8. A disc of any form is moving in its own plane in any manner. Suddenly a point

on it is seized and made to move in some given manner. the initial motion of the disc.

Find

Find the magnitude and line of action of the single impulse which will reduce the disc to rest. 9. Shew that the small oscillations of a dynamical system about a stable position of equilibrium can in general be resolved into a set of principal oscillations in each of which every particle is performing a simple harmonic motion of the same period and phase.

A square on a smooth horizontal plane is formed of four equal rods each of mass m and length a smoothly jointed together. Two elastic strings of natural length a and modulus mλ join the opposite angles. Find the time of a small oscillation.

SYSTEMATIC ZOOLOGY.

Professor Sir Frederick McCoy.

FOR PASS AND HONOUR CANDIDATES.

1. What are the general characters of the subkingdom Vertebrata, and what types are exceptions to any of them? Define briefly the classes into which the sub-kingdom is divided.

2. Describe the chief bones of the skull of fishes used for systematic classification.

3. In what respects do the Leptocardii and the Cyclostomata differ from other Vertebrata?

4. In what respects do the Teleostea differ from the Ganoida?

5. Define the six tribes into which the order Teleostea is usually divided?

6. In what groups of fishes is the air bladder (a) absent; (b) present, without pneumatic duct; (c) with pneumatic duct?

7. In what respects do the Clupeide and the Salmonida agree and differ?

8. Describe the migration of the eye in the Pleuronectide, and describe a few of the genera to illustrate the chief structural variations of the family.

9. Define the eight sub-orders or tribes into which the order Ganoida is usually divided.

10. Define, by structural characters, the order Chondropterygii, and the primary division into the Holocephala, and the Plagiostomata with the chief families of the Plagiostomata.

SYSTEMATIC BOTANY.

Professor Sir Frederick McCoy.

1. Exemplify the " Artificial System of Classification of Plants" by that of Linnæus as applied to Flowering Plants, enumerating his 23 classes, and stating generally the characters on which they are based.

2. Exemplify the "Natural System" by that of De Candolle, showing the characters relied upon for the definition of each of the Classes of Plants adopted by him.

3. Mention the chief orders of the Thalamiflora.

4. How are the Calyciflora divided? Write down the chief orders of each of the subdivisions.

5. How are the Monochlamydea divided? Mention the more important orders of the two subdivisions.

6. What are the sub-classes of the Monocotyledones? 7. How are the Petaloidea divided, and what are the more important orders of each of the subdivisions?

8. Define the Glumifere, and show the characters in which the Cyperaceae and the Graminea agree and differ.

9. Contrast the generative organs and structure of the cones of the Cycadacea and Coniferæ.

10. Give the characters of the sub-classes of the Acotyledones.

PHYSICAL GEOLOGY AND MINERALOGY. Professor Sir Frederick McCoy.

FOR PASS AND HONOUR CANDIDATES.

1. What are the facts shewn by "geological maps' and by geological sections respectively? How are sections made from maps? How are necessary distortions in sections dealt with? Give examples of the more usual ones.

2. What evidence as to the conditions of the interior of the earth is afforded by the precession of the equinoxes, the nutation of the earth's axis, and the difference of the vibration of a pendulum at the surface and at the bottom of a deep mining shaft?

3. What are the conditions necessary for the formation of glaciers, and how is their former presence shewn in localities where they are not now formed?

4. Describe the chief relations between earthquake and volcanic activity.

5. How are craters formed, and how are extinct volcanoes recognised?

6. Explain the methods of classifying rocks from their lithological characters. Whence are the material derived for the stratified rocks?

7. In the Hexakisoctahedron, of 48 equal triangular faces, you have an example of the general formulæ hkl of Miller, abc of Weiss, and m On of Naumann respectively. What is the exact meaning attached to each index of each formula?

8. What do microscopical observers of slices of igneous rocks understand by orthoclastic and plagioclastic minerals, and what relation have the characters referred to to the classification of igneous rocks into "acidic" and "basic"?

9. What are the general chemical, physical, and crystallographic characters of the Felspar group of minerals found in all igneous rocks? Which are the basic, and which the acidic ?

10. Illustrate the methods of notation used for reference to the faces of crystals in all the systems by Miller, Naumann, and Weiss respectively?

STRATIGRAPHICAL GEOLOGY AND

PALEONTOLOGY.

Professor Sir Frederick McCoy.

1. Write down in chronological order all the chief named fossiliferous divisions of the stratified rocks.