4. Draw five parallel lines half an inch apart, the first line heavy and five inches long, the second medium and four inches long, the third fine and three inches long, the fourth simple dots and two inches long, the fifth chain dots and one inch long. 5. Show how to indicate on a plan, hills, water, trees, roads and railways, and print the names of the various objects. 6. Take three points A.B.C., make A.B. 1 inches, 11⁄2 A.C.2 inches, B.C. = 2 inches and describe a circle passing through these points. 7. In a right angled triangle a perpendicular is let fall from the right angle to the hypoteneuse and divides it into two parts 4 inches and 1 inch respectively. Construct the triangle. 1 8. Draw lines containing angles of 15°, 30°, 45°, 60°, 120°, without the aid of a protractor. CANADIAN HISTORY. 1. Who are supposed to have been the first inhabitants of America before the American Indians? Give reasons for supposing them to have been quite civilized. 2. Give the names of the principal tribes of North American Indians in about 1492. How were they located, describe them as to their habits, etc., etc. 3. Which European nation first occupied Canada, when and how did it pass into the control of England? 4. Describe what is known as the "Quebec Act," its date, how it treated the French as to their religion, political rights, etc., etc. 5. State the circumstances which led to the "rebellion of 1837" and its effect on the form of government. 6. When was the Dominion of "Canada" formed. Under what circumstances and what was its effect? GEOGRAPHY 1. Name the principal mountain ranges in North and South America, the principal water-sheds formed by these ranges, and the large rivers in each water-shed. 2. What are the European possessions on the Continent of Africa and the climatic features and leading productions and exports of each of these possessions? 3. Name the principal islands on the Atlantic Coasts of North and South America, the political division to which each of the groups belong, and the leading production of each. 4. Give the boundaries of the Provinces of the Dominion and the location of the territories, also the Capital of each Province and the principal river in each. 5. Name the Counties in the Province of Ontario bordering on Lake Huron and Lake Erie, and also ten of the leading cities and towns of Ontario and the lines of railway passing through each of the cities and towns. 6. A traveller takes a trip from Montreal westward to Pekin, China, via C.P. Railway and ocean steamer. Enumerate the principal rivers and cities he would pass in his route and the approximate distances he would travel by land and water. 1. Explain the methods of measuring an angle by means of degrees and circular measure. (a) Find the circular measure of an angle of 42 degrees, and the angle whose circular measure is . (b) Define the meaning of sign, tangent, secant and compliment of an angle, and prove that in a triangle A. B. C. the sign of (90° - A) Cos A Sec A = √1+tan A = 2. Taking the radius of the earth as 3960 miles, find in circular measure, and also in degrees, the angle subtended at the earth's surface by the radius. 3. In a plane triangle A. B. C. prove the following: 4. Two posts on the bank of a river are observed from the opposite bank. When the observer stands immediately opposite to one of the posts they subtend an angle of 60°. When he has walked 60 feet directly away from the river they subtend an angle of 45°. Find the breadth of the river and the distance between the posts. = == 5. In a triangle A. B. C. given a 25, b = 37, c = 48, find B. 1. Explain the meaning of the terms spherical triangle, polar triangle and spherical excess. 2 In a spherical triangle given A = 66° 30', B=27° 40', a = 87°, find b and c. 3. Given 674° 10′, c-58° 40', A = 84° to find a. CURVES. 1. Define the following terms: Degree of Curve, Radius of Curve, Angle of Intersection, 2. The point of intersection of two tangents is at station 623 + 22, the angle of intersection is 26° 56'. The curve is a 6° curve. Find (a) Radius of curve and length. (b) Tangent distance. (c) Stations for the P. C. and E. C. and deflection angle for the first full station beyond the P. C. 3. Find the long chord and the middle ordinate for a 4° 30 curve with a central angle of 40° 30'. 4. In a case shown in diagram when the point of intersection is inaccessible, a b, was measured as 476° 25', the angle V a b, was measured as 24° 18′, and the angle V b a as 34° 22′. The curve is to be a 3° 30' curve. Find the radius of the curve and distance of P. C. and E. C., viz., the points A and B, from a and b, and also the tangent distance V A. 5. Explain how you would find the middle ordinate of a curve. (a) Find the middle ordinate of a 30 foot rail for a 20° curve. PRACTICAL ASTRONOMY. 1. Define the terms upper culmination, lower culmination, meridian passage, azimuth, amplitude, vertical and prime vertical circles, equinoxial, vernal equinox, right ascension, solstitial colure. 2. One tropical year 366.2422 sidereal days Ditto = Find (a) The difference in time between a mean solar and a sidereal day. (b) If mean solar and sidereal time are together on March 22.6, what will be their difference on July 28.2. 3. The observed altitude of Polaris at upper culmination was 40° 15′ 46′′.8, and at the lower culmination 37° 33′ 56′′.6. What was the latitude of the place ? 4. The latitude of Toronto is given as 43° 40′. What should be the apparent time of sunrise on June 21. 5. On Jan. 12th, 1909, in Lat. 43 06', Long. 79° 26', the observed altitude of the sun's right upper limb was 12° 35′ 30′′, and horizontal circle reading 15° 38′ 15′′. served altitude of the lower left limb Five minutes later the ob was 10° 35′ 15′′, and hor izontal circle reading 16° 13′ 30′′, while the horizontal circle reading on a reference object was 0° 00'. What was the bearing of the latter? (Given the sun's Dec. 21° 38′ 42′′ S.) 6. In No. 6 the times of observation being by a watch 3 hrs. 39 min. and 3 hr. 44 min. respectively, find the watch Cor. on Standard time, the equation of time being + 8 min. 26 sec. 7. Sept. 5th, 1909 Fourth Meridian, Lat. 50° 08′ 08", Long. 110° W. Sidereal time 14 hr. 59 min. 56 sec. (corrected). Horizontal circle reading on line Ditto on Polaris 0° 00' 0° 43' 48" Stars Declination = 88° 48′ 52′′ R. A. = 1 hr. 26 min. 56 sec. Find the correct bearing of the line. 8. Formulæ for Azimuth at elongation of a star is = And for time Cos. T. = Cot. Dec. Tan. Lat. Deduce the above equations. MINES ACT, ETC. 1. (Re Mining Act). State law as to and show by lettered diagrams the different dimensions that regular mining locations may be laid out and how, when they border lakes and rivers. on 2. (Re Drainage Act). State law as to and show particularly how the different forms of assessment are made. 3. (Re Ditches and Watercourses Act). State laws as to and how in a supposed case, the engineer makes his award. 4. (Re Registry Act). State laws as to subdividing into town lots, land, and how plans are to be prepared. Give forms of certificates required. In cases for County Registry Office and Office of Master of Land Titles, etc. 5. How are public roads established and give. the width they may be made, and by what authority? GEOLOGY AND MINERALOGY. 1. To what processes of earth building do the following terms refer? Physiographic Geology, Lithological Geology, Historical Geology, Dynamical Geology. 2. Illustrate by diagram the following geological terms: Anticlinal, synclinal, monoclinal, dip, strike, fault, denudation, inconformable strata. 3. Name some examples of igneous rocks, metamorphic rocks, calcareous rocks, and state where they may be found in Canada. 4. Construct a table showing the conventionally adopted periods of the earth's history as found in Canada. 5. Where in Canada do we find rock belonging to the following formations? Laurentian, Trenton, Utica, Hudson |