c.

d.

e.

f.

g.

h.

i.

j.

k.

7.

m.

"A Monk ther was, a fair for the maistrie.”
"His eyen steep."

"A Frere ther was, a wantoun and a merye
A limytour, a ful solempne man.

In alle the ordres foure is noon that can
So moche of daliaunce and fair langage."
"Of yeddynges he bar utturly the prys."
"He knew wel the tavernes in every toun.
And every ostiller or gay tapstere."

"His purchace was bettur than his rente."
"So gret a purchasour was ther nowher noon."
"It snewed in his hous of mete and drynk[e]."
"But therof needeth nought to speke as nouthe."
"Ne of his speche daungerous ne digne."

"And yit this maunciple sette here aller cappe."

SENIOR FRESHMEN.

Mathematics.

A.

DR. STUBBS.

1. Find the eccentricity of a conic given by the general equation. 2. Find the parameter of the parabola

3. Find the co-ordinates of the intersection of normals to an ellipse at the points x'y', x"y".

4. Deduce the formula in spherical trigonometry

5. Prove completely the formula for spherical triangles

tan =√tans. tan § (s − a) . tan 31 ( s − b) . tan † ( s − c )

6. Convert the equation

x+4x3-8x+4=0

into one whose roots are the sum of the cubes of the roots of the given equation diminished by the first power of each root.

MR. TOWNSEND.

7. The radius of a sphere is 10 ft., and the spherical excess of a triangle on its surface is 10°; required the area of the triangle in square feet.

8. Given, of a spherical triangle, two sides and the included angle; express by logarithmic formulæ the remaining side and angles.

9. A parabola touches the co-ordinate axes at the points x = a, y = b; determine its equation

10. In an ellipse or hyperbola, prove that the parallelogram under any pair of conjugate diameters is equal to the rectangle under the axes.

11. From a given point in either axis of an ellipse or hyperbola draw a normal to the curve.

12. If A, B, C be the three centres, a, b, c the three radii, and a, ß, y the three angles of intersection with an arbitrary circle, of any three coaxal circles; prove the relation

BC. a cos a + CA.b cos ẞ+AB. c cos y = o.

MR. LESLIE.

13. Find the locus of the centre of a conic passing through four fixed points.

14. From the foci of an ellipse perpendiculars FP, F'P' are dropped upon the tangent; find the locus of the intersection of FP' and F'P. 15. Find the equation of the circle which osculates an ellipse at a given point.

16. Determine p and q so that

x2 + px2 + qx + 1 = 0

may have (a) a triple root, (b) two double roots.

17. If m and n denote the number of sides in every face, and the number of plane angles in every solid angle of regular polyhedron, prove that

and hence prove that there can be but five regular polyhedrons.

18. a′ß'y' and a′′ß′′y” denote the arcs connecting two points on the sphere to the corners of a quadrantal triangle, the arc between them, and a, B, y the arcs joining its pole to the corners of the same triangle; prove that

cos a =

cos B'cos y" - cos ẞ" cos y'

sin 0

B..

DR. STUBBS.

1. In a spherical triangle

sin A+ sin B+ sin C 2 cos 4. cos B. cos C

2. If a and b be the semixes of an ellipse, find the first four terms of the expansion of

√ a2 (2 + √/ 2) + b2 ( 2 - √ 1⁄2 + √ a2 (2 - √ 2 + b2 (2 + √ 2)

2

in a series of ascending powers of the eccentricity.

3. The line AB passes through a fixed point 4, and meets a given line PQ in a variable point B; on AB a semicircle is described, cutting & fixed circle in two points; find the locus of the intersection of the common chord with AB produced, taking origin at A, and axes of co-ordinates parallel and perpendicular to PQ.

4. In order to reduce the biquadratic equation

x2 + px3 + qx2 + rx + s = 0

to a reciprocal equation by putting y + h for x, we have a cubic equation to determine h, which reduces to a quadratic when p2s — r2 = 0.

