The written exercises are on the whole tolerably well done. There is, however, considerable room for improvement in this branch of study, and this will continue to be the case until classes are formed specially for the purpose of teaching the youths to translate from and into Telugu, both orally and in writing.

In the subjoined statement, I have classed the exercises in the order of their merit according to my judgment.

(signed) J. D. Sim,

FROM C. F. Chamier, Esq., Tamil Translator to Government, to A. J. Arbuthnot, Esq.,
Director of Public Instruction, dated 2d January 1857, No. 1.

Sir,

On the 19th ultimo, I examined the students at the Presidency College in Tamil, and I have since received from the professor of vernacular literature the papers executed by the same students on the following day.

From the manner in which the students acquitted themselves, I should say that their teachers must have taken great pains with them. The questions put vivâ voce were so seldom unanswered that I am unable to single out any boys as having passed a better examination than their neighbours. All appeared interested in their studies, and all acquitted themselves satisfactorily. As to the written examination, I consider that the papers executed by T. Samiah are the best. In translating from English into Tamil, V. Rajagopaul stands second. In rendering from Tamil into English V. Rajagopaul and A. Kristnasawmy are nearly on a par; perhaps the latter may be classed second, i. e. next to T. Samiah, in this part of the examination,

I regret that I have not time to classify the other papers sent, of which there are about 69 in Tamil and 75 in English; and would suggest that the number of students attempting

the

II.

the written translations should in future be limited to those whom the teachers know to be capable of executing them with tolerable accuracy.

Madras.

FROM the Acting Principal of the Presidency College to the Director of Public
Instruction, dated 25th May 1857, No. 70.

Sir,

I REGRET that in my report on the Presidency College for 1856, lately forwarded to you (which was written in haste in order that the arrangements for the anniversary meeting might not be delayed), I omitted to notice one or two points in reports submitted as appendices which it has since occurred to me ought to have been attended to.

2. The professor of history and English literature alludes to the irregular attendance of the second-year students; these representations I need hardly say are perfectly accurate. There were, however, only 6 students in the class, and of these 3 only were so irregular as to be deserving of censure. To prevent this irregularity, at the commencement of this year I framed some rules regarding attendance, which were posted up in the College Hall, and have been found to work beneficially. I annex a copy of these rules.

3. Mr. Percival's proposal to award scholarships for proficiency in vernacular languages merits, I think, some consideration; although it will certainly not be possible to allot so many as Mr. Percival proposes. If scholarships are to be determined by the results of the Christmas examination, the examination in vernaculars ought to be much less cursory and superficial than it has hitherto been..

4. Towards the close of his report Mr. Percival states that the want of attention on the part of the peons was so great, that it was with difficulty that the daily register was forwarded to me. I notice this complaint, because occurring as it does in Mr. Percival's annual Report, you might be led to infer that the same complaint, made in private, had been disregarded. This, however, is not the case; I was not aware of the difficulty until I found it stated in the Report, and I then immediately placed two peons at Mr. Percival's entire disposal during the hours of vernacular study.

1. ALL students requiring leave of absence must, on the day before that for which leave is required, make a written application to the Acting Principal.

2. The written application must be delivered by the student in person; and be written by the parent or guardian, or in the absence of such relations, by the student himself.

3. Any student who fails to comply with this rule, either by sending the application for leave instead of applying in person, or by omitting altogether to make application, will be considered as being absent without leave.

4. Any student who is detained at home through illness must send a note to the Acting Principal, which must be delivered not later than II a.m. on the morning on which the student is absent, otherwise he will be considered as absent without leave.

5. Any student absent without leave shall be suspended for a period of one week, or longer, according to the discretion of the Acting Principal, and shall, if a scholar, in addition to suspension, be fined a sum not less than two rupees.

6. Any student found guilty of obtaining leave under false pretences, shall be suspended for such periods of time as the Acting Principal may determine; and, if a scholar, shall forfeit his scholarship.

II. Madras.

PRESIDENCY COLLEGE.

Questions proposed to the Students of the Third, or Senior Class.

GEOMETRICAL and ANALYTICAL CONIC SECTIONS.

Examiner, Lieutenant P. O'Connell.

Question 1. The Parabola.-Prove that the square of a semi-ordinate of the diameter at any point is equal to four times the rectangle under the focal distance of the point and the abscissa.

2. Prove that if a right cone is cut by a plane which is parallel to a line in its surface, and perpendicular to the plane containing that line and the axis, the section is a parabola.

3. Prove that the sum of the squares of the conjugate diameters of an ellipse is

constant.

4. Prove that if the right cone is cut by a plane which is not parallel to a line in its surface, and the section is wholly on one side of the vertex, the section is an ellipse.

5. Prove that if a right cone is cut by a plane which meets the cone in both sides of the vertex, the section is an hyperbola.

6. The base of a triangle is constant, and the sum of the angles at the base is also constant: find the locus of the vertex.

7. An ellipse and an hyperbola have the same force; at what angles will the two curves intersect one another: and prove the answer to be true.

NEWTON'S PRINCIPLE.

Examiner, the Reverend John Richards, M. A.

Question 1. Define the terms "limit," "ultimate ratio," and illustrate your definitions by a variety of examples.

2. The areas of similar curvilinear figures are in the duplicate ratio of their homologous sides.

3. Bodies moving from rest under the action of different finite forces supposed uniform, the forces are as the spaces described directly, and the squares of the times inversely.

5. The velocity of a body moving about a fixed centre of force varies inversely as the perpendicular from the centre on the tangent.

6. Define centrifugal force, and supposing a body at any point of its orbit to be for the moment moving in the circle of curvature at that point, find an expression for this force.

