three years', it is fit for use. From the long yellow roots', washed clean', is expressed a juice', which is boiled to a syrup', and formed into cakes and rolls', ready for market`.

Jane. In Spain', Ma', grows another tree that is very useful; it is mentioned in Don Quixotte`.

Mary Ma', sister means the Cork Tree'; we have it in our list.

Ma. Yes; the Cork tree is indiginous; that is, a native of the southern parts of Europe' and Asia. It is a species of the Oak`; and a very handsome tree'. The bark', which is renewed annually', that is', yearly', is the useful part', but it is not gathered for the purpose of making corks until the tree is fifteen or twenty years old'.

Jane. Then', I suppose', the bark of the tree comes off in large round pieces'.

Ma. It does. and to make these flat', they are piled up with the hollow side down', in damp places, and pressed with heavy weights. They are subsequently dried', packed', and shipped to every part of the world. The business of cutting corks of various sizes for common use', is very simple`; though it requires the finest edge tools.

ARITHMETIC.-LESSON 15.

Single Proportion.

RULE. 1. Put that term which is of the same name and kind with that of the answer, in the 3d place for a multiplier.

2. Then, if, from the nature of the question, the fourth term or answer, must be more than the 3d term; place the larger of the two remaining terms in the 2d place for a multiplicand, and the other, in the 1st place for a divisor.

3. Multiply the 2d and 3d, terms together, and divide the product by the 1st, and the quotient will be the true answer, Thus: If 6 apples cost 9 cents, what will 12 apples cost?

1 2

3

4

2 3

1 4

As 6 12 :: 9: 18 Then, 12X9=108÷6=18. Ans.. NOTE In this question, 9 cents, is of the same name and kind with the answer, and stands in the 3d place; the answer must be more than the 3d term, because, 12 apples will, at the same rate, cost more than 6; therefore 12 occupies the 2d place, and the remaining term, 6, the 1st place. Then 12 multiplied by 9, equa s 108; which, divided by 6, gives 18 cents, the answer, in the same name and kind with the 3d term.

When, from the nature of the question, the fourth term or answer must be less than the third term, then the smaller of

the two remaining terms must have the second place, and the larger, the first place.

Thus: If 18 cents buy 12 apples, how many apples will 9 cents buy?

As 18 9: 12: 6,

Then, 9X12-108 18 6 Ans. NOTE. Here the answer is in apples, and the 3d term is in apples, and because 9 cents, at an equal rate, will buy less than 18 cents, the answer will be less than the 3d term; therefore 9, the smaller of the remaining terms, takes the 2d place, and 18, the larger, the 1st place. Hence, it is evident from both statements, that a large multiplier, and small divisor produces a large quotient; while a small multiplier, and a large divisor yields a small quotient. All questions in Single Proportion may be stated and worked in one or the other of the above modes.

Mary. In speaking of the materials which form our dress', we forgot to mention wool'; it comes next in order upon our list.

Jane. I expect Mamma can tell us something very interesting on this subject'. I will, therefore, lay by my brush', and give attention.

Ma. The various operations by which wool', which you know is the hair or covering of sheep', is converted into cloth', are so different and so complex', às not to be easily understood from verbal description', and not very easily described'. Mary. What is the meaning of complex, Ma?

Ma. Complex, means whatever has many parts involved in each other; or what is not simple`.

Jane. Our best wool', I expect', is imported from Spain; and the second best', from England', is it not, Ma'?

Ma. Yes'; but we raise large quantities of excellent wool in our own country'. I will now mention some of the operations through which the wool passes into cloth. After shearing', it is cleansed and dried`; it is then beaten', and all the dirt picked out. It is next oiled', carded', and spun`; then slightly sized and delivered to the weaver in skeins'. He spools and warps the yarn into a web', and then winds it upon the beam of his loom. He afterwards weaves it by throwing the woof in the shuttle across the web', which produces cloth`. The thread of the woof should be one third larger than that of the warp.

Mary. Ma', do explain warp and woof to us'; my ideas are confused'.

Ma. Warp means the threads that extend lengthwise of the cloth or loom', and woof, those which run across the warp, and are thrown in by means of the shuttle'. The cloth is sent to the dressing mills', where it is coloured, purified, fulled,

sheared, brushed, and pressed', and rolled up for market'. But mixed cloth is generally coloured in the wool.

ARITHMETIC.-LESSON 19.

Single Proportion.

It sometimes happens that the given terms in proportion, are of several names, or compound terms; as, pounds, shillings, pence, &c.; in which case, the 1st and 2d terms must both be reduced to their lowest, or some convenient and like name, and the 3d term, to its lowest or some convenient name. Then the 4th term or answer, will appear in the same name and of the same kind with the 3d term. This, however, can be brought back, by reduction, to any required compound terms.

NOTE. Remember that to bring a high name to a low one, you must multiply the higher name by as many of the lower es equals one of the higher. And to bring a low name to a high one, divide the low name by as many of itself as equals one of the high name. These two directly opposite principles, controul every operation in the reduction of compound terms.

If 2cwt. 1qr. of sugar bring £6 - 12, what will 12cwt. bring?

As 9 48 132: 704. for, 133X48-6336÷9= 704s.÷20=£35 - 4.

NOTE. It matters not whether the 2d term be multiplied by the 3d, or the 3d by the 2d, only let one of them be multiplied by the other, and the product divided by the 1st; the quotient will be the answer.

Practical Exercises in Single Proportion.

(1.) If 4 cords of wood cost 8 dollars, what will 16 cords cost?

As, 4: 16 8:32.

For, 16X8=128÷4=$32, Ans.

As, 32: 16 :: 8:4. 16X8=128÷32=4, proof.

OBS. 1. It may be observed, that of the four terms employell in the proposition, two are referred to wood, and two to money. And that they are proportionate; that is, as wood is to wood, so is money to money; or, as wood is to money, so is wood to money.

OBS. 2. The principles upon which proportion is founded, be thus illustrated.

may

If four numbers are proportional, the product of the extremes, is equal to the product of the means. Therefore, a division, either of the product of the extremes, or of the product of the means, by the first extreme, will give the ofher extreme.

Thus: as 4:9: 16:32. And 32X4-198, the product And 8X16=128, the product

of the extremes.

of the means.

Now the last product divided by the first extreme, (128÷4 32) gives the other extreme, and the first product divided by the first means, (128÷8=16,) gives the other means: Hence the propriety of multiplying the 2d and 3å terms together, and dividing the product by the first term.