SURGICAL ANATOMY.

DR. M'DOWEL.

1. What parts must be divided in the removal of the superior maxillary bone?

2. What are the boundaries, and what the contents, of the posterior superior triangle of the neck?

3. Enumerate the muscles which pass between the scapula and the trunk, and mention their several actions.

4. Describe the lateral ligaments of the elbow joint.

5. The surgical anatomy of the external iliac artery?

DR. R. W. SMITH.

1. What are the symptoms of stricture of the rectum, and causes of death? What is the external sign of the existence of the disease? 2. Mention the causes of internal strangulation.

3. Enumerate the secondary affections resulting from gonorrhoea. 4. What are the signs of fracture of the brim of the acetabulum? 5. Write a Latin prescription for a pill containing copaiba, cantharides, and a terebinthinate, to be given in gleet.

MR. WILSON.

1. Define Synechia anterior and Synechia posterior. How do they occur? Describe the treatment appropriate to each.

2. Define Myosis, and state the causes which give rise to it.

3. Describe sanguineous effusions within the eyeball, their locality, origin and cause, and their treatment.

4. Describe Epidemic Ophthalmia; and particularize the appropriate treatment which should be adopted for its cure and prevention in places where large numbers of individuals are congregated, such as schools, barracks, asylums, &c.

5. Describe the appearances usually presented, a fortnight or more after the accident, by an eye into which a grain of shot has entered; and state what special circumstances should be taken into consideration in the treatment of the case.

EXAMINATION FOR DEGREE OF BACHELOR IN

MUSIC.

DR. STEWART.

1. Give the derivation of the word Scale, and explain its meaning as applied to Music.

2. By the Dominant Chord modulations to various keys are effected; assign a reason for this.

3. Resolve the intervals of this chord regularly.

4. How are these intervals treated when the Interrupted Cadence is employed?

5. Give the fundamental basses of the following chords, figure their intervals, and resolve them :

6. What determines Musical Pitch?

7. Explain the principles of the Stave, and enumerate the clefs. 8. What is a Tetrachord; of how many Tetrachords is the Diatonic Major Scale formed; and what interval intervenes between them?

9. Give an example of the fault; "hidden 5ths and hidden 8ves," in part writing.

10. What is "Temperament ?"

II. What are "Harmonics ?"

12. Consecutive or parallel 5ths and 8ths are, for the most part, forbidden in part-writing; can you assign reasons for this?

13. How would you avoid these faults?

(Copies of the following Works placed before the Candidate.)

14. How has Handel avoided the former in the "Hallelujah" from Messiah? and how the latter in the chorus "Worthy is the Lamb" from the same?

15. Can you recall anything in Mozart's Zauberflöte Overture which seems to set one of these rules at defiance; and can you explain and justify Mozart's treatment?

16. Define Counterpoint; give the derivation of that term.

17. Give examples of plain and of florid Counterpoint.

18. What is double Counterpoint? Can you point out what description of double Counterpoint is employed in the first movement of Mozart's

Sonata in C minor; or Beethoven's Sonata in A flat (Op. 26); or Mendelssohn's III. Symphony?

19. Harmonize in four parts (S. A. T. B.), and with the proper clefs, the subjoined phrase from a Choral, figuring the bass.

MAC CULLAGH PRIZE EXAMINATION.

THEORY OF SURFACES.

MR. TOWNSEND.

1. Describe briefly the modular method of Professor MacCullagh for the generation of surfaces of the second order; show that both systems of cyclic planes (or their equivalents) result immediately from it; and explain how far the focal conics are given directly by it.

2. State and prove briefly the principal focal properties of surfaces of the second order resulting immediately from their modular generation, as given by MacCullagh.

3. The modular is but a particular case of a more general method of generation noticed by MacCullagh; explain briefly the latter, and show how the focal and dirigent surfaces are connected in it with the generated surface and with each other.

4. The apsidals of two reciprocal ellipsoids are themselves reciprocal surfaces; give MacCullagh's proof of this, and show that it affords an exemplification of Dr. Salmon's theory of the effect of multiple points on surfaces in modifying the degrees of their reciprocals.

5. Apply the method of homographic division in space to Sir William Hamilton's solution of the general problem :--In a given quadric to inscribe a polygon of any order, whose sides shall pass, in any assigned order of sequence, through a system of given points in space.

6. When four points in space determine a self-reciprocal tetrahedron with respect to a quadric surface, show that any point indifferently on the surface may be made a vertex of an inscribed quadrilateral having its sides passing in any assigned order of sequence through the four points.

7. Describe Dr. Hesse's method of constructing by points the quadric surface which passes through a system of nine given points in space. 8. For two quadrics referred to their common self-reciprocal tetrahedron, and represented consequently by the equations,

ax2+ by2+ cz2 + dw2 = 0, and a'x2 + b'y2+ c'z2 + d'w2 = 0, calculate the values of the five invariants, ▲▲', ', and '; and explain the geometrical significations of their severally vanishing.

9. Explain the nature of the elimination, with the principal steps of the accompanying process of reasoning, by which the equation of the surface of centres of a quadric was obtained by Dr. Salmon.

10. Find, by Dr. Casey's method, the equations of the system of spheres which touch four given spheres in space; and deduce from them, as he has done, those of the system of quadrics inscribed to a given quadric, and touching four given quadrics all inscribed to it also.

MR. WILLIAMSON.

