4. How does Kant prove that all the functions of the Understanding can be discovered by completely exhibiting the functions of unity in judgments?

How does he find from this principle his table of the pure concepts of the Understanding?

Give a brief account of the objections to this table of Categories, and Mr. Mahaffy's defence of Kant.

5. Distinguish figurative synthesis, intellectual synthesis, and synthesis of apprehension.

Mr. Mahaffy contrasts the Conceptualism of Kant and Locke ?
What is Schopenhauer's criticism of the Schema ?

6. State and prove the second Analogy of Experience.

What is the empirical criterion of a Substance?

Kant establishes the law of Continuity of changes, and shows how it is possible to assert such a law a priori?

7. Give the substance of Kant's Refutation of Idealism, and point out the connexion in which the question is discussed in the Critick,

Mr. Mahaffy contrasts the Idealism of Berkeley and Kant?

Mansel accounts for the opposition of the Scotch philosophers to Berkeley, and shows that such opposition was illogical ?

8. Give a sketch of Fichte's Philosophy, with Mansel's criticism; and point out the advances made by Schelling and Hegel beyond Fichte. What corresponds in Fichte's system to the Kantian Ding-an-sich? 9. Give Mansel's examination of the different theories of the Real not founded on Consciousness.

How far do Kant and Mansel differ as to the true principle of distinction between Reality and Appearance ?

Moderatorships in Experimental Science.

JOHN H. JELLETT, B. D.

Examiners.

JOHN R. LESLIE, M. A., Professor of Experimental Philosophy,
JAMES APJOHN, M. D., Professor of Applied Chemistry.
GEORGE L. CATHCART, M. A.

SOUND AND LIGHT.

MR. JELLETT.

1. Explain Dulong's method of calculating the length of a sound

wave.

2. Describe the experiment by which Savart proposed to establish the existence of a musical note very much lower than any note previously.

known, and explain fully the argument of Despretz against the conclusiveness of the experiment.

3. In the case of sound reflected from a fixed obstacle, prove a priori the existence of fixed nodes of vibration, and describe the experiment by which Savart verified the result.

4. Describe the method of determining the index of refraction of a fluid by observing a ray of light refracted at the free surface, and show how to conduct the experiment so that the error arising from the position of the line of collimation of the telescope may be the least possible.

a. With regard to this source of error, the Newtonian method of determining the index of refraction is superior to that alluded to above.

b. In this latter method; the spectrum, as seen in the telescope, is not distinct unless the prism be in the position of minimum deviation. Explain this.

5. Describe the method of Helmholz for observing the tint formed by the composition of two simple colours, and show how the relative intensities of the components may be made to assume any required value.

6. Show how to obtain the index of refraction of a non-crystalline substance by observations made upon the plane of polarization of a polarized ray reflected by this substance.

a. If a, ẞ be the azimuths of the planes of polarization of the incident and reflected rays respectively, show that the angle of refraction will be given by the equation

and hence determine the best position for the plane of polarization of the incident ray. N. B.-The truth of Fresnel's theory is here assumed.

7. If a polarized ray be reflected at the surface of a transparent body, the difference between the phases of the two components (perpendicular and parallel to the plane of incidence) may be made, by a proper determination of the angle of incidence, to assume any required value. Hence, show that circular polarization may be produced by a single reflexion. (a). Why is a very bright light necessary for the exhibition of this phenomenon?

8. State the arguments in favour of the perpendicularity of the vibration to the plane of polarization derived from-a. the phenomena of diffraction; b. the phenomena of double refraction.

9. Show that the determination of the intensity of diffracted light depends upon two integrals of the form

and prove that, in the case of light passing through a hole of any form, these integrals may be reduced to the single integrals,

10. Light incident upon a screen is represented by the formula,

where is the distance of any point on the screen from a fixed point. Describe the appearance presented.

MR. LESLIE.

1. What preliminary experiments must be made with the electrophorus in order to explain the action of Holtz' electrical machine?

2. How does it appear that one-half of the rotating disk in Holtz' machine is on both sides electrified positively, and the other half negatively?

3. Describe the experiments necessary in order to explain the theory of Gramme's magneto-electrical machine.

4. Show that the action of Gramme's machine is in all respects comparable to that of a system of two batteries joined up for quantity.

