powers of two sources of light are compared. The distance between two incandescent lamps, of 16 and 25 candle-power respectively, is 6 feet. Show that there are two positions, on the line joining the lamps, in which a screen may be placed so as to receive equal illumination from each lamp, and determine these positions. Prel. Sc. 1887. 93. On a moonlight night, when the surface of the sea is covered with small ripples, instead of an image of the moon being seen in the sea, a long band of light is observed on the surface of the sea extending towards the point which is vertically beneath the moon. Account for this phenomenon in accordance with the laws of reflection, illustrating your explanation by a figure. Matric. 1882. 94. What is the index of refraction of a transparent substance? A plate of glass 6 inches thick with a refractive index of 1.5 is placed 2 inches above a luminous object. Make a careful full-sized drawing showing the path of a small conical pencil of light through the plate, the axis of the pencil being normal (or perpendicular) to the surface of the glass, and show where the image of the object will appear to an eye placed on the other side of the plate. Matric. 1884. 95. Define the term "the refractive index of a transparent medium," and give an account of experiments by which that of a liquid may be measured. The refractive index of water is 1.33, and the velocity of light in air is 300,000,000 metres per second. Find its value in water, stating the experimental grounds there are for your answer. Ind. C. S. 1885. 96. Under what circumstances is total internal reflection possible? A ray of light passing through a certain medium meets the surface, separating the medium front air at an angle of 45°, and is just not refracted. What is the refractive index of the medium? Matric. 1887. 97. What is meant by saying that the refractive indices of glass and of water are 1.5 and 1.33 respectively? Show for which of these substances the critical angle, or limiting angle of refraction, is the greater. Matric. 1885. 98. An image of a candle-flame eight times as broad as the flame itself is to be thrown, by means of a convex lens, on a wall at a distance of 12 feet from the candle. What will be the focal length of the lens required, and where must it be placed? Matric. 1885. 99. How is the focal length of a convex lens best determined without the aid of sunlight? An object is placed 8 inches from the centre of a convex lens, and its image is found 24 inches from the centre on the other side of the lens. If the object were placed 4 inches from the centre of the lens where would the image be? Matric. 1886. 100. An object 3 inches in height is placed at a distance of 6 feet from a lens, and a real image is formed at a distance of 3 feet from the lens. The object is then placed I foot from the lens. Where, and of what height, will the image be? Matric. 1887. 101. A goldfish globe of 6 inches radius is filled with water. Determine the apparent position of a point inside the globe, 4 inches from its surface, when seen by an eye outside looking along a radius of the globe. Int. Sc. 1884. 102. A small direct pencil of rays from a luminous point enters a refracting medium bounded by a spherical surface. Determine the image of the point. Given a double concave lens of 5 cm. thickness, the radii of curvature of its faces being 15 and 20 cm. respectively. Find the position of the image of a point in the axis 24 cm. from the nearer face, aberration being neglected. Int. Sc. Honours 1884. 103. Trace the position of the image of a bright point formed by a lens consisting of a sphere of glass, of radius 2 inches and refractive index 1.5, when the point moves from an infinite distance up to the sphere. Int. Sc. Honours 1885. 104. Explain fully how you would determine experimentally the index of refraction of a plano-convex lens for sodium light. Int. Sc. Honours 1883. 105. A luminous point is placed in the axis of a glass hemisphere, for which μ = 3/2, at a distance of a foot from the plane surface; if the radius of the hemisphere be 9 inches, show that the rays after passing through it will be parallel. Camb. Schol. 1886. 106. A small air-bubble in a sphere of glass 4 inches in diameter appears, when looked at so that the bubble and the centre of the sphere are in a line with the eye, to be 1 inch from the surface. tance? (u=1·5.) What is its true dis- 107. A convex lens of 6 inches focal length is used to read the graduations of a scale, and is placed so as to magnify them three times; show how to find at what distance from the scale it is held, the eye being close up to the lens. Owens Coll. 1886. A 108. A pair of spectacles is made of two similar lenses, each having two convex surfaces of 10 and 20 inches radius respectively, and a refractive index 1.5. person seeing through them finds that the nearest point to which he can focus is I foot away from the glasses. What is his nearest point of distinct vision? Camb. M.B. 1885. 109. How is a spectrum obtained by diffraction? How does such a spectrum differ from a prismatic spectrum? If a grating with 100 lines to the millimetre is placed in front of a slit illuminated with monochromatic light, and the angular distances of the 1st and 2d images are found to be 2° 18′ and 4° 35′ from the central image, what is the wave length of the light? sin 2° 18'0401. sin 4° 35'0799. Balliol Coll. 1881. 110. Light from two exactly equal and similar small sources very close together falls on a screen. Account for the bands seen, explaining the difference in the appearance, according as the light is white or of some definite refrangibility. The distance between the two sources of light is 184 cm., and the distance between the sources and the screen is 112 cm.; a series of bright and dark bands at a distance of .036 cm. apart is observed on the screen. Find the wave length of the light used. Ind. C. S. 1885. 111. The minimum deviation of a ray of light produced by passing through a prism of angle 60° 6' 20" is 42° 40′ 20′′. Show how to use these results to determine the refractive index of the glass prism, and find it, having given L sin 51° 24'9.89294, L sin 30° 4′ = 9.69984, Int. Sc. Honours 1886. SOUND Velocity of Sound. Newton proved that the velocity of sound in any medium is given by the equation V=E/D, E denoting the elasticity and D the density of the medium. The elasticity of a fluid is defined as being the ratio of any small increase of pressure to the proportional decrement of volume thereby produced. It can be shown that the elasticity of a perfect gas is equal to its pressure, provided that its temperature remains constant during the compression. A geometrical proof of this important proposition is given in Maxwell's Theory of Heat. It may also be proved as follows:Let V be the volume of a given mass of gas under the pressure P. Now suppose the pressure to increase by a small amount p, and let v be the decrement of volume thereby produced the pressure is now P+p, and the volume V – v. If the gas obeys Boyle's law, the product of these two quantities is equal to the product of the original pressure and volume, or PV = (P+p)(V − v), Since both the quantities p and v are small, their product may be neglected (p. 17); thus Vp=Pv. Now the proportional decrement of volume (or decrement per |