1. Investigate the locus of points whose polar quadrics with respect to a surface are cones; and show that the surface locus intersects the given surface in its parabolic points.

2. Adopting Gauss's notation, prove that the radius of curvature, p, of any normal section of a surface may be derived from the following equation:

✓EG - F2

=

Do du2 + 2D du dv + D2dv2

3. Hence prove the following expression for the measure of curvature at any point on a surface,

(EG — F2)9 *

4. Apply this last form to prove that if a flexible but inextensible surface be deformed in any way, its measure of curvature at every point remains unaltered.

5. If the element of the arc of a curve traced on an ellipsoid be expressed by the formula ds2 = dp2 + P2dw2, determine the value of P for any point.

6. Prove that every cubical surface contains twenty-seven right lines; and show how geometrically to construct a system of twenty-seven lines which can belong to the same cubical surface.

7. If one of the two sheets of the surface of centres of a surface be a sphere, investigate the nature of the second sheet, and of the lines of curvature of the surface.

8. If a geodesic polygon circumscribe a line of curvature on a quadric, and if all the angles but one move on lines of curvature, prove that this also will move on a line of curvature, and that the perimeter of the polygon will be constant when the lines of curvature are of the same spe

cies.

9. Prove that the differential equation of the circular sections of an ellipsoid is

αμ

dv

and find the differential equation of the system of orthogonal curves.

10. Adopting Mr. Sylvester's canonical form for a cubic, investigate the values of the fundamental invariants, A, B, C, D, and É.

EXAMINATION FOR THE BERKELEY MEDALS.

ARRIAN.

DR. INGRAM.

1. Translate the following passages:

A. Beginning, Εν ᾧ δὲ αὐτῷ ἐναυπηγοῦντο μὲν αἱ τριήρεις, κ. τ. λ. Ending, κατὰ πήρωσιν ἀπόλεμοι ἦσαν.

Anab., vii. 21. B. Beginning, Κήτεα δὲ μεγάλα ἐν τῷ ἔξω θαλάσσῃ βόσκεται, κ. τ. λ. Ending, καὶ πέντε ὀργυιὰς ἀνηκόντων τὸ μέγαθος.

2. Translate the following :

Ind., 30.

α. οὔτ ̓ οὖν ποθεῖν τι αὐτὸς ὅτου κύριος ἦν ̓Αλέξανδρος δοῦναι, οὔτ ̓ αὖ δεδιέναι, ὅτου κρατοίη ἐκεῖνος, ἔστιν οὗ εἴργεσθαι.—Anab. 7, 2. b. καὶ ὁ μὲν ἀνήγετο ὡς τι ἐρῶν.—7, 11.

c. λόγος δὲ τις καὶ οὗτος ἐφοίτα ἀφανὴς παρὰ τοῖς τὰ βασιλικὰ πράγματα, ὅσῳ ἐπικρύπτεται, τοσῷδε φιλοτιμότερον ἐξηγουμένοις, καὶ τὸ πιστὸν ἐς τὸ χεῖρον μᾶλλον, ἢ τὸ εἰκός τε καὶ ἡ αὐτῶν μοχθηρία ἄγει, ἢ πρὸς τὸ ἀληθὲς ἐκτρέπουσιν.—7, 12.

α. πληρώματα δὲ ἐς τὰς ναῦς καὶ τὰς ἄλλας ὑπηρεσίας πορφυρέων τε πλῆθος καὶ τῶν ἄλλων.—7, 19.

e. ἔλεγε γὰρ ἡ ἐπιστολὴ κατασκευασθῆναι Ηφαιστίωνι ἡρῷον καὶ ὅπως ἐπικρατήσῃ καλεῖσθαι ἀπὸ Ηφαιστιώνος, καὶ τοῖς συμβολαίοις καθ' ὅσα οἱ ἔμποροι ἀλλήλοις ξυμβάλλουσιν ἐγγράφεσθαι τὸ ὄνομα Ηφαιστίωνος.-7, 23.

f. ὑπὸ δὲ τὴν ἕω ἔπλωον ἔξω τῆς νήσου κατὰ ῥηχίην στεινήν· ἔτι γὰρ ἀνάπωτις κατεῖχε —Ind. 22.

9. ἐνθένδε ὁρμηθέντες ἔπλωον ἀκραεὶ.—24.

h. τῇσι κώπησιν οὐ κατὰ σκαλμὸν ἤρεσσον.—27.

i. τούτων (φοινίκων) τοὺς ἐγκεφάλους κόπτοντες ἐσιτέοντο.—29. 3. Translate the words-ἁλιτενής, μηλοφόροι, πρασοειδής, ῥικνός, ὑπερδέξιος, φολιδωτός, ἀποσαλεύω, βλακεύω, κλαδόω. What peculiar sense of καταστρέφω do we find in Arrian? What is πεῖραν καθιέναι ? 4. ταύτης τῆς χώρης, ἥντινα ἰσθμὸν αποφαινομεν εκ τοῦ κόλπου τοῦ ̓Αραβίου κατήκοντα ἐς τὴν Ἐρυθρὴν θάλασσαν.—Ind. 43. Write a geographical note on these words.

5. Write a short geographical account of the Persian Empire under the heads (a) Persis, (b) Susiana, (c) Media, (d) Ariana, (e) the Northern Provinces.

6. With what modern localities have the following been identified : Pasargadae, Ecbatana, Maracanda, Patala, Palimbothra, the city of the Malli, Alexandria Ariorum?

f