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Technical and Bibliographic Notas/Notas tachniques at bibliographiquas

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Q-

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1 2 3

EOYAL AGHICULTUEAL COLLEGE.

SESSIONAL EXAMINATION, JUNE 24, 1851.

Morning — Mathematics & Arithmetic.

1. If the two sides of a right angled triangle are
respectively 30 feet and 60 feet ; What is the length
of the third side ?

2. If the radius of a circle be 60 feet, what are
its circumference and area ; and show how you obtain
the value of T=3. 141 59?

3. What is remarkable about the regular hexagon
inscribed in a circle ? And how has the sexigesimal
division of the circle been obtained from this relation,
also point out the advantages of the decimal division,
and convert 6° ,, 3 ,, 3 into decimal seconds ?

4. What is the difference between '25 and J, and
express * 1 1 T as a vulgar fraction ?

5. Extract the square root of 9876*543 and the
7th root of the same by logarithms.

6. Given one side of a triangle = 60 feet and
two angles respectively 45° and 7 5° to find the other
sides and angles ? And also the area ?

7. If in a triangle two sides are given, 50 feet and
100 feet respectively and the included angle 30^,
what is the 3rd side and the other angles ? And the
area?

8. The sides of a triangle are respectively 36, 48,
and 60 feet, find the angles and area ?

9. Prove Ptolemy's theorem, and deduce from it
the following relation, expressed in Trigonometrical

language.

When rf and e represent any two arcs, and r the radius
r. Sine (^/ie) =: Sine ■>]. Cos e ± Cos tj . Sine e

and from this prove that in trigonometrical language

r Sine i; = 2 Sine | rj . Cos i rj ;
show also how this is used in finding the rule or for-
mula for the area of a triangle in terms of the sides.

10. Solve the equation 2a? -{ Ja? i 3 — 5x=\ — 2a?.

'a/i(fU^

iJl

Evening. — Surveying & Engineering.

1. Point out the optical and mathematical prin-
ples and the mechanical contrivances by which the
Sextant is suited to measure angles ; and prove that it
can indicate correctly the magnitude of anv angle less
than 120°.

2. What is the height of a tower, the angle of
whose elevation is 45° at a distance of 1 .3 chains ?

3. How many square miles are in the area of a
triangular Estate, whose sides are 30 miles, 60 miles,
and 36 miles respectively.

4. How does the water act in Irrigation, and state
the princfptewules for irrigation, as well as the most
suitable soils for water meadows ?

5. Write down detailed instructions for Draining
a 50 acre Field, including size of main drain, &c., the
fall of which may be made 8 feet in a mile.

6. What difference would you be called on to
make in order to secure the same results, if the fall
was only 4 feet per mile ?

7. How rr^ich cutting would you require in order
to remove a hill 1 mile long on an ordinary road, whose
slope in either direction you find 400 feet in a mile,
so as to leave it 1 in 20.

8. Describe all the instruments employed and the
processes gone through in the collection of the follow-
ing notes ; reduce them and plot the section by writing
figures for height and distances, (or to a scale of 3
chains to an inch horizontal and 20 feet to an inch
vertical;) also, write down the elevation of one end
of the section above the other ;

Back
Staff,
feet.
3.56

Fore
Staff,
feet.
2.25

4.26

5.38

6.83

5.32

3.66

17.44

Distance
in links.

300

On B. M.
R.A.C.

Avenue

500

gate-post.

700

1000

Farm
Buildings

^^A^^^^