VII. Describe Butler's argument for the compatibility of 'necessity' with design in the constitution of nature. Discuss the allegation that he has fallen into a confusion between two contradictory theories, fatalism and the doctrine of universal necessity.

VIII. Explain precisely the nature and limitations of Butler's appeal to human ignorance. How does he meet the objection that "the answers...given to what is "objected against Religion may equally be made use of to invalidate the proof of "it, since their stress lies so very much upon our ignorance"?

B.

HOOKER'S ECCLESIASTICAL POLITY, BOOK V.

1. GIVE a general sketch of the character and progress of the Puritan movement in England during Elizabeth's reign. Write an account of the following writings: (a) the Admonitions of Parliament, (b) the Christian Letter.

2.

Trace the main course of Hooker's argument up to the beginning of the Fifth Book.

3. Explain carefully the following passages:

(a) "Whatsoever is natural to Deity, the same remaineth in Christ uncommunicated unto his manhood."

(b) "We hold it in regard of the fore-alleged proofs a most infallible truth that Christ as man is not everywhere present. There are which think it as infallibly true that Christ is everywhere present as man, which peradventure in some sense may well enough be granted."

4. What is Hooker's opinion as to the validity of Baptism by lay hands, and on what considerations is it based?

Examine his defence of the administration of interrogatories to infants at Baptism.

5. Define precisely the terms Transubstantiation, Consubstantiation; and describe the position of the "Sacramentaries" in the Eucharistic controversy.

6. On what grounds does Hooker urge the observance of Sunday? How does he meet the objection to other Festivals that "because God hath left it to all men at liberty that if they think good to bestow six whole days in labour they may, neither is it more lawful for the Church to abridge any men of that liberty which God hath granted, than to take away the yoke which God hath laid upon them and to countermand what he doth expressly enjoin"?

7. How does he justify the use of the words "Receive the Holy Ghost," &c. in the Ordering of Priests?

Which of the above words are accented on the penultimate?

3. Write down the suffixed and construct forms of and plural; explaining the vowel changes which take radicals.

and, in singular place under the first two

4. Write the following singulars with suffixes of the 3 sing. masc. and 2 plur. masc.

wan, nena, na, obiy, me, nya, bea, me, ais, mala

5. Write out the Niphal of p, and the Hiph'il of ; indicating wherever the tone falls on the penultimate syllable.

6. Give the suffixed forms of

p, ie, by (sing, and plur.) and M (sing. and plur.); indicating wherever the tone falls on the penultimate syllable.

7. Examine the use of the Infinitive absolute in Hebrew, and give examples.

8. Classify and give instances of Hebrew nouns which are feminine by signification but not in form.

each.

9. Translate the following sentences, and explain and illustrate the construction of

10. Translate into pointed biblical HEBREW:

Then said Mercy, Sir, I see nothing; but Christiana held her peace.

But said the Interpreter, Look again; she therefore look'd again and said, Here is not anything but an ugly Spider, who hangs by her hands upon the wall. Then said he, Is there but one Spider in all this spacious Room? Then the water stood in Christiana's eyes, for she was a woman quick of apprehension; and she said, Yes, Lord, there is here more than one. Yea, and Spiders whose Venom is far more destructive than that which is in her. The Interpreter then looked pleasantly upon her, and said, Thou hast said the truth. This made Mercy blush, and the Boys to cover their faces, for they all began now to understand the Riddle.

Then said the Interpreter again, The Spider taketh hold with her hands as you see, and is in King's Palaces. And wherefore is this recorded, but to shew you, that how full of the Venom of sin soever you be, yet you may by the hand of faith lay hold of and dwell in the best Room that belongs to the King's House above?

The Pilgrim's Progress.

MATHEMATICAL TRIPOS.

PART III.

MONDAY, January 7, 1884. 9 to 12.

[Each candidate is not to send up answers to more than five questions.]

1 B. DEFINE a Bessel's Function of any order, and prove that Explain, without proving, the method of expanding a function in a series of the form ZAJ(nx), the summation extending to all by J (nb) = 0.

Apply this to shew that if x-ba = ΣL„J。 (nx),

(x), when possible, values of n given

2 B. Shew that an ellipsoid with three unequal axes is a possible form of equilibrium for a mass of homogeneous liquid which is rotating as a rigid body about a fixed axis.

Shew that gravity at any point in the liquid will vary as the length of the normal to the surface of equal pressure intercepted by the equatoreal plane.

3 B. A system is in a configuration of equilibrium in a conservative field of force; shew that the equilibrium will be thoroughly stable if in that configuration the potential energy be a minimum.

Shew that the existence of equal roots in the equation determining the periods of the principal vibrations does not of necessity imply instability, and in that case point out what is implied.

A rod of mass M and length 2a is capable of turning about one end; to its other end n equal weightless strings each of length b and carrying a mass N/n are attached, and the whole is capable of motion in one vertical plane under gravity. Shew that in the system of possible co-existent vibrations there are (n-1) periods each equal to Tb/g and the remaining two are π/p, and π/P, where P1, ± P2 are the roots of the equation

-

{(}M + N) p2 − }g (M+2N)/a} (p2 — g/b) = Np1.

Shew further that if the vibrations be not confined to one plane then of the possible modes of vibration there are 2 (n + 1) periods, and of these 2 (n-1) have the value √b/g, and find the others.

CLXXXIII.

A A