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8. What is the colligated acid which has been found by Liebig in human urine? what the proximate principles into which it may be resolved, the formula of each of these, and that of the original acid?"

9. How is a solution of gelatine obtained, and what are the particulars in which it differs from one of albumen? Mention also the two vegetable acids, solutions of which are best distinguished by one of gelatine.

10. Write the general formula for the alcohols, and explain how amylic alcohol is converted into valerianic acid, this into valerianate of soda, and this into valerianate of zinc.



1. Distinguish parasites from epiphytes; and green from coloured parasites.

2. Explain the anatomy of a leaf, stating the contrivances for maintaining its healthy condition, and the causes of its final decay.

3. Explain the terms used to express the various cohesions and adhesions of stamens.

4. Give instances of a concrete, single style occurring in plants having an apocarpous or deeply-lobed ovary.

5. How are Gentianeæ known from Apocynea? and what are the ordinary medical properties of these Orders, respectively?

6. How are Jasmineæ known from all monopetalous Orders with regular corollas? and what is their chief product?

7. Distinguish Myrtacea from Rosacea (Sub. Ord. Pomea) by characters of flower and foliage.

8. What are the principal characters of the flower, inflorescence, and foliage in Rhamneæ ?




1. Calculate the number of cube yards in a railway cutting of the following dimensions:-Base at formation level, 30 ft.; the lengths being, from the commencement at A to B, 540 ft.; from B to C, 810 ft.; from C to D, 1080 ft.; the heights at A o, at B 23 ft., at C47 ft., and at D=0 ft.; the side slopes being to 1. Each separate block and the total quantity must be brought out in cubic yards.


2. Supposing the fencing to be 5 yds. on each side, compute number of acres and decimals of an acre, to two places, required for the cutting in No. I.

3. Calculate the number of square yards of soiling of the slopes in the excavation in No. 1.

4. Give in full detail the proof of the formulæ employed in the answers to Nos. 1, 2, and 3.

5. In a segmental arch, 54 ft. span, and 9 ft. rise, calculate (a) the radius, (b) the length of the arc of the intrados, and (c) the cube yards of masonry in the sheeting of the arch; the depth of the voussoirs being 2 ft., and the distance from face to face of the bridge equal 30 ft.

6. In the segmental arch in last question it was required to draw the elevation at the full size on the platform, calculate the ordinates at points 8 ft. and 19 ft. from either springing.

7. If the arch had been a semi-ellipse, with the same rise and span as in No. 5, compute the ordinates at the same points as in No. 6.

8. The string course and parapet of a bridge, 560 ft. long, have a slight curvature, being a circular arc 5400 ft. radius; calculate by the approximate method the rise at the middle point, and at the points 140 ft. from the centre on each side.

9. A railway crosses over a road, 30 ft. wide, at an angle of 45°; the bridge carrying the railway is 30 ft. wide from face to face. Calculate

(a). The oblique span and length of the impost.

(b). The soffit breadth of the voussoirs, which are 57 in number.

(c). The angle ẞ, and the number of courses which comes nearest to equality with the "divergence of the courses."

10. In the same bridge as No. 9, compute the angle 4, the depth of the arch sheeting being 3 ft.; giving the proof of the formula you employ.

II. The winding strips being the same length as the depth of the courses, and held 3 ft. apart; calculate in inches and decimals the excess of the broad end of the strip which gives the twist of the bed.

12. On the contour lines on the accompanying plan, draw a line from the point A which shall have an inclination of one in nine.

13. The upper part of an excavation requiring a flatter slope than the lower part, consisting of rock or firm ground; investigate and fully prove the formula for computing the cubic content of the upper blocks of the cutting; and deduce the expression for the error of the approximate method, pointing out when it is in excess, and the contrary.



1. A mass, a ton weight, rests on a rough horizontal plane; required the coefficient of friction, if a pressure of 56 lbs. be the least force that will suffice just not to move it.

2. A square pillar, 20 feet high, I foot broad, and 1 tons weight, is supported in a position inclined 66° to the ground by a horizontal rope attached to its uppermost edge; required the tension on the rope.

3. In the same case, required the least coefficient of friction that will suffice to prevent the pillar falling by sliding on the ground.

4. A wall of brickwork, 50 feet long, 20 feet high, and 1 feet thick, sustains the pressure of a roof applied at its upper internal edge, and inclined 35° to the horizon; required the greatest weight of the roof that will not overturn the wall.

5. The section of a river wall of granite whose specific gravity = 2.7 a rectangular trapezium, of which the sloping side is turned to the water, and inclined 80° to the horizon; if the water be 20 feet deep, required the least breadth of base that will prevent the wall being overturned.

