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good parent. If a case like this were presented to a thousand persons, from as many different parts of the world, there would be but one judgment and one feeling; all would judge the conduct of the son to be blameable. Different degrees o moral disapprobation would be felt by those whose moral ence in the opinion entertained of his conduct. All would feel disapprobation, accompanied by a desire for the punishment of the offender. It is found that savages appear to have but an obscure exercise of conscience, but in proportion as their minds are cultivated, this faculty becomes more manifest, and operates more forcibly.

the historical fact adduced by Dr. Paley, from the history of Valerius Maximus, is not at all suited to his purpose; because the case is very complex, and one on which it is difficult to determine at first view, what the true moral character of the action is. The facts, as related by him, are as follows: The father of Caius Toranius had been proscribed by the Trium-faculty was in a cultivated state; but there would be no differvirate. Caius Toranius-coming over to the interests of that party-discovered his father's place of concealment to the officers who were in pursuit of him, and gave them, withal, a description of his person by which they might distinguish him. The old man, more anxious for the safety and fortunes of his son than for the little that might remain of his own life, began immediately to inquire of the officers whether his son were well, and whether he had done his duty to the satisfaction of the generals. That son (replied one of the officers), so dear to thy affections, has betrayed thee to us; by his information thou art apprehended, and diest.' With this, the officer struck a poniard to his heart, and the unhappy parent fell, affected not so much by his fate, as by the means to which he owed it." Now, the question is, if this story were related to the wild boy caught some years ago in the woods of Hanover, or to a savage without experience and without instruction, cut off in his infancy from all intercourse with his species, and consequently under no possible influence of example, authority, education, sympathy, or habit, whether or not such a one would feel upon the relation any degree of that sentiment of disapprobation of Toranius's conduct which we feel.

In our judgment, such a case would afford no criterion by which to determine whether men possess constitutionally a moral sense. For, in the first place, the trial would be no better than if the question were proposed to a child two years old, in whose mind the moral faculty is not yet developed. A human being, arrived at adult age without instruction or communication with others, would be-as it regards to the mindin a state differing very little from that of infancy. It is not held that the moral sense will be exercised without the usual means by which human faculties are developed. If an organical defect in the brain should prevent the intellectual faculties from coming into exercise, the unhappy individual thus deprived of reason would prove nothing in regard to the operations of reason where it is developed. So, also, if a human being were brought up from early infancy in a dark dungeon, and if no information were communicated to him, the mental faculties would not be developed, and it would be absurd to have recourse to such a one to ascertain what faculties belong to the human mind. The same remark will apply to the case of the wild boy, referred to by. Dr. Paley; and also, though in an inferior degree, to savages of the most degraded class.

THE MORAL FACULTY, ORIGINAL AND UNIVERSALIf conscience were not an original faculty, enabling us to form a conception of moral qualities, man could never acquire such an idea by any other means. The opinion, therefore, that moral feelings are merely the effect of instruction and education, is erroneous. For every class of simple ideas there must be an appropriate faculty, without which these ideas can never be acquired. In regard to the bodily senses, this is too evident to be called in question. Without the organ of vision, the simple idea of light and colours could never be communicated by any instructions; without the organ of hearing, no idea of sound can be conveyed; and so of the other senses. And it is equally true of that knowledge which is acquired by what some have called the internal senses. If there were in man no such faculty as taste, by which beauty is perceived, no idea of the beautiful could possibly be communicated. A horse has no perception of the beauty of a scene which perhaps enchants his rider, even though the animal sees all the objects with equal distinctness. So it is in regard to moral qualities. There must be an original faculty to give us the simple idea which we have of morality; otherwise the idea of virtue or vice could never have entered the human mind, and the feelings of moral obligation, of which all men are conscious, would never have been felt.

We are aware that those who advocate the utilitarian scheme, resolve all our ideas of morality and moral obligation into the mere principles of benefit or injury, apprehended to be connected with each action. Dr. Paley informs us, that the subject continued to be involved in impenetrable mystery, until he took this view of it.

It is deemed useless to argue this point; it cannot be decided by reasoning. The appeal must be made to the consciousness of every man.

Let it then be fairly understood what it is which is asserted in regard to conscience, as an original, universal faculty. It is, that every human mind, when its faculties have been developed, and have arrived at some degree of maturity, dis-examination of this subject has not been made. It is recomcerns a quality in certain actions which is termed moral; that is, it intuitively perceives that some actions are right and

some wrong.

