Mathematics.

EUCLID AND ARITHMETIC.

Morning Paper.

1. Define a superficies, a right angle and a rhombus. Distinguish between a segment, and a sector of a circle; also between a direct and indirect demonstration.

2. Draw a straight line at right angles to a given straight line from one extremity of the same.

3. If there be two straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Hence prove that the area of a rectangle is equal to the product of the base and its altitude.

4. The angle at the centre of a circle is double than at the circum. ference upon the same base.

Is this true when the base is greater than a semi-circle?

5. Describe a circle about a given triangle. Can a circle always be made to pass through any three given points which are not in the same straight line?

6. From a given point in one side of a parallelogram produced, draw a line which shall bisect the parallelogram into equal parts.

7. The middle point of the hypothenuse of a right-angled triangle is equally distant from the three angular points.

8. Two chords of a circle are given in position and magnitude, describe the circle.

9. Distinguish the difference between the local and absolute value of a digit.

10. If 27 seers of sugar cost 7 rupees, 5 annas, 7 pie, what will 49 maunds 15 seers cost?

11. If a man buys 170 mangoes when they are 12 annas per hundred, and 190 when they are 1 rupee, 2 annas, 3 pie, and sells the whole at the rate of 15 annas 5 pie per hundred; does he gain or lose by the transaction, and how much?

12. Divide 7854 by 279. Explain the operation, and the meaning of the remainder.

Arithmetic and Algebra.

Afternoon Paper.

1. In Addition and Subtraction of fractions, explain why it is necessary to reduce them all to a common denominator.

Add ‡, 2§ and together.

2. If a vessel sails 500 miles in 2 days 18 hours, how far will she sail between September 4 at 6 o'clock in the morning and October 3 at 9 o'clock in the evening?

3. If 500 marks be allowed for a paper of 12 questions and to each of a certain 8 of them the average is given, to the remaining four they are given in the proportion, 4, 5, 7, 9, find the number allowed to each?

4. By cross-multiplication find the area of a surface whose length is 34 feet, 7 inches, 5 primes, and breadth 26 feet, 9 inches, 7 primes; state clearly the magnitude of each unit in the result?

5. A person bought 4 per cent. Government paper at a discount of Rs. 17 per cent. and 5 per cent. at a discount of 12 annas per cent.; find the rate of interest in each case, and the advantage per cent. of the second purchase over the first?

6. What is the difference between am and am in Algebra, and what meaning do you assign to the latter when M is negative or fractional? 7. Prove amn - bmn is divisible by both am bm and an - bn, find the first and second, and the last but one, and the number of terms in each quotient?

8. Define Common Multiple. Find the least Common Multiple of

9.

Prove the rule for Division of Decimals.

Divide 12 by 1728, 16 by 960, and 12·5 by ·0025.

10. Extract the square root of

x2 y2 х
+
y2 x2

+

y

11. Solve the equations.

x + y
= 5.

(x2 + y2) (x2 + y3)

- 1 and cube root of 1.092727.

9x+7

36

12. A carriage is furnished with a mechanical contrivance by which the difference of the number of revolutions of the fore and hind wheels is registered, the circumference of the fore-wheel is 7 feet, and that of the hind wheel 9 feet. What is the distance gone over, when the fore-wheel has made 300 revolutions more than the hind wheel?

Geography.

Morning Paper.

1. What is the shape of the Earth? How is it known to be of such a shape?

2. What is the circumference of the Earth in English miles? What is the longest diameter of the Earth in English miles, and what difference is there between the longest and shortest diameter ?

3. Are the degrees of latitude and longitude of the same length at all places? If not, how do they vary?

4. If two men start from London, one to travel east and one west round the globe, when they meet again in London will they agree as to the number of days since they parted?

5. Explain why, at the north pole, there is for part of the year no day, and for another part of the year no night.

6. How many zones are there? What are their names? Between what degrees of latitude do they respectively extend?

7. A table of the principal rivers of the world in the order of their length.

8. A similar table of the principal mountains of the world in the order of their height.

9. How do you find the latitude and longitude of a place on the terrestrial globe?

10. How do you find, by the terrestrial globe, when the sun is vertical at a given place and hour?

Afternoon Paper.

11. Draw a map of England, and give the positions of London, York, Liverpool and Bristol.

12. Draw a map of the Mediterranean Sea, shewing the countries immediately adjoining it, and the principal rivers on or near its shores.

13. Draw a map of India, shewing the position of the principal cities, and the course of the Ganges, of the Indus and of each of the five rivers of the Punjab.

14. If a Railroad were laid down in nearly a direct line between Calcutta and Delhi, through what districts would it pass, and near what large cities?

15. Name the principal rivers of America, and describe where they rise, and into what sea each falls and the general direction of its course. 16. What large islands are comprehended in the "West Indies?" How are they situated with respect to one another?

