGIC.

The Board of Examiners.

1. May an abstract name in any case be considered general? Examine carefully any reasons which have been given in favour of an affirmative

answer.

2. What objections have been taken to the use of Euler's circles by Hamilton or Jevons? How may these circles be properly used to illustrate the opposition of propositions?

3. Does a categorical proposition always imply the existence of objects denoted by the terms which it contains? Consider this question with reference to (a) universal and (b) particular propositions.

4. What is meant by a "strengthened syllogism"? Illustrate by the fourth figure. Examine the statement that "the fourth figure is only the first with a converted conclusion."