1. The business of Vital Statistics consisting of inquiries as to the health and well-being of a community, state generally what circumstances should be observed, recorded, and analyzed in order to secure a useful result?

2. In order to arrange a mass of observations of one kind, two methods are essential-the one arithmetical, the other graphic. State how the first is conducted-1° by the aid of a logarithmic table, 2° by the aid of a slide-rule; how the second-1° by means of a curve referred to a base line, 2° by means of a curve referred to a centre.

3. What is meant by density of population? The population and acreage of the largest counties in each of the four provinces, expressed in thousands, are as follows:

Express numerically their population densities referred to that of the whole of Ireland as 100, its population being 5160, and acreage 20,200 in thousands.

4. What is meant by the term-so commonly used, and as commonly misunderstood-expectation of life? How does it differ from vie probable of Continental writers ?

5. The 'mean lifetime,' according to the English Life Table, is for males 39.91, for females 41.85; and according to Farr's Healthy Districts Life Table, 48.56 and 49.45 respectively. What is the exact meaning and significance of these figures?

6. Is there any foundation for the commonly-received opinion that there are critical periods of human life, and especially a grand climacteric at 63 ?

7. What is the normal law of increase of population? How may populations be estimated from year to year after a census has been passed until the next census?

8. How may the number of deaths in a town be computed, during any period, from having the weekly rates of mortality as printed in the returns ?

9. What is the annual rate of mortality for the Healthy Districts of Dr. Farr?

10. What is a Life Table ? Enumerate those which are best known in this country and abroad.

MR. LEECH.

1. State generally the object of the Public Health (Ireland) Act, 1878, and describe the machinery by which it is carried into execution.

2. State generally the duties of a Medical Officer of Health under the Act. Under what circumstances is he entitled to extra remuneration for his services ?

3. What are Nuisances, and what are the duties of a Sanitary Authority with respect thereto ?

4. What are Offensive Trades? How should an Urban Sanitary Authority proceed in case of such a trade being carried on outside its district ?

5. State the restrictions imposed by the Act upon the prosecution of legal proceedings against Sanitary Authorities or their officers.

6. Distinguish primary and secondary evidence. When is the latter admissible?

7. Enumerate the circumstances which may render a witness incompetent.

8. State the several cases in which the personal opinion of a witness is admitted as evidence.

9. What are the exceptions to the rule that hearsay evidence is inadmissible?

10. Under what circumstances is a prisoner's statement admissible as evidence against himself?

SCHOOL OF ENGINEERING.

ENTRANCE EXAMINATION.

MECHANICS.

DR. TRAILL.

1. How would you apply three forces represented by the numbers 3, 4, and 5 to a particle, so that it should remain at rest?

2. Find the resultant of two forces P and Q, acting on a body, and inclined to each other at an angle .

3. Show how to find the component, in any direction, of a force acting in any other direction. In what direction can there be no such component ?

4. Find the centre of gravity of a plane triangle.

5. Draw an arrangement of pulleys, so as to show that there is a mechanical advantage in their use.

6. Show that the moments of two forces, round any point on their resultant, are equal and opposite.

7. Two weights, of 33 lbs. and 4 lbs. are hung at the ends of a straight lever whose length is 92 inches; find where the fulcrum must be placed for equilibrium.

8. Find the horizontal force necessary to keep a weight of 15 lbs. on an incline of 45°.

9. What equation connects velocity, time, and space?

(a) In the case of uniform velocity.

(b) In the case of a constant force acting.

10. A train travels over 100 miles in 2 hours, find the average velocity referred to feet and seconds.

JUNIOR CLASS.

MR. PANTON.

1. Given cos A = 1, sin B = 1; find the value of tan (A + B). 2. Given the base of a triangle c= 1095, and the adjacent angles A=57° 12′, B = 24° 45′ ; calculate the remaining sides.

3. Given the three sides of a triangle a=309.86, b=154.33, c=365; calculate the angles.

4. Find the area of a quadrangular field, whose angles taken in order are A, B, C, D, from the following measurements: - AB = 78.24, AC= 115, AD = 65.7, BAC = 31°42′, CAD = 54° 19′.