5. How is it proved that the quantity of heat developed by the discharge of an electric battery is independent of the resistance of the circuit, and only varies with the charge and the surface of the battery ?

6. Prove the formula for the temperature at any point of a voltaic circuit, and state the consequences deduced from it by Jamin.

7. Assuming the expression for the action of elementary currents,

f=

i'

dsds' (sin 0 sin e' cos & - k cos e cos 0'),

How does Jamin show that n = 2 ?

8. Prove in the last formula that k = .

9. Determine the direction of the force exacted by an indefinite rectilinear current on a finite current.

10. Explain from theory the rotation of a current by a solenoid.

11. What experiments may be made to account for the fact that the current in an induction coil is always apparently in the same direction?

12. Describe the action of the condenser and of the bundle of iron wires in a coil, and compare the heating effect with that of an ordinary voltaic battery.

13. Calculate the moment of inertia of a bar magnet, (a) when it has the shape of a right-angled parallelopiped, (b) when it is a hollow cylinder.

14. The moment of inertia of a magnet may be obtained by observing the time of vibration on the addition of a gun-metal cylinder of known weight and size?

15. In measuring the horizontal intensity of the earth's magnetism the following formula is used,

16. A short needle is deflected by a bar maguet in the usual way; prove the formula

1.5 tan o

'5 tan o'.

17. Give the theory of the instrument used for finding the small changes in the horizontal magnetic force.

18. Give the general theory of a dip-circle.

MR. CATHCART.

1. Assuming Regnault's formula for the total heat of steam, and that the specific heat of water is

c = I +00004t + ·0000009t2,

determine the constants in Clausius' formula for the latent heat of steam, λ = a - b. t, by the condition that it shall be true for = 100o.

2. Deduce Boyle and Mariotte's law from Bernoulli's theory of gases. 3. Favre and Silbermann's method of determining heats of combustion?

(a). From their result, what is the temperature of a complete combustion of hydrogen in oxygen ?

4. The heat generated in a mass of ice by falling from infinity to the Earth's surface would only suffice to decompose a fractional part of it into its elements ?

5. How has the dilatation of crystals by heat been investigated? (a). The dilatation of iodide of silver is remarkable?

6. How is the temperature of a medium found by a mercurial thermometer when part of the stem projects beyond the inclosure?

7. What are the principal experiments which have been made on diffusion of heat?

8. How is the polarization of heat demonstrated?

(a). Polarized heat is affected by magnetism?

9. Pouillet's method of measuring solar heat radiated to a given place?

(a). How did he determine its total amount?

10. The weight of a litre of dry air in Paris (lat. 48° 50′), at 60 metres above the sea level, is 129318 grammes; what does it amount to in Dublin (lat. 53° 23′) at an altitude of 10 metres?

11. Regnault's method of investigating the compressibility of liquids? (a). Define the coefficient of compressibility, and state its value at o' for mercury and for water.

12. Describe any one of the methods accurately by which the mean density of the Earth has been investigated.

13. What is the principle of Sprengel's air-pump? Is it employed in any other apparatus ?

14. What are the different methods of determining the density of a gas or vapour?

DR. APJOHN.

MINERAL CHEMISTRY.

1. Explain Wohler's method of preparing pure Titanic acid, and detail the method of analysis you would employ in the case of a Titaniferous iron, also including alumina, lime, and magnesia.

2. The iron and titanium in a solution of both metals has been determined volumetrically. How is this accomplished?

3. How is the combined carbon and the graphitic carbon of pig-iron estimated with precision?

4. Zinc may be estimated by a volumetric process in which ammonia, ferrocyanide of potassium, and permanganate of potassium, are employed. Give a description of it.

5. Ferric iron in solution may be estimated volumetrically, hyposulphite of sodium and iodine being the only re-agents used. Give the particulars of the process, and its theory.

6. The amount of chlorine present in ordinary waters is at present usually determined by a volumetric process. What is it?

7. Winkler estimates iron by a volumetric solution of cuprous chloride. Explain this method.

8. How would you make the analysis of a substance containing iron, aluminum, zinc, uranium, and chromium.

9. The valuation of ores of manganese may be conducted in several ways. Give a description and explanation of those with which you are acquainted.

10. There are three distinct processes for the separation of Nickel and Cobalt. Write a description and explanation of them.

II. In a solution containing mercury, cadmium, and zinc, how may the amount of each metal be determined?