product of

Whence the numbers are found to be 5 and 8.

14998 × 3 = 40 =

Applying

8 persons were concerned.

following five figures.

DRAWING.

In continuation cf my remarks in your last impression, I beg to send the They are to be drawn on the black-board. The teacher takes his chalk and

or fireplace? Does the window open from Derow, or avove: Du༠ དཔས‧ bour keep Cochin China fowls? Is J. N. a strong or a delicate man? Does he easily catch cold? Does he refer to winter or summer? Has he only himself to consult? We certainly do not recommend that the window should be open in winter if the room is small and the sleeper delicate; we recommend in this case the open door. If he is vigorous and the weather mild, we constantly practice the habit ourselves. J. N. demands a reason. A philosophical one would require some paper. A sleeping man consumes oxygen, and eight hours is a very long time to shut out a fresh supply, but what can get through the key-hole. On the other hand a draught causes the moisture of perspiration (which is greater during sleep) to become vapour, and the process of evaporation cools the body, as vapour requires a larger amount of heat.-ED.]

following five figures.

DRAWING.

Yours respectfully

FAUST.

In continuation cf my remarks in your last impression, I beg to send the They are to be drawn on the black-board. The teacher takes his chalk and

stands near the board dictating one line at a time, at the same time drawing the line on the board himself.

See that every child keeps up, and that each line is done properly, before another is attempted. The paper or slate is to be kept in one position before the learner, and never moved for the convenience of making a line. The hand must not be placed on the side of the slate as a guide in drawing straight lines.

(1.) To draw a square.

Draw any perpendicular line A. B. Divide it into two equal parts in (1.) Place 1-2 on each side the point (1) equal to half the line. Join 2 and 2 with A and B-when the square will be completed. Erase all dotted lines when each fig. is completed.

(2.) To draw a circle.

Draw a square as above. Then draw a circle round it. The sides of the square and the four corners will serve as guides to the eye, to draw the circle correctly at its proper relative distances.

(Allow no one to rest the finger on the centre and so strike the circle.) (3.) To draw a vase.

Draw a perpendicular line A. B. Divide it into three equal parts in 1-2. Bisect from 2 to B. in 5. On each side of point (1) place 1-3 equal to the line. At top place on each side A 4 equal 2-5. Drop perpendiculars (4-6) from their ends upon 1-3. Join 3-5. Divide 4-6 into three equal parts. Place the curves on the lines as in the figure.

Finish as above by straight lines at top, and place a foot to it.

It may be asked why go so mechanically to work? My answer istime is saved, -symmetry and correctness are more easily secured, and the art is learnt much faster. The student is better able to guide his eye, by having a series of points (straight lines), from which he is to keep his curves at proper distances. The most intricate figures can always be simplified by two or three straight lines.

(4.) To draw a jar.

Draw a perpendicular line A. B.

Divide it into 4 parts in 1-2-3.

Trisect from A. to 1 and 1 to 2 in points 8-9-6-10. Place line A-9 on each side of point 9 in 9-5.

Place on each side B. in B-4.

Place A-7 on each side of A. in A-11 and 6-12.

Join points 11-12-5-4.

Draw curves and finish as in figure. A handle is readily placed in its proper position.

(5.) To draw a bottle and glass.

Only a few lines will be indicated as it will be assumed the method is partially comprehended.

A-B. is bisected in 1. The lower portion is again bisected in 2 and the upper trisected in 3-3'

A-5 equals from A to 3.'

2-6 from 2 to 3.

1-4 from 1 to 2.

I will show in my next how a few more intricate figures may be mastered, as leaves, &c.

I shall be glad to attempt to meet difficulties that may be experienced by enquirers,

H. E.

Examination Papers.

CHELTENHAM NORMAL COLLEGE.

MIDSUMMER, 1858.

ARITHMETIC AND EUCLID.

FIRST YEAR.

ARITHMETIC.

SECTION I.

1. Divide £125 13s. 114d. equally an ong 42 persons; and, supposing 15 of then to have received their portions, and of the rest only 22 to appear, how much might be given to each of these?

2. What will it cost to carpet a room 21ft. 10in. long, and 13ft. 9in. broad, the carpet being yard wide, and costing 5s. 6d. per yard?

3. A contract is to be finished in six months ten days; and 50 men are to be set to work at once; at the end of of this time it is found that only of the work is done: what extra number of hands will be required to complete the contract, the last man employed working 12 hours per day, while the first lot worked throughout ten hours per day?

SECTION 11.

I. What truths are assumed in the process of dividing by ? Demonstrate each step of the process.

2. Find the value of

3. Show how to reduce a circu ating decimal to a vulgar fraction, and demonstrate the process.

Find the value of '0432; 09318; and 11.287

SECTION III.

1. Find the difference between the Simple and Compound Interest of £40 13s. 4d. for three years, at 4 per cent.

2. At what price must linen, which cost 2s. 741. per yard, be sold, so as to gain 5 per cent., besides allowing a discount of 5 per cent. to the purchaser? 3. How much stock may be purchased by the transfer of $2,500 stock from the 3 per cents. at 94 to the 3 per cents. at 97, and what change in income would be thus effected?

EUCLID.
SECTION I.

1. Upon the same base and on the same side of it, there cannot be two triangles, which have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.

What methods does Euclid employ in the demonstration of a Theorem? Describe each fully.

2. "The opposite sides of parallelograms are equal." State and prove the converse of this proposition.

3. If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side: namely, the side opposite to the equal angles in each; then shall the other sides be equal, each to each, and the third angle of the one equal to the third angle of the other.