7. Supposing the moon to move in a circle about the earth's centre under the action of a central force which varies inversely as the square of the distance, and which at the distance of the earth's radius generates a velocity of 32.2 feet in a second, determine the time of her revolution in her orbit.

=

=

60 Y

-N.B.-'s radius
γ 20,921,665 Eng. ft.
radius of D's orbit
π= 3,1416

8. A body described a semi-circle under the action of a force tending to a centre
infinitely distant, find the law of force.

9. A body moves in a parabola, find the law of force tending to the focus.

10. If any number of bodies move in ellipses about a common centre of force, which is the focus, the squares of the periodic times are proportional to the cubes of the major axis.

11. The arc of a cycloid measure from the vertex to any point equals twice the chord of the generating circle, which touches the curve at that point.

12. Find the time of oscillation of a heavy particle moving in the arc of a cycloid.

II.

Madras.

DIFFERENTIAL CALCULUS.

Examiner, Lieut. P. O'Connell.

Question 1. Explain the meaning of the term "limit," and give two or three examples of
functions which arrive at certain limits when their independent variables
either vanish or become infinite.

2. Explain the sense in which the terms vanish and infinite are used in the differ-
ential calculus.

3. Expound f (x) = log (1 + x).

4. Given z and 7 both functions of a third variable z, it is required to express the
successive differential co-efficients of 7 with respect to r in terms of those
of 7 and r with respect to z.

Find the values of x corresponding to a maximum and a minimum value of u.

Find the value of x, when u is a maximum.

7. A person being in a boat three miles from the nearest point of the beach, wishes
to reach in the shortest time a place five miles from that point along the
shore, supposing he can walk five miles an hour, but pull only at the rate
of four miles an hour, required the place where he must land.

8. Determine the greatest cylinder that can be described in a given cone.

PROBLEMS.

Examiner, the Reverend John Richards, M. A.

Question 1. Draw the triangle, whose sides are represented by the equations 9 = x + 1; 5; 2x+9=7 and find its area.

x + 29

=

3. Find the length of a perpendicular let fall from a point (a b) on a line whose

a + b cos.

b + a cos,

inclined at an angle w.

6. A second's pendulum is found to lose 20 seconds a day; determine the quantity
by which its length should be increased or diminished.

7. Find the equation to the normal at the extremity of the latus rectiem in the
ellipse 349 (2) = 9.

8. If S. P. and H. P. be any focal distances of an ellipse, find the locus of the
centre of the circle inscribed in the triangle S. P. H.

9. Determine the position and dimensions of the following curves,

10. A pendulum which beats seconds at the equator is found to gain five minutes
a day at the pole, compare the forces of equatorial and polar gravity.

11. The velocity of a body moving in a parabola at any point: the velocity in a
circle whose radius the focal distance, :: ✓ 2: 1.

=

12. Find the cylinder of greatest volume that can be enclosed in a given cone.

II. Madras.

GUIZOT'S HISTORY OF CIVILIZATION IN EUROPE.

Examiner, Edmund Thompson, Esq., M.A.

Question 1. " History should be comprised of facts." How must we understand these words? What is the connexion between history and civilization? How may we ascertain the meaning of the latter?

2. Examine the relations which exist between social and individual development.

3. Contrast the civilization of modern Europe with that of other countries and periods.

4. How has the Roman empire contributed to European civilization?

What

attempt was made to promote representative government in the latter days of
the empire, and with what success? Why and to what extent did the clergy
take the lead in the municipalities?

5. Investigate the meaning of the term "political legitimacy."
political legitimacy." Why should
aristocracy, monarchy, theocracy, and democracy all lay claim to it? What
lessons may we derive from the circumstance?

6. What causes gave rise to attempts to free Europe from barbarism? In what
did these attempts consist? Why and to what extent were they unsuc-
cessful?

7. How is philosophy associated with history? Show that the feudal form was universal in the 10th century. What do you infer from this fact? What distinction do you draw between the expressions "feudal form" and "feudal principle"? Draw a portrait of the feudal lord as an individual and in his relations to feudal society.

8. What do you understand by a political guarantee? Why was such a guarantee impossible under the feudal system? Briefly sum up the merits and shortcomings of this system.

9. Investigate the nature of Government with especial reference to the employment of force. On what two great principles does good Government rest? How far did the Christian Church, from the fifth to the twelfth century, carry out these principles.

10. How did the Christian people influence their Government during this period? Illustrate the principle of this influence from English and French history. Describe the political working of the Church, and its predisposing causes.

11. Contrast the burgher and borough of the twelfth, and the burgher and borough of the eighteenth century. What was the origin of borough charters, and what change did they produce in the condition of the boroughs? Describe borough Government in the twelfth century.

12. To what period in the history of civilization does the twelfth century belong? In what does the interest of this period principally consist? What are the main characteristics of the other periods?

13. What causes led to the Crusaders? What peculiarities did their expeditions exhibit? Contrast the views of the earlier and later Crusaders, and carefully describe the effect of the Crusades on national intercourse, the Church, feudal tenures, and the borough system.

GENERAL PAPER in MODERN HISTORY.

Examiner, Edmond Thompson, Esq., M.A.

Question 1. Sketch a map of Europe, showing how the Roman Empire was divided amongst the barbarous nations which overthrew it.

2. Give some account of the character and policy of Charlemagne.

3. How did the Papacy become a temporal power? Describe the character and Pontificate of Gregory VII.

4. Was Henry the First the rightful heir to the Crown of England? Describe his character and policy. In what other cases have the ordinary rules of inheritance been violated in the succession to the English throne?

5. What do you mean by the term pragmatic sanction? Give some account of any transaction bearing that name?

6. What