6. Find the equation of the line joining the two points 1y1, x2 y2, and form the equation of the perpendicular upon this line from the point

7. Find the condition that the line y = mx +c may touch the circle x2 + y2 = a2, and hence find the equation of the tangent at the point x'y'.

8. Shew that two tangents can be drawn to a parabola from an external point.

Prove that the tangents at the points x'y'; x"y" meet in the point

9. Find the equation of the line joining two points. on an ellipse whose eccentric angles are given.

Shew that if a chord of an ellipse be drawn parallel to a fixed line the sum of the eccentric angles of the extremities of the chord is constant..

10. Shew that the general equation of the second degree can always be reduced to the form.

Ax2 + By2 + 2Gx + 2Fy + C = 0.
Draw the curve

3x2+5y2+6x+20y+3=0.

11. Define a definite integral, and if (x) be the function from which (x) springs by differentiation, prove that

S p(x) dx = 4(b) — 4(a).

12. Explain fully the process of integration by substitution, and shew how to find the limits of the transformed integral.

14. Find the area of a loop of the curve aby2 + b2x6 = a2b2xa.

15. Find the volume generated by the revolution about the axis of x of the curve in question 14.

SYSTEMATIC ZOOLOGY.

The Board of Examiners.

1. What is the classification usually adopted for the Rhizopoda? Define the groups larger than

genera.

2. Define the families of the Madrephyllaceae, and give the more important reasons which have been advanced for and against the Zoantharia rugosa being classified with them.

3. Define all the divisions larger than families into which the Acalephæ are systematically grouped.

4. Define the sections of the Diptera larger than families, and enumerate the families properly coming under each.

5. What characters of the Anomura separate them from the Brachyura and Macroura in the systematic classifications?

6. Into what divisions larger than genera are Trilobitida systematically divided?

the

7. How are the Rudistes classified, and on what grounds have their relations to the Palliobranchiata and the Lamellibranchiata respectively been maintained?

8. What families constitute d'Orbigny's order Pleuroconcha, and why are the Corbiculidæ excluded from that group in the systematic classifications? 9. Briefly characterise the chief families of the Pectinibranchiata.

10. In the classification of the Vertebrata what differences in the grouping of the classes arise from giving chief weight to the temperature of the blood or to the foetal membranes respectively?

COMPARATIVE ANATOMY AND ZOOLOGY.

The Board of Examiners.

1. What are the structural characteristics of the Infusoria?

2. What are the anatomical peculiarities of the eightrayed Corals, and how are they classified?

3. Give the chief differences in anatomical structure and development between the Gymnophthalmatous and the Steganophthalmatous Pulmograda.

4. Describe the structure of the Hirudinidæ, and explain the use of their external characters for the zoological classifications of Savigny, de Blainville, or any other authors.

5. Describe the parts of the mouth made use of for the zoological classifications of each of the Orders of Insects.

6. What are the chief anatomical characteristics of the Cirrhopoda, and how are they classified?

7. What are the structural peculiarities of the Brachiopoda, and how are the Families defined into which the group is zoologically divided?

8. Describe the respiratory organs of the Mollusca made use of for definition of the main subordinate zoological groups.

9. What are the chief structural characteristics of the Dibranchiate Cephalopoda, and how are they classified into subordinate groups?

10. Describe in due relative order all the Autogenous Elements and Exogenous parts found in Vertebræ.

PHYSICAL GEOLOGY AND MINERALOGY.

The Board of Examiners.

1. Set down the more important arguments used for and against the various assumptions of geologists as to the nature of the material forming the interior of the earth.

2. Explain the experimental means used to determine the mean density of the earth, and what bearing has the result on the suggestion that the interior of the earth is composed of similar materials to the crust?

3. What are the principal differences between the Plutonic and the Volcanic Rocks? Enumerate the chief Plutonic Rocks, with their mineral constituents, and give some explanation of their having been formed in the main before the Volcanic ones.

4. What is the chief mineral characteristic of the Acidic Rocks, and what are the general mineralogical differences from the Basic Rocks?

5. How has the so-called central heat of the earth been determined? And how does this bear on the arguments for and against the fluidity or solidity of the interior?

6. What are the chief geological sources of the mechanical forces which have disturbed the surface of the earth? Give examples of the way in which the chief kinds of disturbances have been produced.

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