revolving around a line in its plane is the product of the area and the length of the path described by its centroid. Find the volume of the solid obtained by rotating a segment of a circle around its chord. 7. Shew how to reduce a given system of forces to a single force at an arbitrary origin and a couple. Prove that the resolved part of the couple in any direction is the sum of the moments of the forces about a line through the origin in that direction. 8. State and prove the principle of virtual work for a system of bodies. The joints of a plane polygon of bars are smoothly constrained to move in given directions. If P1, P, .... Pn are the external forces on the joints in those directions, shew that for equilibrium * P, cos Bi .... cos 2r-1 cos art1 .... cos an = 0 where an, B, are the angles the sides at the pih joint make with the direction of Pro 9. Shew how to find the c.p. of any plane polygonal area immersed in a heavy liquid. A rectangle is immersed in three liquids of densities p, 2p, 3p, the top of the rectangle being in the surface of the first liquid and the area immersed in each liquid the same. Shew that the depth of the c.p. is five-sevenths of the depth of the lower side below the surface. 10. Shew that if, in an atmosphere at uniform tempera ture, a series of heights are taken in A. P. the densities of the air decrease in G. P. Hence find an expression for the difference of the altitudes of two stations in terms of the barometric heights, obtaining an approximate numerical value for the constant involved in the expression. 11. Investigate the vertical oscillations of a floating body, neglecting the motion of the liquid. SYSTEMATIC BOTANY. Professor Sir Frederick McCoy. 1. Describe the “ Artificial System” of classification of Plants proposed by Linnæus. 2. Write down the orders and the classes of flowering, Plants according to the artificial system of a 3. Write a short account of the principles on which the “Natural System” has been proposed by various botanists. 4. Write down, in systematic order, the sub-classes of Dicotyledonous Plants according to the Natural System of De Candolle, with their brief definitions. 5. Define the class Monocotyledones or Endogence, with the distinguishing characters of the subclasses according to De Candolle. 6. Write a short account of the characteristic peculiarities of the class of Acotyledonous Plants and the Acotyledonous sub-classes. 7. Contrast the characteristics of the Natural Order's Nymphæacece or Water Lilies and the Papaveraceæ or Poppies. 8. To what order do the Apple, Loquat, Plum, and Almond belong, and how are the sub-orders discriminated ? 9. Define the sub-class Glumiferoe, and set out in detail the characters in which the orders Cyperacece or Sedges and Gramineæ or Grasses agree and differ. а 10. Write a brief account of the characters and classi fications of the Natural Order of the Alyce. PHYSICAL GEOLOGY AND MINERALOGY. Professor Sir Frederick McCoy. 1. How are Limestones formed ? Explain the dif ferent ways in which rocks of this kind may be formed, and the sources of the material. 2. Write down the chief characters observed of Coral Reefs, and their classification, with the theories of the origin of Atols, suggested by Darwin and Murray respectively. 3. Explain fully the origin and general characteristics of conformities, unconformities, thinning-out, false bedding, and faults in rock masses. 4. Explain the mode of origin and relation to geological structure, the three chief kinds of Valleys, Valleys of Elevation, Valleys of Denudation, and Synclinal Valleys. 5. What precautions are necessary in taking the directions of dip of strata by compass ? 6. Why are geological sections generally on two different scales, the vertical and the horizontal, and how are the resulting distortions dealt with? 7. Describe all the chief variations in the nature, origin, and composition of concretions in Igneous and in Aqueous rocks. 8. Exemplify all the symbols used to denote strati graphical characters on geological maps. 9. What observations have been made for determining the density of the earth with their geological bearings ? 10. How are minerals classified ? Give the nature of the chief groups formed by each method generally used, and the mode of classifying crystals; defining each group. STRATIGRAPHICAL GEOLOGY AND PALÆONTOLOGY. Professor Sir Frederick McCoy. 1. Write down all the formations in chronological order. 2. What significance have geologists given to uncon formities in defining the limits of geological formations, and what objections may be reasonably made to some of these views ? 3. What are the main characteristics of the Tertiary formations ? Write down the modern subdivisions with their general characteristics. 4. What relation have the English Bone Caves to the so-called glacial beds in time ? 5. What are the relations of the Mammaliferous Crag to the other crags to the Northern drift, and to the bone-cave deposits ? Enumerate the chief genera of Mammalia and Mollusca showing the relations referred to. 6. Give the generic characters of Elephas, Sus, Hippopotamus, Rhinoceros, Equus, as the chief 7. Give the generic character and geological range in time of the chief Ruminantia of the Tertiary formations. |