rest. Prove also that it is equal to half the space which would be described in the same time with the last velocity continued constant.

3. State and prove the second law of motion.

A body is projected vertically upwards with a velocity which will carry it to a height 2g feet,-after how long a time will it be descending with a velocity g?

4. Given the velocities of two balls whose masess are A and B, and elasticity c,-find their velocities after a direct collision.

5. A body descends down an inclined plane; find the accelerating force and velocity at any point, and show that if u and v be the velocities at two points, v2 u2=2 gy, where y is the difference of the altitudes of the points above a horizontal plane. 6. The path of a projectile in vacuo is a parabola, and the velocity at any point is that acquired in falling from the directrix.

7. A body is projected vertically upwards from a point A with a given velocity,-find the direction in which another body must be projected from a point in the same horizontal line with A, so as to strike the first body.

8. If v1, V2, V3, be the velocities at three points of the path of a projectile, where the inclinations to the horizon are 3a, 2a,

9. A pendulum which vibrates seconds at the surface of the earth, loses 10" in 2 hours when taken to the bottom of a mine; find the depth of the mine, supposing gravity to vary as the distance from the centre of the earth.

FOURTH CLASS.

TRIGONOMETRY.

1. In a triangle two sides and the included angle are given,

find the remaining angles.

If one of the given sides be half the other and the included angle 60°, find the other angles.

2. Prove that

(cosa + √ 1 sina)m = cosma + √

for all values of m.

I sin ma)

3. An equilateral triangle and an equilateral and equiangular pentagon have the same perimeter compare the radii of the cir cles inscribed in them.

4.

Having given tana, tan ẞ &c., find tan (a + B + ......) the number of angles being 2n + 1.

5. Expand the sine of an angle in a series ascending by powers of its circular measure. Point out the step in the process at which the circular measure is introduced and state the advantage which arises from its introduction.

Calculate sin 648" to seven places of decimals.

Cos (0 α

= and

b

Cos (0-3)

prove that Cos (a - ẞ)

b',

7. From the extremities of the base AB of a semicircle two chords, AC, BD, are drawn, intersecting in E; join DC, and prove that

area of triangle DCE (area ABE). Cos? (A + B).

=

8. On the sides of an equilateral triangle three squares are described. Compare the area of the triangle formed by joining the centres of these squares with the area of the equilateral triangle.

English Essay.

Friday, April 7th.

FIRST AND SECOND CLASSES.

Lives of Great Men all remind us
We can make our lives sublime,
And departing leave behind us
Footprints on the sands of time.

Footprints, that perhaps another
Sailing o'er life's solemn main,

A forlorn and ship-wrecked brother
Seeing shall take heart again.

Longfellow.

Not fortune's slave is Man: our state
Enjoins, while firm resolves await
On wishes just and wise,
That strenuous Action follow both
And Life be one perpetual growth

Of heavenward enterprise.

Wordsworth.

THIRD AND FOURTH CLASSES.

A country which has no National Literature, or a Literature too insignificant to force its way abroad, must always be, to its neighbours, at least in every important spiritual respect, an unknown and misestimated country.

Vernacular Translation.

Saturday, April 8th-Morning Paper.

FOR ADVANCED SCHOLARS.

Carlyle.

Translate the following passages into Bengali.

I cannot call riches better than the baggage of virtue; the Roman word is better, "impedimenta ;" for as the baggage is to an army, so is riches to virtue; it cannot be spared nor left behind, but it hindereth the march; yea, and the care of it sometimes loseth or disturbeth the victory; of great riches there is no real use, except it be in the distribution; the rest is but conceit; so saith

G

Solomon, "Where much is, there are many to consume it; and what hath the owner but the sight of it with his eyes?" The personal fruition in any man cannot reach to feel great riches: there is a custody of them; or a power of dole and donative of them; or a fame of them; but no solid use to the owner. Do you not see what feigned prices are set upon little stones and rarities ?—and what works of ostentation are undertaken, because there might seem to be some use of great riches? But then you will say, they may be of use to buy men out of dangers or troubles; as Solomon saith, "Riches are as a stronghold in the imagination of the rich man ;" but this is excellently expressed, that it is in inagination, and not always in fact for, certainly, great riches have sold more men than they have bought out. Seek not proud riches, but such as thou mayest get justly, use soberly, distribute cheerfully, and leave contentedly; yet have no abstract or friarly contempt of them; but distinguish, as Cicero saith well of Rabirius Posthumus, "In his desire of acquiring fortune it was evident that he sought not the gratification of avarice, but means for enlarged benevolence."

My sentence is for open war; of wiles,
More unexpert, I boast not them let those
Contrive who need, or when they need; not now.
For while they sit contriving, shall the rest,
Millions that stand in arms, and longing wait
The signal to ascend, sit lingering here
Heaven's fugitives, and for their dwelling-place
Accept this dark opprobrious den of shame,
The prison of his tyranny who reigns

By our delay? No, let us rather chuse,
Arm❜d with hell flames and fury, all at once

O'er heaven's high towers to force resistless way,

Turning our tortures into horrid arms

Against the Torturer; when to meet the noise

Of His almighty engine he shall hear
Infernal thunder; and for lightning see
Black fire and horror shot with equal rage
Among his angels; and his throne itself
Mix'd with Tartarean sulphur, and strange fire,
His own invented torments. But perhaps,
The way seems difficult and steep to scale
With upright wing against a higher foe.
Let such bethink them, if the sleepy drench
Of that forgetful lake benumb not still,
That in our proper motion we ascend
Up to our native seat: descent and fall
To us is adverse.

Saturday, April 8th — Afternoon Paper.
FOR OLD SCHOLARS.

Translate the following passage into English :-সভাসদ্ কহিলেন আপনকার জনকের স্বহস্তাক্ষর লিখিত যে লিপি আছে সেই লিপি কালিদাসকে দেউন্। রাজা বলিলেন সে কোন পত্র। সভ্য কহিলেন সে পত্রী এই যাহাতে লেখা আছে যে অয়না-শজ আষাঢ়মাসান্ত দিবসে মধ্যাহ্নকালে এই নারিকেল বৃক্ষের উপরে অনেক স্বর্ণ আমি রাখিলাম। আমার পর আমার উত্তরাধিকারী ষোড়শবর্ষবয়স্ক প্রাপ্তব্যবহার হইলে লইবে ইতোমধ্যে কদাচিৎ হস্তসাৎ করিবে না।

কালিদাস তোমার পৈতৃক মহাজন অতএব তুমি নিষ্কপটে ঐ সকপট মুদ্রাঙ্কিত পৈত্র চীরক লেখ্য পৈত্রকর্জ পরিশোধনার্থ তাঁহাকে দেও যেমন ঋণ তাহার তেমনি শোধন