17. Write down, in a tabular form, the Latitude and Longitude of the following places and the country in which each place is situated:

Aden, Antwerp, Bagdad, Cairo, Colombo, Delhi, Dover, Edinburgh, Florence, Genoa, Greenwich, Jerusalem, Leipsic, Macao, Oporto, Pekin, Portsmouth, Quebec, Singapore.

English Translation.

THE OPERATIONS OF NATURE INCESSANT.

Though Nature appears to suffer some of her works to decay, she is only varying her attitudes. Nothing is permitted actually to decay— matter, as well as spirit, existing to eternity; for in the dunghill of putrefaction are secreted the germs of future reproduction.

Perpetual changes glide on in endless continuity; valleys rise to mountains; mountains sink to valleys; the ending of summer is the beginning of autumn, and in the lap of winter are concealed the embryos of spring.

Ever attentive to her interests, Nature replaces in one spot what she has displaced in another :-ever attentive to beauty, and desirous of resolving all things into their original dependence on herself, she permits moss to creep over the fallen column, and ivy to wave upon the useless battlement.

Time, with his gradual but incessant, touch, withers the ivy and pulverizes the monument; but Nature, who conceives and executes at one and the same moment, whose every thought is a system, operation in an unlimited orbit, jealous of prerogative, and studious of her creations, expands with one hand what she compresses with another. Always diligent she loses nothing; she condenses only what she appears to lose.

From the beginning of time, no one object, so created, has evaporated— not one atom, in the infinite divisibility of matter, has been lost :-not the minutest particle of what we denominate element, nor one deed, word, or thought of any of his creations have ever once escaped the knowledge, nor will ever escape the memory of the Eternal Mind.

Bengali Translation.

সভাপৰ্ব্ব ৷

কুরু পাণ্ডবদিগের বিবাদ ও যুদ্ধ বর্ণনা মহাভারতের মূল তাৎপৰ্য্য । লিখিত বা বাচনিক যাবৎ জনশ্ৰুতি প্রমাণে এ ঘটনা অমূলক বোধ হয় না, এবং যদিও তৎসম্বন্ধীয় ভূরি বিষয়ের বাহুল্য বর্ণনা আছে, এবং লোকের ধর্ম্ম ও সংস্কার ঘটিত নানা কাল্পনিক আখ্যান তাহার সহিত সংশ্লিষ্ট আছে, কিন্তু তাহার সমস্ত বিবরণ অপ্রমাণ বলা যায় না। মহাভারতের সংজ্ঞা মহাকাব্য, অতএব কাব্য মধ্যে যে অবিকৃত স্বরূপ ইতিহাস থাকিবে এমত সম্ভব হয় না, কিন্তু তাহার অনেক স্থানে, বিশেষতঃ মধ্যে মধ্যে অনুষঙ্গাধীন যে ভূরি ভূরি উপাখ্যান উত্থাপিত হইয়াছে, তন্মধ্যে বিক্রমাদিত্যের বহুকাল পূর্ব্বে এদেশে যাদৃশ ধর্ম্ম, রাজনীতি ও লোকাচারাদি প্রচলিত ছিল, তাহার সবিশেষ বৃত্তান্ত প্রাপ্ত হওয়া যায়। সভাপর্ব্ব ইহার এক উদাহরণ স্থল ৷

পাণ্ডবেরা রাজ্যার্দ্ধ প্রাপ্ত হইয়া ইন্দ্রপ্রস্থে যে সকল কার্য্যানুষ্ঠান করেন তাহার বিবরণ, এবং বিশেষতঃ রাজসূয় যজ্ঞের বৃত্তান্ত সভাপর্ব্বের বক্তব্য হইয়াছে । যুধিষ্ঠির যশ, মান, প্রতাপে সকল রাজার প্রধান হইলেন, অতএব তাঁহারদিগের নিকটহইতে কর গ্রহণ করিয়া চক্রবর্ত্তী পদাভিষিক্ত হইবার নিমিত্তে রাজসূয় যজ্ঞানুষ্ঠানের মানস করিলেন। পরামর্শ স্থির হইলে তাঁহার ভ্রাতৃগণ দিগিজয়ে যাত্রা করিলেন ৷ নানা দিগদেশস্থ ভূপতিদিগের নিকট' কর গ্রহণ করিয়া রাজধানীতে প্রত্যাগমনপূর্ব্বক সর্ব্বাগ্রজ যুধিষ্ঠিরকে সমস্ত সমর্পণ করিলেন ৷ সে সকল রাজার নিকট কর গ্রহণমাত্র এতাদৃশ দিগ্বিজয়ের প্রয়োজন ছিল, নতুবা তাঁহারদিগের