MR. TOWNSEND.

5. For the parabola whose equation in rectangular co-ordinates is

determine the co-ordinates of the focus and the equation of the directrix.

6. For the ellipse or hyperbola whose equation in rectangular co-ordinates is

ax2 + 2hxy + by2 = k

determine the quadratic whose roots are the squared reciprocals of the two semiaxes.

7. Show that, for all values of the two angles a and ß, the two pairs of lines whose equations are

2 cos za + 2xy cos (a + B) + y2 cos 26 = 0

x2 sin 2a + 2xy sin (a + (3) + y2 sin 2,3

are the two pairs of conjugates of an harmonic pencil.

=0

8. If a, b, c be the three sides of a spherical triangle, and k the radius of the circle to which it is self-reciprocal, prove that

tan k =

(cos b cos c sec a 1). (cos c cos a sec b-1). (cos a cos b sec c4 sin s. sin (sa). sin (s - b). sin (s - c)

I)

MR. LESLIE.

Find the equation of the locus of the centre of a conic which touches the lines x = 0, y = 0, y = ax + b, y = a'x + b'.

10. If r, r', r" denote focal radii of an ellipse which are inclined to each other at angles of 120°, prove that

II. Prove that the equation of the normal to an ellipse may be written in the form

and hence deduce the equation of the locus of a point such that two of the normals which can be drawn from it may coincide.

12. In a spherical triangle, prove that

2B-E

2C-E

a

b

xin (24 - E): sin ( 25-5) : sin (10~)- tan tan tan

2

Logics.

2

2

2

PROFESSOR ABBOTT.

1. Discuss the objections that have been urged against the Syllogistic Theory.

2. State Whately's definition of Logic, and show how he arrives at it. 3. State Mr. Mill's view of the Syllogism.

4. Explain the principal theories of Predication.

5. State and illustrate Whately's rule for ascertaining in practice what is really the predicate of a proposition. How does he apply it to the proposition, A is not B (where the emphasis is on not)?

6. What is the meaning, and what the application, of the maxim, "Nota notæ est nota rei ipsius"?

7. Explain the meaning of "second intention" according to Whately, and according to the older logicians, respectively.

8. State Whately's solution of the fallacy :

therefore,

Food is necessary to life;

Corn is food;

Corn is necessary to life;

and examine its correctness.

9. Examine briefly the nature of the hypothetical Syllogism.

10. Examine Zeno's argument against the possibility of Motion.

11. If a hypothetical proposition is not certain, but only probable, show that the reasoning from the remotion of the consequent to that of the antecedent is invalid.

MR. JELLETT.

1. It is proposed to prove by induction that all bodies which possess a certain property A, possess also a certain other property B; what rule should be followed in choosing the instances of which the induction is composed?

a. Two bodies agree only in the qualities A and B, therefore every body which possesses one of these qualities also possesses the other; state whether this argument be valid or invalid, and give the reason of your answer.

2. He who believes the Scripture to have proceeded from Him who is the Author of Nature may well expect to find the same sort of difficulties in it as are found in the constitution of Nature.

Arrange this argument in logical form:

a. State the exact logical nature of the argument from analogy, when used to refute another argument.

3. "Every person practically lays claim to infallibility, inasmuch as he always believes himself to be right in his opinions." Arrange this argument in logical form, and determine whether it be valid or invalid; giving the reason of your answer.

determine whether this argument be valid or invalid.

5. "With some of them God was not well pleased, for they were overthrown in the wilderness."

State this argument as a syllogism.

6. When an extenuating circumstance is alleged in the case of a crime, it is commonly replied, "That is no excuse." Point out the fallacy involved in this answer.

MR. TARLETON.

1. Prove that the Dictum de omni et de nullo includes all the general and special rules of Syllogism; hence show that with the exception of useless modes there are none legitimate except those received.