7. Explain the construction and use of an alternating current transformer. How can the power supplied to the primary circuit be measured? 8. Describe an electric pyrometer, explaining how it is graduated and used. 9. Describe a hot-wire voltmeter. How would you ascertain whether its readings were correct? DRAWING. Examiner-W. BANKS GWYTHER, ESQ., F.R.I.B.A. N.B.-Drawings are to be done in pencil only, but given and construction lines and results should be clearly distinguished. Neatness and accuracy will be recognised in giving marks. 1. The figures in the margin indicate full marks. Draw the scale of which is the representative fraction, so 25 that yards and feet can be read. 2. A true pyramid which has a hexagonal base of 14 inch side and 50 is 4 inches high rests on a table and is tilted on one of its sides until it just balances, after which it is turned so that the plane of its axis is inclined at 45° to the vertical plane. Draw its plan and elevation. 3. Make scale drawings of the three items figured I, II, and III in 75 the sheet of illustrations handed to you, employing the scale uoted under each. 4. Show by means of a freehand perspective sketch a view of the well 50 as indicated at IV in the accompanying sheet of illustrations, assuming your eye to be raised 5 feet above the ground. B.E. Examination. 1905. DIFFERENTIAL AND INTEGRAL CALCULUS. The figures in the margin indicate full marks. 1. Find from the definition of a differential coefficient the differential 30 coefficient of tan s and log æ. Differentiate 2. If u-f(y, z), y and z are functions of 2, shew that 30 das+ dys + das 3. If f(x+h) be expanded in a series of ascending integral powers of 30 h, shew that the remainder after n terms is 5. If a make ƒ (») a maximum or a minimum, shew that fl (a)=0. 30 Find the altitude of the cone of least volume, which can be circum. scribed about a sphere of radius R. 6. Define integration as the sum of an infinite number of vanishing 80 quantities, and shew how it involves the inverse of differentiation. 7. Explain what is meant by a formula of reduction. Find a formula 30 of reduction for 8. Find the formula for the length of a curve in polar coordinates. Find the length of (1) the cardioid; (2) an arc of the equiangular spiral. 9. Find the area of (1) the cycloid; (2) the loop of the curve 3+ y3=3axy. 30 30 1. Give a mathematical proof that the pressure in a heavy liquid is 20 the same in all directions. 2. Distinguish between resultant pressure and whole pressure. In 30 what case do they coincide? A hollow cone filled with water is held with its circular base downwards and its axis inclined at an angle to the vertical; find the resultant pressure on the base. 3. Shew how the pressure in a given horizontal direction on a curved 30 |