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6. The locus of the centres of all plane sections of an ellipsoid whose planes pass through a given point is another ellipsoid.

7. A B is an arc of a curve, such that a particle starting from B and moving along any portion of it with a velocity u, and then along a straight line to A with velocity v may always arrive at A after the same time, shew that the equation to the curve is

-V0

Nu - 02

1 = a where a = the initial radius vector A B, A being the origin.

8. Two particles start siniultaneously from the same point and move along two straight lines, one with uniform velocity and the other from rest with uniform acceleration. Prove that the line joining the particles at any time is a tangent to a fixed parabola.

9. A particle is describing an ellipse about the focus; when it comes to the extremity of the minor axis, the absolute force is diminished by one-third. Find the position and dimensions of the new orbit, and prove that the distance between its focus and the centre is bisected by the minor axis of the original orbit.

10. A heavy particle of weight W is moving in a medium in which the resistance varies as the nth power of the velocity ; prove that if f be the resistance when the direction of motion makes an angle with the horizon,

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11. The distance between two places on the same parallel of latitude a is measured along that parallel and found to be c. Shew that if c be taken as the length of the great-circle arc joining the places, the error made is less than

tano tan sec® o where d is the diameter of the earth, and

../c sec al sin p = cos , sin

2d

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12. A spectator on the earth's surface is supposed to move so as to have the sun always on his meridian at a constant altitude, the sup's motion in the ecliptic being supposed uniform. Show that ^, I the spectator's latitude and longitude at time t are given by the equations : (i) a = w– 8 {cos} (ii) = 8 sin i cos a.

(cosa where & is velocity of the sun in the ecliptic, w the angular velocity of the Earth about its axis, i the obliquity of the ecliptic, a, 8 the R. A, and declination of the Sun.

(cos

Premchand Kopchand Studentship Examiwation.

1881.

ENGLISH LITERATURE. Examiner--MR. W. H. Paulson, M. A. 1. Comment on the following extracts, noticing verbal, metrical and grammatical peculiarities.

No more, up peyne of leesyng of youre heed !
By mighty Mars, he schal anon be deed,
That smyteth eny strook that I may seen!
But telleth me what mester men ye been,
That ben so hardy for to fighten heere,
Withoute jugge or other officere ?
Two woful wreeches been we, two kaytyves,
That ben accombred of oure owne lyves;
And as thou art a rightful lord and juge,
Ne yeve us neyther mercy ne refuge.
Lo her this Arcite and this Palamoun,
That quitely waren out of my prisoun,
And mighte han lyved in Thebes really,
And weten I am bir mortal enemy,
And that hir deth lith in my might also,
And yet hath love, maugre hir eyen two,

Ybrought hem hither bothe for to die! 2. Modernize

a. As touching the proposition, which the Physiciens entreteden in this cas, this is to sain that in maladies that a contrarie is warished by another contrarie, I wold fain knowe how ye understonde thilke text.

b. Though so were that thou haddest slain of hem two or three, yet dwellen ther ynow to wreken hir deth. And though so be that youre kinrede be more stedefast and siker than the kin of youre adversaries, yet, natheles, your kinrede is but a fer kinrede; they ben but litel sibbe to you, and the kin of youre enemies ben nigh sibbe to hem.

3. State the authorship of, and explain the allusions in the following:

Hear how Timotheus' varied lays surprise,
And bid alternate passions fall and rise,
While at each change the son of Libyan Jove,
Now burns with glory, and then melts with love!
And call him up, who left half told
The story of Cambuscan bold,

a.

c. He that meets me in the forest to-day shall meet with no wiseacre I can tell him. Master Stephen, you are late. Ha, Cokes, is it you ? Aguecheck, my dear knight, let me pay my devoir to you. Mister Shallow. your worship's poor servant to command. Master Silence, I will use few words with you. Slender, it shall go hard if I edge not you in somewhere. You six will engross all the poor wit of the company to-day. d. Dead Shepherd, now I find thy saw of might,

" Who ever loved, that loved not at first sight ?? e. Very few and very weary are those who are in at the death of the Blatant Beast.

The morning-star of song, who made
His music heard below.
Oh mighty-mouthed inventor of harmonies.
“ Concluding all were desperate sots and fools,

Who durst depart from Aristotle's rules.”
Explain these lines, and examine, in reference to these rules,
Shakespeare's Tempest and Winter's Tale.

5. "Lord Byron, like Wordsworth, had nothing dramatic in his genias. He exhibited his characters in the manner not of Shakespeare. but of Clarendon.” Explain and, as far as you can, illustrate this statement.

