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- 8. Find the number of cubic yards in a concrete pier whose base is 6' x 10' and whose upper face is 4' x 8', if the height of the pier is 12'.

9. Find the volume of metal in an iron collar in the shape of a zone of a sphere; if the radius of the upper face is 3 in. and the lower face 5 in., the distance between them being 4 in., when through the centre of the zone is a conical hole, whose radius on the upper face is 2 in. and on the lower 3 in.

FACULTY OF PRACTICAL SCIENCE.

ASTRONOMY.

1. (a) Give the celestial terms corresponding to terrestrial latitude and longitude.

(b) Define celestial latitude and longitude.

2. Given the moon's horizontal parallax as 57' and the earth's radius as 3960 miles, find (a) the moon's distance, and (b) the moon's diameter in miles, her angular diameter being 32'.

3. (a) Why does the moon present always the same face to us?

(b) Give the variation to this statement.

4. State clearly the difference between the functions of the siderial clock and the mean time clock.

5. Explain the difference between a siderial year and a tropical year.

6. How does the constellational zodiac differ from the conventional one?

7. The moon's siderial period is 27.32 days.

(a) Find her synodic period, and (b) show why the epact increases by 11 days annually.

8. Explain the phenomenon of a total solar eclipse.

9. What is meant by "the eclipse periods of a year", and why are they variable?

10. Define "equation of light" and "constant of aberration".

FACULTY OF PRACTICAL SCIENCE.

MATHEMATICS II.

A.

1. The sides of a triangle are 2-y-3; x-2y=4 and 3x+2y=8. Find (a) the coordinates of the centroid, (b) the angle between any two sides.

2. Find the equation of the circle passing through the points (1, 1), (2, -1) and (3, 2). Also find the radius of the circle and the coordinates of the centre.

3. (a) An arc of a circle, whose radius is 12 inches, subtends an angle 60° at the centre. Find the position of the centre of gravity of the arc.

(b) A square, side 18 inches, is divided into four triangles by the diagonals. Find the centre of gravity of the area formed by three of these triangles, using Guldinus' Theorem.

4. Find to two decimal places the volume of a parallelepiped whose direction edges are 2 in., 3 in., and 4 in., and face angles at a corner 100°, 110°, and 120°.

B.

5. Deduce the fundamental formula

cos a=cos b.cos c+sin b. sin c.cos A.

6. For Polaris on April 10, 1901, d=88° 46′ 53′′; the right ascension a=1 hr. 22 min. 27 sec., the sun's right ascension S1 hr. 12 min. 5 sec, the latitude of the place of observation is 44° 13' N. Find the azimuth at greatest elongation; and also the mean times of the observation.

7. The point of departure is at latitude 29° 37' N., and the course starts at the bearing S.40° 20′W. and follows a great circle until a North Polar distance of 69° 15′ is reached. Find the angle at which the course cuts the meridian through the point of arrival.

8. On May 1, 1901, at latitude 44° 13' N., and longitude 5 hrs. 6 min. W. at 7 hrs. 37 min. A.M., as shown by the watch, the apparent altitude of the sun's upper limb was 28° 10′ 52". Find the error of the watch on mean time, given the sun's declination for this time and longitude 14° 58' N., sun's semi-diameter 0° 15' 54". Refraction for the observed altitude 0° 2′ 6′′. Sun's horizontal parallax =0° 00′ 8′′. Equation of time is 2 min. 55 seconds to be subtracted from apparent time.

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