3. Describe minutely the dangers that primarily threaten the life of a patient after a severe burn, and those which remotely occur, even when the patient is apparently almost well.

4. Recount carefully all the characters and symptoms of congenital dislocation of the shoulder and hip joints; also the progressive symptoms arising in the cases up to thirteen or fifteen years of age.

5. Contrast fracture of the epiphysis of the lower end of the humerus, with dislocation of both bones of the forearm backwards, and the surgical treatment of each.

MR. WILSON.

1. Describe the symptoms, pathology, and treatment of keratitis punctata.

2. Enumerate and explain the most prominent symptoms usually found in glaucoma.

3. Particularize those injuries which are most likely to be followed by sympathetic ophthalmia in the uninjured eye.

4. Describe congenital cataract, mentioning its varieties, and the mode of treatment applicable to each.

5. Mention the tumors which occur within the eyeball, and the conditions which may simulate such tumors, and how they are to be distinguished.

SURGICAL ANATOMY.

DR. M'DOWEL.

1. Give the relations of the common iliac arteries. Mention the differences in the relations of the arteries of each side.

2. Describe, in their order, the parts which lie between the os hyoides and thyroid cartilage. What operative proceeding may be rendered necessary in this space?

3. Mention, in their order, the parts which lie in front of the elbow joint.

4. Under what circumstances might it be necessary to apply a ligature to the external carotid artery? How would you proceed to accomplish this operation?

5. Describe the lachrymal gland. What are its relatiors? Under what circumstances has it been extirpated?

SURGERY.

DR. M'DOWEL.

1. Describe an enchondroma. In what situations is such a growth most frequently met with? What is the prognosis, and what the treat

ment?

2. Describe appearances of the limb in a case of phlegmonoid erysipelas when the disease is fully established. What constitutional symptoms are usually present? What treatment, local and general, would you adopt?

3. Mention the different forms of ulcer which are met with in the tongue. What are the distinguishing characters of each?

4. How would you proceed to reduce a dislocation of the femur on the dorsum of the ilium by the method of manipulation ?

5. What are the characters of an enctite tumor? What methods of treatment may be selected by the surgeon in different cases? and mention the circumstances which would influence your selection.

MAC CULLAGH PRIZE EXAMINATION.

THEORY OF ROTATION.

MR. TOWNSEND.

1. Assuming that a rigid body, capable of free motion round a fixed point, may be transferred, from either of any two possible positions to the other, by a pure rotation through a definite angle, round a definite axis passing through the point; given, with the fixed point 0, the origi nal and displaced positions, 41 and B1, 42 and B2, of any other two of its points A and B, determine by any method the axis and angle of rotation.

2. Assuming that a rigid body, capable of free motion in unlimited space, may be transferred, from either of any two arbitrary positions to the other, by a rotation through a definite angle, combined with a translation through a definite interval, round and along a definite axis in space; given the original and displaced positions, A1, B1, C1, and A2, B, C, of any three of its points A, B, C, determine by any method the axis, angle, and interval of twist.

3. Assuming that two elementary twists a and 3, about two arbitrary screws A and B, of definite pitches a and b, may be compounded into a single elementary twist y, about a third determinate screw C, of definite pitch c; given all particulars for the two component screws A and B, determine them by any method for the resultant screw C.

4. Prove the fundamental dynamical property of reciprocal screws with respect to the equilibrium of bodies restricted in absolute freedom, viz., that when, of two screws A and B, of pitches a and b, a wrench about one (A) is unable to produce a twist about the other (B), then, reciprocally, will a wrench about the latter (B) be unable to produce a twist about the former (A).

5. For a body possessing three degrees of freedom, show by any method that, of its entire system of possible displacement screws, and of the entire corresponding system of reciprocal screws-

(a). All screws of the former system, having a common pitch ±p, are generators of the same system of a quadric surface in space.

(b). All screws of the latter system, having the opposite pitch 7 p, are generators of the opposite system of the same quadric surface.

(c). The several quadrics, for different values of p, are concentric, coaxal, and concyclic; and their common axes are screws of both systems, of equal and opposite pitches.

6. A rigid body, previously in unconstrained equilibrium in free space, being supposed set in motion by a single impulsive force; show by any method that

(a). When the initial axis of twist velocity is a principal axis of the body, the initial motion is a pure rotation; and, conversely, when the initial motion is a pure rotation, the initial axis of twist velocity is a principal axis of the body.

(b). For different initial axes of pure rotation having a common direction in the body, the locus of the corresponding centres of percussion is a right line, passing through the centre of inertia of the body, and lying in the plane determined by the axes.

