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This issue of bank notes will cause a general advance in the prices of commodities.

This general advance of prices will check exportation and encourage importation.

This decrease of exports and increase of imports will turn the exchanges against us.

The exchange being turned against us, will cause a demand for the exportation of gold.

This demand for the exportation of gold will cause the notes to be taken to the bank of England, and payment demanded in gold.

The notes in circulation will thus be diminished, and the currency will again be placed in a sound state.

The sorites, it will be seen, embraces a number of arguments connected together. It is therefore called a chain of reasoning. It resembles a chain in this, that if one link be broken, the whole argument is destroyed. In the example we have just given, the third link is denied by Mr. Tooke, who contends that an increase in the amount of the circulation has no effect on the prices of commodities. Were this doctrine demonstrated, the chain would be broken, and the whole reasoning annihilated.*

The sorites is the form of reasoning employed in mathematical deductions. If you pay attention, I will give you an illustration of this, and explain it so clearly, that you will be able to understand all the operations, even though you may not have learned algebra. I take the question from one of my old school-books :

"When first the marriage knot was tied
Betwixt my wife and me,

My age did hers as far exceed

As three times three does three;

But when ten years and half ten years

We man and wife had been,

Her age came up as near to mine

As eight is to sixteen.

Now tell me, I pray,

What were our ages on the wedding-day?"

I will presume at starting that you know the sign + denotes plus or more, the sign denotes minus or less,

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"A chain may be composed of both strong and weak links, but its strength as a chain can never be greater than that of the weakest link in it."-Bailey, p. 58.

X denotes multiplication, and denotes equality. Now then we will begin. The figures 1, 2, &c., at your left hand express the number of operations.

1. Let the age of the wife on the wedding-day be represented by the letter z.

2. Then, as the husband's age to the wife's is as "three times three to three," his age must be three times z, say 3 r.

3. Ten years and half ten years are equal to fifteen years. 4. At the end of fifteen years the wife's age will be z + 15, that is, z added to 15.

5. And the husband's age will be 3 x + 15, that is, three times z added to 15.

6. By the question, the wife's and the husband's ages should at this period be in the proportion of 8 to 16. As 8 is to 16 so is + 15 to 3x + 15; expressed thus;

8: 16 :: + 15 : 3 x + 15.

7. Now you know by the rule of three, that if the two extremes (that is, the first and the fourth terms) be multiplied together, the product will be the same as the product of the multiplication of the two means (that is, the second and third terms). Now,

3+15 multiplied by 8 give 24x + 120, and

+15 multiplied by 16 give 16 x + 240.

8. As these two products are equal to each other, we thus form our equation;

24+ 120 16x + 240.

You will read the equation thus,-Twenty-four z plus 120 equal sixteen plus 240.

9. Our next operation will be to transpose the 16 zx to the other side of the equation. In doing this we must of course change the sign. As it is now plus, we must make it minus. Our equation will then stand thus ;

240;

24x · 16x + 120 = that is, 24 x minus 16 x plus 120 equals 240. 10. We will now deduct the

tion will stand thus;

16 x from the 24 x. The

8x+120 240.

equa

11. We will now transpose the 120 to the other side of the equation, changing its sign of course, thus;

8x= 240-120;

that is, 8 x equals 240 minus 120.

12. We will now deduct the 120 from the 240, and the equation will stand thus ;

8 x

120.

13. We will now divide both sides of the equation by 8, and we shall have,

1 x = 15.

14. Now then we have discovered the value of x; that is, we have found that the age of the wife on the wedding-day was 15 years. And as the husband's age was as three times three to three, his age must have been 45. Then after ten years and half ten years-that is, 15 years—the wife's age would be 30 and the husband's 60, which is as eight is to sixteen.

You see what a beautiful process of reasoning we have gone through, and with what certainty we have arrived at the result. This is called mathematical reasoning. It is the kind of reasoning employed in Algebra, Geometry, Astronomy, Navigation, and the other Mathematical Sciences.

I will close this Section by another problem :

"While I was coursing on the forest grounds,
Up starts a hare before my two greyhounds:
The dogs, being light of foot, did fairly run,
Unto her fifteen rods just twenty-one.
The distance that she started up before
Was fourscore fifteen rods just and no more.
I pray you, scholar, unto me declare,

How far they ran before they caught the hare?"

