than ID, and why does it not move in the same direction in cases of myopia of ID and less?

4. What are the modern views with regard to the nature and causes of glaucoma? Give the signs and symptoms of acute glaucoma, and point out in what way they differ-(a) from those of chronic glaucoma ; and (b) from those of a severe attack of iritis.

5. What are the dangers attendant on swelling of the lens in cases of traumatic cataract, and how would you endeavour to avert them?

6. What is Holmgren's Test for Colour Blindness, upon what theory of the colour sense is it based, and in what diseases do you expect to find defective colour perception?

SCHOOL OF ENGINEERING.

ENTRANCE EXAMINATION.

MR. PANTON.

1. If the square of one side of a triangle be equal to the sum of the squares of the remaining sides, the angle opposite to that side is a right angle?

(a) The sides containing the right angle of a right-angled triangle are 8.5 and 20.4, calculate the length of the perpendicular from the right angle on the hypotenuse.

2. Prove the proposition which determines the relation between the square of one side of any triangle and the squares of the other two sides, and hence write down the expression for the cosine of any angle of a triangle in terms of the sides.

3. In a given circle inscribe a regular hexagon.

(a) If the side of a regular hexagon inscribed in a circle be 10 inches, calculate the area of either segment into which this chord divides the circle.

4. Prove that two triangles which have an angle in one equal to an angle in the other, and the sides about the equal angles reciprocally proportional, are equal in area.

(a) How is the area of a triangle expressed in terms of two sides and the included angle ?

5. Rationalise the denominator of the fraction

√23 V12

√23 + VI2

and calculate its value to 5 decimal places.

10. Given log 3 = .47712, and log 5 = .69897 find the value of log V675.

JUNIOR CLASS

1. Given the three sides of a plane triangle, a 174.07, b = 232, c345; calculate the angle A.

2. A base line of 200 yards is measured on one side of a river; the lines joining its extremities to an object on the opposite side of the river are observed to make with the base line angles of 68° 2′ and 73° 15′, respectively; calculate the distance of this object from each extremity of the line.

3. In a quadrangular field ABCD the following measurements are made:-BC=265 yds., AD=220 yds., AC=278 yds., AE = 100 yds., CF 70 yds. (where E and F are the feet of perpendiculars BE and DF let fall on the diagonal AC); calculate the area of the field in acres.

4. Find the perimeter of a regular polygon of 25 sides inscribed in a circle whose radius is 14 inches; and determine by what amount it differs from the circumference of the circle.

5. Calculate, by the aid of the tables, to 5 decimal places, the superficial area of a sphere whose volume is 70,000 cubic feet.

6. In order to calculate the area bounded by a curved line, thirteen equidistant ordinates are measured as follows:

10, 11, 12, 14, 16, 18, 21, 24, 28, 29, 29, 27, 24,

the common interval being 1.5; find the area included between the first and last ordinate.

10. Prove Maclaurin's theorem, and apply it to expand cos 3x to the fourth power of x.

11. Draw a rough tracing of the curve

6y=2x3 + 3x2 - 12x+6,

and find the values of x which correspond to the maximum and minimum values of y.

12.

Prove, by any method, that the volume of a pyramid is equal to the area of its base multiplied by one-third of its altitude.

DR. TRAILL.

1. How far will a force equal to the weight of 25 lbs. move a mass of 1000 lbs. in 5 seconds?

2. A body moving with uniform acceleration traverses 544 feet in the ninth second of its motion; find the acceleration.

3. If the two equal weights in Attwood's machine be each 31 oz., find what additional weight should be added to either to get up in both, in one second, a velocity of one foot per second.

4. Find, in the same case, the tension on the cord, and the pressure on the axle of the pulley over which it passes.

5. The arms of a false balance are to one another as 24 to 25; the weights are in a pan suspended from the longer arm; find the real weight of a body whose apparent weight is 96 lbs. ; what would it appear to weigh, if the arms were transposed?