7. In the rotation of a rigid body round a fixed point, no external forces acting, determine by any method

(a). The geometrical relation connecting the axes of principal moment and of instantaneous rotation, in any position of the body.

(b). The kinematical representation of the motion of the body in space, by aid of the momental ellipsoid of the point.

(c). The formula for the time of revolution of the invariable line in the body, by aid of the ellipsoid of inertia of the point.

8. For the particular case of the preceding, in which the invariable line of the motion describes in the body either centro-cyclic plane of the ellipsoid of inertia of the point; show how, all initial particulars being supposed given, the exact position of the body in space may be determined for a given time.

9. In the small oscillations of a rigid body capable of free motion round a fixed point, in the vicinity of a position of stable equilibrium under the action of any system of forces which have a potential; all particulars being supposed given, investigate by any method-

(a). The cubic determinant whose roots give its three periods of harmonic vibration under the action of the small unbalanced forces developed by displacement.

(b). The equations of the two concentric ellipsoids whose common triad of conjugate diameters determines its three axes of harmonic vibration under the same action.

10. In the motion of a top on a rough horizontal plane under the action of gravity, the body terminating in a small hemispherical extremity in contact with the plane, and its motion commencing with a rapid rotation round its axis of figure; show that, under ordinary circum

stances

(a). The axis of figure, whatever its original inclination to the horizon, becomes rapidly vertical.

(b). The vertical position of the axis is attained with a comparatively small loss of kinetic energy in the body.

PRECESSION AND NUTATION.

PROFESSOR R. S. BALL.

1. Prove the following equations given by Laplace:

dq

A + n ( C − B) r = (C– B) (P cos p – P' sin ø),

dt

dr

B + n (A − C) q = ( A − C) (P' cos 4 + P sin ø),

dt

where A, B, C are the principal moments of inertia of the Earth; q, r, n the angular velocities about the axes of x, y, z; the angle between the axis of x and the vernal equinox; and P, P' functions of the mass and position of the disturbing body.

2. Show from the nature of the problem that we have very nearly

and that when A is taken equal to B, the equations of the last question combined with

3. If a and be the geocentric right ascension and declination, and if R be the distance and M the mass of the attracting body from the Earth, prove that the equations may be written

4. The action of both Sun and Moon being considered, show that while the expression for contains one term which increases indefinitely with the time, the expression for 0 consists exclusively of constant and periodic terms. What important physical consequences arise from this difference in the nature of 0 and ?

5. Assuming the Earth to be symmetrical about its polar axis, prove that its velocity of rotation about that axis remains rigorously uniform notwithstanding the influence of an attracting body.

6. According to the Nautical Almanack for 1875 the nutation of the obliquity of the ecliptic is

9". 2237 cos — 0". 0895 cos 2Q + 0". 5507 cos 20, where is the mean longitude of the Moon's ascending node, and the true longitude of the Sun. Determine the theoretical values of these three coefficients.

7. Why must the coefficient of cos 2 be determined by observation, and why ought the two smaller constants to be determined by calculation ?

8. What is the argument of the term which should be added to the expression of Question 6 if the first power of the eccentricity of the Earth's orbit were retained?

9 Assuming the total precession to amount to 50" seconds per annum, compute the amounts arising from the action of the Sun and Moon separately.

JO. How does the comparison of the theory of precession and nutation with observation give any information with respect to the law of density of the interior of the Earth?

EXAMINATION FOR THE BERKELEY MEDALS.

POLYBIUS.

DR. INGRAM,

Translate the following passages :—

1. Beginning, Οἱ δὲ περὶ τὸν ̓Αρατον, οὔτε κατιδόντες, κ. τ. λ. Ending, ἠναγκαζον φεύγειν προτροπάδην.

2. Beginning, ἀλλὰ τῶν πραγμάτων αὐτοῖς κατὰ, κ. τ. λ. Ending, ἐκέλευσεν αὐτοὺς εἰς φυλακὴν ἀπαγαγεῖν.

3. Beginning, Απαντησάντων δὲ των περὶ τὸν Θεόδοτον, κ. τ. λ. Ending, πάντα τὰ κατὰ τὰς πολεμικὰς παρασκευάς.

4. Beginning, 'Ο δὲ καθοπλισμὸς τῶν ἱππέων νῦν ἐστι, κ. τ. λ. Ending, καὶ τεταγμένην ἔχουσι τὴν χρείαν.

1. Translate the words ἀθεσία, αἴθυγμα, ἀσυρής, γροσφομάχος, ἐπισυρμός, κακεντρέχεια, παραγωγιάζειν, ῥητίνη, σελίς, σιάλωμα.