5. A right cone, whose height is 20 feet, contains 8000 cubic feet; find the circumference of its base.

8. Find the values of which make the expression sine cos20 a maximum or minimum.

9. The equation of a parabola being y2=4mx, find the area of a portion included between the curve, the axis, and an ordinate let fall from any assumed point on the curve.

10. Find an expression for the surface of a portion of a sphere cut off by a plane at a given distance from the centre.

DR. TRAILL.

I. How far will a weight of 100 lbs. be moved by a pressure of 1 lb. in 20 seconds?

2. A particle moves with a uniform acceleration for 15 seconds, during which time its velocity increases from 60 feet to 100 feet per second; find the space traversed in the 15 seconds.

3. When the units of time and space are respectively the second and the foot, the acceleration of a moving body is 5; what would be its measure if the velocity were measured in yards per minute?

4. If a body be projected at an angle of 45°, show that its range on a horizontal plane will be equal to 4 times the height to which it ascends. 5. A tripod formed by three rods of different lengths sustains a weight; show how to determine the relative pressures on the three rods.

6. If a screw makes 10 turns in a cylinder a foot long, and if the length of the power arm be half a foot, find the mechanical advantage. 7. Find the size of an iron shot that weighs 60 lbs. [sp. gr. of iron = 7.8].

8. The edge of a hollow cube of lead [sp. gr. = 11.35] is 8 centimetres, its thickness is 2 centimetres; find its weight in water.

9. A rectangle is immersed in water with one side on the surfaceshow how to divide it by a horizontal line into two parts, on each of which the whole pressure shall be the same.

10. In a siphon barometer, the mercury in the open end falls through what change does this indicate in the barometric pressure?

4mm ;

JUNIOR CLASS.-SUPPLEMENTAL.

PHYSICS.

MR. FITZGERALD.

1. Find the density of a body which weighs 63 grms. in air, and 35 grms. in a liquid whose density is .85.

2. The coefficient of expansion of iron is .000012 per degree Centigrade, and its coefficient of compressibility is .00002 per ton per sq. centim. find the force of expansion of a bar 150 sq. cm. in section when heated through 50° C.

3. What degrees Centigrade correspond to the following degrees Fahrenheit : 10, 0, 32, 60, 212, 500?

4. Calculate the weight of air at 15° C. and 750 mm. that is displaced by a balloon of 3000 cub. meters capacity. air at o° C. and 760 mm. is 1.293 grms.]

[The weight of 1000 cc. of

5. Describe any method of measuring specific heats.

6. Describe how an electrophorus works.

7. Describe how galvanometers are made.

8. Explain how rotatory motion is produced in electro-magnetic machines.

9. Describe how spectroscopes are made.

10. What is the condition of the air at the loops and at the nodes, respectively, in a sounding organ-pipe?

CHEMISTRY.

DR. EMERSON REYNOLDS.

1. If given pure silver nitrate, how would you use it to illustrate the law of definite proportions?

2. Required 5 liters of chlorine gas (at o° C. and 760 mm.); calculate the weight of MO2 that must be used to produce the gas.

3. How is sulphuretted hydrogen gas prepared? What changes occur when it is passed into (a) chlorine water; (b) lead nitrate solution; (c) zinc sulphate solution ?

4. Give an account of the properties of marsh gas. Find the volume of air required for its complete combustion.

5. What is "choke damp"? How is it detected?

6. Give a short account of the manufacture of coal gas.

7. What is the composition of borax? How is it obtained? For what metallurgical purposes is used?

8. What is the composition of quartz? By what means can it be dissolved?

MINERALOGY.

PROFESSOR SOLLAS.

1. Make a freehand drawing of a crystal of quartz, introducing, with their appropriate symbols, as many faces as you can.

2. A large number of mineral species can be recognised at sight: give an account of those characters (excluding crystalline form) which render this possible.