6. If two forces be represented by the two diagonals of a parallelogram, what relation will their resultant have to the sides of the parallelogram ? 7. A bar of cast iron (sp. gr. =7.2), whose length is 10 decimetres and cross section 50 square centimetres, weighs 34 kilograms. Is there any flaw in the casting? If so, what is its size?

8. If the base of a cylinder have a radius of 10 inches, and if in the cylinder there be mercury to the height of 2 inches, and a layer of water

above the mercury to the height of 8 inches, find the total pressure on the base of the cylinder (sp. gr. of mercury

=

13.6).

9. Show that if a cube or a sphere be filled with liquid, the total pressure to which it is subjected is three times the weight of the liquid it contains.

10. If the atmosphere be supposed to have a uniform density of .0013, find its height in miles, taking the average height of the barometer at the sea level at 30 inches.

MR. JOLY.

1. Explain how the metric units of weight and volume are derived from the fundamental unit of length. How was the length unit obtained ?

Draw up tables showing the multiples and submultiples of these units arranged in order.

2. A regular hexagonal pyramid is placed with its apex one inch above. the H. P.; its base, which is horizontal and uppermost, measures one inch on each edge; the altitude of the pyramid is 2". Draw plan and elevation.

3. Find the shadow cast on the H. P. by the pyramid of last question. 4. The pyramid of question 2 is cut by a plane, making 45° with the horizontal plane, and having its horizontal trace at right angles to the vertical plane; the cutting plane bisects the base of the pyramid. Obtain the surface of section.

5. Draw an ellipse (axes 3" and 2") by any method.

6. An angle of 45° is contained by two lines, one of which makes 60°, the other 45°, with the horizontal plane. Reduce the angle contained by the two lines to the horizon.

7. Construct a scale of 6" to one statute mile, showing one mile and one thousand feet. What is the R. F. of this scale ?

8. Knowing the ratio that English measure of length bears to Irish, deduce graphically from the foregoing scale a similar one for Irish measurement. (If question 7 is not put in, show how you would set about the deduction.)

9. A parallelopiped, 2" × 1" x 1", rests with one of its faces on a horizontal plane, and another inclined at 15° to a vertical plane. Draw a horizontal projection of the solid, when the horizontal plane has been raised through 30° about a hinge at right angles to V. P. 10. Read the vernier scales submitted to you.

1. Explain how to calculate the specific gravity of a substance, such as gunpowder, which is partially soluble in water.

2. The coefficient of expansion of iron is .0000067 per degree Fahrenheit calculate the expansion between summer and winter of a girder 250 ft. long.

(a) What work would it do in a year if it were subject to a stress of 125 tons?

(b) What power would it be developing?

3. Explain how the coefficient of expansion of a gas may be measured.

4. Describe any method of measuring specific heats.

5. Calculate the weight of aqueous vapour in a room 10 ft. by 20 ft. by 30 ft., when the pressure of the vapour is .75 in., and its temperature 75° F. [N. B.-The density of aqueous vapour relative to air is .622, and the weight of 1 cub. ft. of air at 32° F. and 30 in. is .08 lbs.]

I

6. Explain how to determine the kind of electricity on a body by means of a gold-leaf electroscope.

7. Describe how electro-magnets are constructed.

8. Explain how to produce an induced current by means of a magnet. (a) Describe how long this induced current will last, and the direction of the force this induced current exerts on the magnet.

9. Describe experiments to show that solids can be set in vibration in series of loops and nodes.

10. What are the laws of reflection of a ray of light ?—and deduce from them the way in which a pencil of rays is reflected.

DR. EMERSON REYNOLDS.

1. Calculate the percentage of chlorine in pure common salt

2. Find the weight of oxygen gas obtainable from one gram of potassium chlorate (K = 39. 0 = 16).

3. Required the weight of potassium nitrate necessary for the production of 10 grams of nitric acid (N = 14).

4. Trace the chemical changes that occur within the leaden sulphuric acid chamber.

5. How is "bleaching lime" made? Explain by an equation the action of dilute sulphuric acid on the body.

6. Give an account of the extraction of sulphur from iron pyrites.

7. How is the diamond proved to be pure carbon ?

8. A compound afforded on analysis