- unless an age too late, or cold ”

“ Climate, or years damps my intended wing." How far was Milton justified in these misgivings?

ENGLISH LITERATURE, II.

Examiner-MR. W. H. PAULSON, M. A. 1. “Spenser writ no language.”

“Spenser wrote in a Gothic style." Examine these statements, and describe the Spenserian stanza giving instances of its employment.

2. Give some account of the fashion of Aliteration in poetry. 3. Explain

So, as a painted tyrant, Pyrrhus stood,
And, like a neutral to his will and matter,
Did nothing.
Cut off even in the blossoms of my sin,
Unhousel'd, disappointed, unanel'd.

- we are men, my liege!
Ay, in the catalogue ye go for men;
As hounds, and greyhounds, mongrels, spaniels, curs,
Sbonghs, water-rugs, and demi-wolves are clept
All by the name of dogs; the valued file
Distinguishes the swift, the slow, the subtle,
The housekeeper, the hunter, every one,
According to the gift which bonnteous nature
Hath in him closed, whereby he does receive
Particular addition, from the bill
That writes them all alike; and so of men.'

And the imperial vot’ress passed on,
In maiden meditation, fancy-free.
He, that a fool doth very wisely hit,
Doth very foolishly, although he smart,
Not to seem senseless of the bob; if not
The wise man's folly is anatomized

Even by the squandering glances of the fool 4. Distinguish between the Mysteries and Moralities, and give allusions to them from Chaucer and Shakespeare.

5. Describe the reformation of the stage effected by Jeremy Collier.

6. “Or Jonson's learned sock be on.
Explain accurately what is here meant.

" what thon would'st highly
That would'st thou holily; would'st not play false,

And yet would'st wrongly win.” Discuss how far these words are descriptive of the Character to whom they are applied.

8. Mention the chief sources of Shakespeare's plays.

ENGLISH LITERATURE, III.

Examiner—MR. W. H. PAULSON, M. A. 1. The perfect historian is he, in whose work the character and spirit of an age is exhibited in miniature."

“ History, in its ideal perfection, is a mixture of poetry and philosophy."

show how near Macaulay himself approached to the ideal, which he has here formed.

2. Give some examples of noteworthy forgeries and impostures in the history of English Literature.

3. Explain a. “The metaphysical school of poets." 6. “Johnson's speech, like Sir Piercy Shafton's Euphuistic elo

quence, bewrayed him under every disguise.”
“ Cowper was the forerunner of the great restoration of

English Literature.”
Oh, thon, whatever title please thine ear,
Dean, Drapier, Bickerstaff, or Gulliver,
• Here lieth one, whose name was writ on water :'
But, ere the breath, that could erase it, blew,
Death, in remorse for that fell slaughter,
Death, the immortalizing winter flew,
Athwart the stream, and time's monthless torrent grew
A scroll of crystal, blazoning the name

Of Adonais. Explain these lines of Shelley's and describe the characteristics of the poet to whom he refers.

5. Give some account of the poems, from which the following extracts are taken:

“He must not float upon his watery bier
Unwept nor welter to the parching wind,

Without the meed of some melodious tear.” b. “A white-haired shadow, roaming, like a dream,

The ever-silent spaces of the East." 6. Contrast or compare Dickens and Thackeray as novelists. 7. Of what nature and by whom are the following works:

“History of John Bull.” “ Splendid Shilling.” Venice Preserved." “ Ion.” “Frankenstein.” “Romola ” « Eothen” “Critic.” “The Bairad." "Castle of Otranto." “ The ring and the book."

ENGLISH ESSAY. Examiner-MR. W. H. PAULSON, M. A. Select one of the following subjects : 1. The rise and development of Novel. writing in England. 2. Lord Bacon and his works.

3. “As civilization advances, poetry almost necessarily declines" --Macaulay.

POETRY.
Eraminer-REV. K. M. BANERJEA, D. L.

Sisupalabadha-Naishadha. 1. a Translate into English the first four slokas in the following passage, i. e., from the words atafay to the word picqua:

बौतविघ्नमनघेन भाविता

सन्निधेस्तव मखेन मेऽधना ।
काविहन्तमलमास्थितेादये।
__ वासरश्रियमशोतदौधितौ ॥ १४ ॥८॥
खापतेयमधिराम्य धर्मतः

पर्यपालयमवौधञ्च यत् ।
तौर्थगामि करवै विधानत-

स्तज्जषख जुहवानि चानले ॥ ८॥

तं वदन्वमिति विष्टरश्रवाः

श्रावयवथ समस्तभूभृतः । व्याजहार दशनांशमण्डलव्याजहार एवलन्दधद्वपः ॥ १२ ॥

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