2. Apply the theory of induction to show how the electric 9 effects of several bodies may be added together. 3. If electric attraction is inversely as the square of the 10 distance, shew that there is no force within an electrified spherical shell. 4. It is desired to protect from lightning a building on whose roof there are several masses of metal. What measures should be adopted? 5. An electric charge Q is imparted to an insulated solid sphere of one foot in radius. The sphere is surrounded by a concentric spherical shell of radius 14 inches and in metallic connection with the earth. Calculate the capacity of the system. 6. Investigate the distribution of electricity on the surface of a spheroid. If we propose to deduce the distribution on a circular plate from that on a spheroid we find that the density at some points becomes infinite. What inference do you draw? 12 9 9 8 7. The cells of a voltaic battery are sometimes arranged for 10 quantity and sometimes for intensity. Explain the difference between the two arrangements. 8. Describe Ampère's theory of magnetism and apply it to explain the magnetism of the earth. 9 9. You are given a magnet and a pair of similar un magnetised 10 needles in order to make an ordinary astatic needle. How would you examine whether the needles were suitably magnetised before you proceeded to combine them? What is the difference in behaviour between an ordinary astatic needle and one that is perfectly astatic ? BOTANY, I. Examiner-DR. GEO. KING. 1. Give an account of the Linnæan System of Classification of plants. 2. Describe the ovule in Loranthaceæ, and in Gnetaceæ. 3. 4. Describe the ovary and its contents in the flower of Santalum. Describe the modifications of style and stigma found amongst Compositæ, and state how these have been used by systematists in dividing that order into sections. 5. Describe the flowers of Cynodon and Vanda. Compare them with flowers of the ordinary monocotyledonous type. Describe the mode of fertilization in Vanda. 6. Sketch briefly the morphology and life-history of Salvinia. 7. Give a short general description of the natural vegetation of the delta of the Ganges. 8. Give as many examples as you can of indigenous Indian plants that have (a) winged seeds 9. Describe the floral envelopes in Phoenix, Nelumbium, Mussaenda. 10. Describe the fructification of Funaria, Adiantum, Marchantia. BOTANY, II. Examiner-DR. GEO. KING. 1. Give a general account of the influence of temperature on vegetation. 2. Describe the sexual reproduction of Ferns. 3. What are the advantages of cross-fertilization? Give examples of the various ways in which it is secured in Nature. 4. What is meant by Cleistogamy? Give two examples of its occurrence in Indian plants. 5. Give an account of the manner in which Coal has been formed, and enumerate the chief fossils found in Indian Coal. 6. Give the geographical distribution of the Natural orders to which Nymphæa, Magnolia, Nephelium, Melia, Cinchona, Jatropha and Cyperus belong. 7. What is Aleurone? Where does it occur, and how may it be recognised? 8. Describe the objects mumbered 1, 2, 3. BOTANY, III. Examiner-DR. GEO. KING. 1. A copy of Roxburgh's Flora Indica and three plants numbered 4, 5, and 6 are herewith given to you. Find out the names given to these plants by Roxburgh, and state to what Natural orders they belong. 2. Define the terms Monopodial, Sympodial, Helicoid, Scorpioid as applied to inflorescences. 3. What is meant by the term Carnivorous as applied to plants. Give examples of carnivorous plants; state how they are supplied in nature with animal food, and how they assimilate it. 4. Describe the changes which occur in a phanerogamous ovule after fertilization. 5. Define the term Bark and describe the Histological changes which lead to the production of some of its most characteristic forms. 6. Describe the chemical and morphological changes that occur in the passage from the herbaceous to the woody condition in the shoot of a dicotyledonous tree. 7. Give a full account of the processes of Assimilation and Metastasis. 8. Give a brief description of the fossils named Stigmaria, Lepidodendron, Calamites, and state in what strata they are found. 9. What is the oldest known fossil vegetable? State in what strata it occurs. Honor Examination. 1881. ALGEBRA, TRIGONOMETRY, THEORY OF 2. Shew how to convert a surd into a continued fraction, and prove that the last quotient before the quotients occur is twice the first. 3. Prove that the distance between the centres of the circumscribing and inscribed circles is radii of these circles. R2-2 Rr, where R and rare the From a point P perpendiculars PL, PM, PN are drawn to the sides of a triangle ABC: shew that twice the area of the triangle LMN is equal to (Rd2) sin A sin B sin C, where R is the radius of the circle circumscribing the triangle ABC and d the distance of its centre from P. 4. Investigate an expression for cos a in exponentials; and prove that the sum of n terms of the series 6. Investigate Newton's method of approximating to the real roots of an equation. Prove that if c be very near a root of the equation ƒ (x) = 0 the root is 7. If S, represent the sum of the rth powers of the roots of the 8. Form the equation the roots of which are the squares of the differences of the roots of the equation 3 + q x + r = 0. Hence or in any other way find the condition that this equation may have a pair of imaginary roots. Find whether the equation x3 has imaginary roots. - 9. Obtain an expression for the by the three lines Ax + By + C A" x + By +C" = 0. (a2 + b2 + c2 ) x + 2abc = 0 10. When the equation to a conic is given in the form ax2 + 2 c'xy + by2 + 2 a'y + 2b'x + c = 0 find the co-ordinates of the centre. Also prove that the eccentricity is given by the equation 11. Find the equation to a hyperbola referred to its asymptotes as axes. Shew that the equation to the chord joining two points may be put in the form x cos a cos B + y sin a sin ẞ = c sin (a + B). where c tan 0, c cot @ are the co-ordinates of any point on the curve. 12. If (xy) (ax+ By)2 + 2gx + 2fy + c = 0 be the equation to a parabola, the equation to its axis is Examiner-MR. W. GRIFFITHS, M. A. 1. Shew that the equation to a conic circumscribing the triangle of reference is Shew also that the condition that the conic may be a rectangular hyperbola is l cos A+ m cos B + n cos C = 0. If a right-angled triangle be inscribed in a rectangular hyperbola prove that the perpendicular from the right angle on the hypothenuse is a tangent to the curve. 2. Having given the locus of one focus of the conic √ Ta + √ mB + √√ñy = 0, shew how to find the locus of the other focus. Prove also that if the above curve be a parabola the co-ordinates of the focus are proportional to 3. When a point is in motion in a curve, find its accelerations along, and perpendicular to, the tangent at any instant. A circle is described by a particle under the action of two forces to the ends of a diameter. If r, r' be the distances of the particle from the two centres of force; P, P' the forces, prove that 4. A particle is projected from a given point in a given direction and with a given velocity, and moves under the action of a central attraction varying inversely as the square of the distance. Find the orbit and also the conditions that it may be an ellipse, parabola or hyperbola, and find the values of the major axis, eccentricity, and area described in a unit of time. If the particle move in a resisting medium, find the general effect on the major axis and eccentricity. 5. A particle is constrained to move on a given smooth plane curve, under the action of given forces in the plane of the curve, find the velocity and the pressure on the curve. If the curve be a parabola whose axis is vertical and vertex uppermost, and gravity the only force acting shew that the pressure focal distance of the point, the inclination of r to the vertical, and h its vertical distance from a fixed line. Hence shew that a particle projected freely will describe a parabola. 6. A heavy particle is projected vertically upwards in air, the resistance of which is measured by 12 (velocity); prove that, if U, V be the velocities with which the particle leaves and returns to the point of projection. 7. Investigate the general equation of continuity. If the motion be symmetrical in all directions about a fixed centre, write down the equation in its simplest form. |