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MEDICAL JURISPRUDENCE.

DR. BRADY.

1. What is the cause of death in drowning? What the corresponding appearances (signs of drowning) in dead body; and why are those appearances sometimes wanting?

2. Contrast the physical characters of the lungs before and after respiration has taken place. State the object with which the Hydrostatic Test is employed, the objections that have been made to its use, and how far they are valid.

3. Describe the symptoms of an acute case of poisoning with Corrosive Sublimate.

4. What process would you employ to discover this poison in the contents of the stomach ?

5. What are the distinctive marks between Hypochondriasis and Insanity (Melancholia)?

UNDERGRADUATE HONOR EXAMINATION PAPERS.

Michaelmas Term.

EXAMINATION FOR THE DEGREE OF BACHELOR OF ARTS.

Moderatorships in Mathematics and Mathematical Physics.

Examiners.
C. GRAVES, D. D., Professor of Mathematics.
J. H. JELLETT, A. M., Professor of Natural Philosophy.
GEORGE SALMON, A. M.
John W. STUBBS, A. M.
RICHARD M. CONNER, A. M.

DR, GRAVES.

1. The base, c, of a spherical triangle is measured, and the two adjacent base angles, A and B, are found by observation. Supposing that small errors da, dB, are committed in the observation of A and B, what will be the consequent error in the computed value of C?

2. Develope (1 + 2)its and et cos cos (r sin 8), by. Maclaurin's theorem, carrying the development as far as the terms containing 26,

3. What is the guth differential coefficient of tan- ?
4. Eliminate the arbitrary functions and y from the equation

%=30(y) + y4(x). 5. Find the values of

(*1) (6%** – 1) + 27%

24" (e2** — 1)

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(sin x) sin, when :=0. 6. Find the maximum value of

u=(x + 1) (+1) (3+1), 3,4, z, being subject to the condition

af by a= A.

7. What is the length of the normal between the surface of the ellipsoid

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+ +

12 and the plane of xy?

8. Find the equations of the line of greatest inclination passing through a given point on the same surface.

9. Find the equation of the cylinder circumscribed about the same surface, and having its generatrices parallel to a given right line.

10. Prove that the lines of curvature of the ellipsoid are determined by the system of differential equations :

du ydy, zdz
+ +

69

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dH

=0.

MR. CONNER, 11. Find the degree of the equation of the curve, whose intersection with a given curve determines the points of contact of its double tangents; also the degree in which it involves the coefficients of the equation of the given curve.

12. A line of constant length moves between two given lines; find the equation of the evolute of its envelope.

13. If tangents be drawn to a curve of the third degree from its points of intersection with the line ax +By + yx=0, prove that the points of contact will lie on the curvedH dH

dH

dH ан
- M

-N
+ M м

-L
dy
de

dx dy Assuming that the result of substituting == M, y=- L, ero in A+ U is PAU1+z?Qx; and that

dQx k-Qkin = M

L
+

40-Qx-1
dr dy
kz

dQx-1
(BE-

+(BD - AE) da

KH +(AC-L')

(n-1)2

1); 14. Find the number of tangents that can be drawn to a curve from a double point on it.

15. Determine geometrically the three points whose polars are the same with regard to both systems in the general case of reciprocals.

16. Investigate the number and nature of the foci of the curve, whose equation is ld + md' +nd" =0; d, d' and d" being the distances from three given points.

dQk1 dy

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Pk-1.

INTEGRAL CALCULUS AND ALGEBRA,

MR. SALMON.

sins

- my = .

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dr

dy

1. Find S {x + V(1 + 32)}" dx and set (tan I + 2 tanss) ds.
2. Integrate the following equations :
dy

dy
+y=m sin .

de d

d +

+ da

dr 3. Integrate the equations :

dy
day

dy
(x2 + y2) = 342

duz?

di 4. Integrate the equations : dy

dy +x

+y = sin ns dx2 de

d.: dr dry dy

- 3 + 2y = 3%.

da?
5. Integrate the simultaneous equations-
(a) dy = zdt,

ds = ydi.
da
(6) = ax + by, = d'x + Vy.
dt

dt 6. Examine if the following equation fulfils the condition of integrability, and if so, integrate it :

(y2 + yz + x2) dx + (32 + I2 + 22) dy + (x2 + IY + ) dz = 0. 7. Integrate the partial differential equations

px +2y 2% = my. px + qy = 284V (az – 32). 8. Integrate

px + 2q = y. Py + x +y = 0. P(x + y) + (y - 3) = 5. 9. Integrate rx2 +282y + tya + px +2y=0,

rr? - ty=ry. 10. Integrate % = pq and p= (qy + )2.

X'

f'+ f" D) U &c 12. Prove that every algebraic equation has a root.

13. Find the conditions that an algebraic equation of the fourth degree should have two pairs of equal roots.

14. Prove that every prime number of the form 4m + 1 is the sum of two squares. 15. Prove Wallis's theorem,

2.2.4.4.6.6

&c. 1.3.3.5.5.7

2

PHYSICS.

PROFESSOR JELLETT. 1. A flexible string moves under the action of any forces, its extremi. ties being constrained to move in two fixed grooves. If no special forces act at the extremities, the tension will vanish unless the string be perpendicular to the groove.

2. Determine the range of a projectile on a given plane, knowing the velocity and direction of projection.

3. Find the force necessary to sustain a heavy body on a rough inclined plane.

4. Find the equations of equilibrium of a point on a smooth surface whose equation is

u=0.

5. A sphere floats in water whose density is double that of the sphere; determine its position of equilibrium.

6. Determime the time of vibration of a simple circular pendulum.

1. Determine the curve formed by a rectangular sail under the influence of the wind.

2. Deduce from the principle of small oscillations the values of the inclination and azimuth of a conical pendulum, sc. :

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tant

3. Define the instantaneous axis of rotation, and show that in the case of a solid of revolution, where no forces act, it moves like a right conical pendulum.

4. Deduce the equations of oscillatory movement of a floating body, symmetrical with regard to a vertical plane. 5. Define the metacentre, and show

a. That the old method of determining it was erroneous.
b. That the rule derived from this erroneously determined point, as

to the stability of the oscillation, was correct. 6. The equation of the caustic is derived from that of the reflecting curve by eliminating between a system of three equations; determine such a system for the case of divergent rays.

MR. STUBBS. 7. Calculate to a third approximation the mean motion of the nodes of the Moon's orbit considered as circular.

8. Expand the values of T, P, and $ in the lunar theory, neglecting quantities of the fourth order.

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