6. The roadway of a suspension bridge, supported by four chains between piers of equal height, is 1 ton weight per foot; if the span be 100 feet, and the central dip of the chains 720 feet, required the tension at the lowest point of each chain, its own weight being neglected.

7. A uniform horizontal bar, 20 feet long, 4 in. deep, and 3 in. thick, is supported but not fixed at its extremities; required its central deflection under the action of the weight placed at its middle point, which if applied longitudinally would extend or compress it o.1 inch.

8. A sphere, 112 lbs. weight, rolls down a rough inclined plane under the action of gravity; if the length of the plane be 100 feet, and its inclination to the horizon 30°, required its time of descent in seconds.

9. A uniform bar, 10 feet in length, and 56 lbs. in weight, revolving uniformly 20 times per minute round its middle point, strikes at either point of trisection against an elastic sphere, 7 lbs. weight; if the sphere be at rest before the collision, required its velocity after.

10. The rim of a fly wheel, revolving uniformly five times per minute, is annular in form, 1 ton in weight, I foot in thickness, and 20 feet in mean radius; estimate in foot pounds the entire work accumulated in it.



1. Calculate the pressure of steam raised at a temperature of 250°.
2. Find its relative volume.

3. How much does the last result differ from that given by the empirical formula?

4. Calculate the work done by the evaporation of a cubic inch of water at 212°.

5. If w is the work done when the steam is cut off, and W the whole work after the steam has expanded E times, prove the following formula:

W = w(1 + λog E).

6. Calculate the whole work done for a tenfold expansion.

7. How may this be calculated by Simpson's rule?

8. What are the two fundamental equations for a double-acting stationary engine?


1. The sides of a right-angled triangle are 3 and 4; what are the segments into which the hypotenuse is divided by the perpendicular from the opposite vertex?

2. Solve the equations,



1. Differentiate

√x + 2 =√/2x+7,



x + I

x + 2

3. What is the cube of 1+√3?

4. Divide the angle 80° into two parts such that the sine of one may be three times the sine of the other.

5, And such that the tangent of one may be three times the tangent of the other.

= 2

6. Find the angles and area of the triangle whose sides are 537, 784, 626.

7. If 6 sin 20-3 cos 20 = 1, find 0.

8. Trace the curve whose equation is

3. Expand, by Taylor's of h.

4. Find the value of

y=x+1+x√16 – x2.


+ 4 + 2x

+log (x+2+√x2 + 4x + 5) + tan -1



2. What will be the result of substituting x + h for x in x1 — 4x3 +6x2 −7x+8 ?


x - sin x

theorem, tan (x + h), according to the powers

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when x=0.

sin x

5. What values of x make (x-2)3 (3 − 4x)2 a maximum or a mini

mum ?

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7. Find the intersection of two planes, whose horizontal traces are parallel.

8. Prove that if a line be perpendicular to a plane, either projection of the line will be perpendicular to the corresponding trace of the plane.

9. Exhibit the angle which two intersecting lines make with each other.

10. Find the points of intersection of a line and a cone-
(a). When the line is perpendicular to the horizontal plane.
(b). When the line has any position.



1. Given the directions of three forces which equilibrate at a point, and the magnitude of one of them; determine the magnitudes of the other two.

2. If forces proportional to the lengths act perpendicularly at the middle points of the sides of any polygon; prove that they will equilibrate each other.

3. A mass of given weight rests on a rough horizontal plane; given the coefficient of friction, determine the magnitude and direction of the least force that will suffice just not to move it.

4. A beam capable of motion round a hinge is supported in a position inclined to the vertical by a cord attached to a fixed point; given the particulars of the cord and beam, determine the tension on the cord and the pressure on the hinge.

5. A body is drawn along a rough horizontal plane by the weight of a descending body to which it is attached by a cord passing over the edge of the plane; given the coefficient of friction, required the tension on the cord.

6. In the ascent and subsequent descent of a body projected vertically upwards in vacuo, and acted on by gravity; prove that the ascending and descending velocities are equal at all common altitudes.

7. State and prove the proportion which gives the statical from the dynamical measure of the centrifugal force of a body of given mass revolving uniformly in a circle of given radius.

8. In the direct collision of two imperfectly elastic spheres; given the masses, and velocities before impact, determine the velocities after.

9. A cylindrical vessel filled with water stands on a horizontal plane; determine where an orifice should be made in its side so that a horizontal jet of the water should have a given range on the plane.

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