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of the generating lines, the enveloping planes, and the cuspidal edge. Explain also the form of the surface about such an edge.
10. Explain the effect of the sun's disturbing force in rendering the moon's orbit oval, supposing the undisturbed orbit circular; and find the ratio of the axes of the oval orbit.
11. A uniform flexible string is suspended by one end, and performs small movements in a vertical plane; form the differential equation of the motion, and thence obtain, in a series, the transcendental equation whose roots determine the periodic times of the various possible symmetric oscil. lations.
12. Obtain the equations of motion of a rigid body moveable about a fixed point, in terms of the angular velocities about the principal axes through that point.
Prove that the rotation of a free body revolving round a principal axis through its centre of gravity is stable or unstable according as that axis is one of greatest or least, or else one of mean moment of inertia.
13. Shew that a small lunar atmosphere would affect the duration of an occultation, but not sensibly affect the apparent diameter of the moon.
14. How do you account for the remarkable effect of wind on the intensity of sound?
15. Find the condition of achromatism of an eye-piece composed of a solid block of glass with a thin lens of different glass cemented to it on the end next the eye, the surfaces being worked spherical.
16. Find the attraction of a prolate spheroid on an internal particle.
A mass of homogeneous fluid is subject to the mutual gravitation of its particles, and to a repulsive force tending from a plane through its centre of gravity and varying as the perpendicular distance from that plane; shew that the conditions of equilibrium will be satisfied if the surface be a prolate spheroid of a certain ellipticity, provided the repulsive force be not too great.
17. Account for the spectra formed by a fine grating; and supposing the grating placed obliquely to the incident light, find an expression giving the length of a wave of light in terms of quantities which may be observed.
18. If a continuous medium be continuously displaced, shew that the most general displacement of an element of the medium consists of a displacement of translation, the same as that of a point P taken in the element, a rotation round some axis through P, and three elongations along three rectangular axes passing through P.
19. Expressing the equations of motion of a fluid in a form in which the particle is supposed to remain the same in differentiations with respect to the time, and supposing the density either constant or a function of the pressure, and the forces such that Xdx + Ydy + Zdz is a perfect differential, obtain first integrals of the three equations resulting from the elimination of the pressure. Are these equations altogether independent of each other? What important theorem may be proved by means of these integrals ?
20. Describe fully some one experiment by which it may be shewn that two streams of light from the same source, polarized in rectangular planes, and afterwards brought to the same plane of polarization, do or do not interfere according as the light from the primitive source is or is not polarized.
N.B. It is not to be assumed that the colours of crystalline plates in polarized light are due to interference.
TRANSLATE into LATIN PROSE : Men have, in general, a much greater propensity to overvalue than undervalue themselves, notwithstanding the opinion of Aristotle. This makes us more jealous of the excess on the former side, and causes us to regard, with a peculiar indulgence, all tendency to modesty and selfdiffidence, as esteeming the danger less of falling into any vicious extreme of that nature. It is thus, in countries, where men's bodies are apt to exceed in corpulency, personal beauty is placed in a much greater degree of slenderness, than in countries where that is the most usual defect. Being so often struck with instances of one species of deformity, men think they can never keep at too great a distance from it, and wish always to have a leaning to the opposite side. In like manner, were the door opened to self-praise, and were Montaigne's maxim observed, that one should say as frankly, I have sense, I have learning, I have courage, beauty or wit; as it is sure we often think so; were this the case, I say, every one is sensible, that such a flood of impertinence would break in upon ns, as would render society wholly intolerable. For this reason custom has established it as a rule, in common societies, that men should not indulge themselves in self-praise, or even speak much of themselves; and it is only among intimate friends, or people of very manly behaviour, that one is allowed to do himself justice. Nobody finds fault with Maurice, Prince of Orange, for his reply to one, who asked him, whom he esteemed the first general of the age: The Marquis of Spinola, said he, is the second. Though it is observable, that the self-praise implied is here better implied, than if it had been directly expressed, without any cover or disguise.
To be translated into Latin ELEGIACS :
Her breathing soft and low,
Kept heaving to and fro.
So slowly mov'd about,
To eke her living out.
Our fears our hopes belied
And sleeping when she died.
And chill with early showers,
Another morn than ours.
To be translated into GREEK IAMBICS:
AND either tropic now 'Gan thunder, and both ends of heaven; the clouds, From many a horrid rift, abortive pour'd Fierce rain with lightning mix'd, water with fire In ruin reconcil'd: nor slept the winds Within their stony caves, but rush'd abroad From the four hinges of the world, and fell On the vex'd wilderness, whose tallest pines, Though rooted deep as high, and sturdiest oaks, Bow'd their stiff necks, loaden with stormy blasts, Or torn up sheer. Ill wast thou shrouded then, O patient Son of God, yet only stood'st Unshaken! Nor yet staid the terror there; Infernal ghosts and hellish furies round Environ’d thee, some howld, some yell’d, some shriek’d, Some bent at thee their fiery darts, while thou Sat'st unappall'd in calm and sinless peace !
SUBJECT for Latin Essay:
TRANSLATE into GREEK PROSE:
Of the great mass of affections remaining, some have the greatest power to torment, and some to bless. The furious paroxysm of anger, and the scowling brow of discontent, with all the pale pining, the restlessness, and the crime, which make bad men scourges no less to themselves than their neighbours, have been often described by poets, and are proverbial among mankind. The man who harbours such guests in his mind, if ever he awaken from the madness which they inspire, confesses himself miserable under them, but he seldom knows how to escape from their control. Yet there was, probably, a time in his life when he might have done so. But when such affections have waxed mighty, so that one suffers in constraining them, they are properly called passions, and the same change of name might have been applied to the appetites. When however any conflict, such as has been mentioned, takes place, it is far more terrible with an emotion which absorbs the whole personal being than with an appetite which only torments the body. Here then, as before, I wish you to observe, that if any man comes off triumphant in the struggle with the worst enemies that ever assail his peace, and with calm brow leads resentment or jealousy a silent captive, he obtains this deep joy only through the religious sentiment which the theory of the materialist tends to obliterate. “Is that altogether the case ?” asked Wolff, “ or do not scenery, music, and in general either quiet or distraction calm the disturbances of the mind ?” “Perhaps in such things there is a mitigating power,” replied Blancombe; “ especially in the roar of ocean, or the deep stillness of the mountains. For in such places there dwells silently something of the majesty of their Maker ; but after all, it is chiefly in virtue of the religious solemnity with which such things imbue the mind, that they have power to tranquillize it. Otherwise, the mere physical relief through any variety of silence or of noise can only divert for a time, and does not reach the deep sources of the more turbid passions.”
SUBJECT for LATIN HEXAMETERS:
TRANSLATE (with brief marginal notes) the following passages :
Beginning, Καμοί προσέστη καρδίας κλυδώνιον, κ.τ.λ.
Æsch. Choeph. 175. Explain the metaphor in the first line.
Beginning, 'Αλλ' άνδρα χρή, κάν σωμα γεννήση μέγα, κ.τ.λ.
SOPH, Ajaz. 1056.