1. For the distance they ran put x.

2. Then the distance the hare ran will be x 95 rods. 3. Then as 21 is to 15 so is x to x

21: 15 :: x: x

95.

95

4. Then multiply the two extremes

together and the two

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means together, and we have an equation, thus :

21 x

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15 x.

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=

=

1995.

332 rods.

Distance run by the dogs, 3324 rods.
Do. (95 less) run by the hare, 237 do.
As 21 is to 15 so is 332 to 237.

SECTION VI.

SERIES OF REASONINGS.

We have shown that a chain of reasoning consists of a number of reasons so connected with each other, that the failure of one reason would destroy the whole argument. A series of reasoning denotes a number of reasons all bearing to prove the same sentiment, but so far unconnected with each other, that the failure of one reason does not weaken the force of the others.

It is impossible to lay down rules whereby a number of reasons may be so arranged as to produce the best effect in establishing the point for which they are adduced. Indeed, people who are sufficiently skilled in logic to be able to maintain their sentiments in a set discourse, must have acquired that systematic habit of mind which will suggest the best rules for the arrangement of their thoughts. For the sake of the young we will transcribe a few rules, which have chiefly a reference to the writing of themes, published by an author who has had great experience in tuition :

"In treating of method in reasoning, it is common to divide it into two kinds, analysis and synthesis. All, however, that seems necessary to be said in this treatise concerning these distinctions, is, that in the mode of reasoning called synthesis, the proposition is the conclusion sought; but in the reasoning called analysis, the conclusion cannot be previously proposed; for till the arguments on which it depends are unfolded, it is presumed to be unknown. In reasoning synthetically, the arguer knows beforehand what is to be established: and he may, at his option, propose it first, and add his arguments afterwards, or he may neglect to state the intended proposition, till he has brought forward what he has to advance in support of it. In reasoning analytically, the arguer lays down nothing to be proved, nor has he any foreknown conclusion in view, but he goes on, unfolding one argument after another, till he reaches a conclusion. Analysis, therefore, is the way by which we attain truth; synthesis, that by which we communicate it. We pursue the method of analysis, when, not having formed our judgment on a subject, we think to ourselves in order to form one: we pursue the method of synthesis,

when our judgment is formed, and we undertake to convince others. It is scarcely necessary to add that in writing themes, the principle on which we proceed is synthesis.

"Before anything more particular is advanced on the method of writing themes, it must be mentioned, that the manner in which a theme is given out, determines what latitude is allowed to the writer in treating it. When a theme is given out thus— 'On education,' On a knowledge of the world'the theme may be called unlimited; for the writer is left to lay down any propositions to be proved which he may think fit, provided they bear a due relation to the subject. But a particular proposition being laid down to be proved, necessarily limits the theme; as for instance, when a theme is given out thus-Man is the creature of education; A proper knowledge of the world is favourable to virtue.' This kind of theme is called a thesis,- -a Greek word signifying position or proposition;—in the plural, theses. An unlimited theme generally contains many theses; for whenever the writer goes into a new branch of his subject, he must lay down, or have in view, some new proposition, that is, a thesis. In a limited theme there is but one main proposition, to which every other ought to be subservient. This main proposition is called, by distinction, the thesis, and the theme which is written in support of it, takes the same name."

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Suppose the theme given out to be 'Friendship;'-teachers recommend the pupil to consider it under the following heads :the Definition; the Cause; the state in ancient and in modern times; the Advantages; the Disadvantages. Proper answers to the following questions will form such a theme as is here required:

1. What is friendship? 2. What is the cause of friendship? 3. What was anciently thought of friendship, and what examples are on record? 4. What is friendship often found to be in these days? 5. What are the benefits of true friendship? 6. What are the evils of false friendship ?"

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'When, instead of an unlimited title, a thesis is given out to be proved, teachers recommend the following heads as helps to find the arguments :-the Proposition; the Reason; the Confir mation; the Simile; the Testimony; the Example; the Conclusion. Under the first head, the writer restates his thesis in such a shape, that the arguments he designs to use will easily connect with it. Under the second, he brings forth the strongest direct internal argument he can find in proof of it, that is, from the nature of the thing, from enumeration, from the cause, the effect, the adjuncts, the antecedents, or the consequents. Under the third, he tries to strengthen his proof by showing the absurdity of the contrary proposition, or by advancing some fresh argument of whatever kind that is not taken from the same source as the

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