Another objection to the historical fact adduced by Dr. Paley, is, that it presents to the mind, not a case of simple, unmixed good or evil, but a complex case, in which-before a judgment can be formed of the action of the son-it must be decided whether a man ought to be governed by a regard to the welfare of a parent, or to the public good. If the son believed that the party in pursuit of his father was promoting the public good, he might feel that he ought to be governed by this rather than by filial affection. Here, then, we have presented a complex and difficult case in morals, about which men would be very apt to differ; and we are to determine whether all men-even those totally uneducated-would view it in the same light.

If any one persists in declaring that he sees no evil in any action but as it is evidently detrimental to human happiness, nothing can be said in the way of argument to alter convictions derived from his own consciousness. All that is proper to be said is, that the mind of such a person is differently constituted from that of most men; cr rather that an impartial mended to such persons carefully to scrutinise the exercises of their own minds; they will perceive that the idea of virtue or moral good is entirely distinct from that of mere utility. There is, indeed, a connexion between these two things which is very intimate, and this seems to have misled many in their judgments. Virtuous conduct leads to happiness, and is always beneficial; yet our idea of its moral character is not derived from this consideration, but from the nature of the action itself.

A MORAL FACULTY BEING SUPPOSED, WHETHER
ITS DICTATES ARE UNIFORM?

One of the strongest objections which has been brought against the doctrine laid down is, that among men of different countries, and of entirely different education, there is no immorality of the same actions. Whereas, it is alleged, that agreement in their judgments respecting the morality or if such a faculty were originally a part of man's constitution, there would as certainly be uniformity, as in the perception of objects by the external senses. Now, if the dictates of conscience in men of different countries do so much differ, does it ation makes them? And what is gained by maintaining the not show that the moral feelings of men are just what educaexistence of a moral faculty, as part of man's original constitution?

To render the case a suitable one to be a test of the question under consideration, it should be supposed that the father was acting in conformity with the strictest principles of rectitude; that his life was sought by wicked men, aiming not at the good of the commonwealth but its destruction; and that the son, in betraying the place of his concealment, was actuated by mercenary motives, or by unjust and unnatural dislike to In the chapter of his Moral Philosophy, under the head "The Moral

Sense."

It will, we think, be admitted, that in all countries and conditions in which men have been found, there exists a perception of a difference in the moral character of actions; that is, some things are accounted wrong, which ought not to be done, and some right which ought to be done.

fundamental truths, there has never been any difference of opinion. It is not meant that all men distinctly think of these primary truths in morals; for many are so inattentive, or so much occupied with sensible objects, that they can scarcely be said ever to reflect on the subject of moral duty. But let an act of manifest injustice be performed before their eyes, and among a thousand spectators there will be but one opinion, and but one feeling. If a strong man, for example, violently takes away the property of one weaker than himself, and for no other reason than because he covets it, all men will condemn the act. So, if any one who has received from another great benefits, not only refuses to make any grateful return, but, on the contrary, returns evil for good, all men will agree in judging his conduct to be wrong. All intuitively discern that for a ruler to punish the innocent and spare the guilty, is morally wrong. It is not true, in fact, that there is no agreement among men as to the fundamental principles of morals. Their judgments on these points are as uniform as on the axioms of mathematics; as in their agreement that the concerning the greenness of the grass, or the varied colours of the rainbow.

Again, it has never been pretended as being a matter of fact, that between men of different countries there is a total difference in the opinions entertained respecting what is right and what is wrong. A few cases only of difference are alleged, in which this discrepancy is observed; but in regard to those actions which are reckoned good or evil, there is a general agreement. As to those in which there seems to be a fundamental difference, an explanation will be given hereafter. No nation, or tribe, or class of mankind has ever held that it is a virtuous and proper thing to do injury to men, or that there is no more harm in taking away life than in preserving it. It has never been held that ingratitude-though everywhere common in practice-is a commendable thing; or that deceit and fraud are as praiseworthy as honesty and fair dealing. .. There is in every country a difference made in the estima-starry firmament is grand and beautiful; yea, as uniform as tion of the character of men, derived from the course of their conduct. Some men are reckoned good in the public estimation, while others are considered wicked; the former obtain esteem, the latter are despised. That course of conduct which secures a good reputation, does not in any country consist of actions which we consider wicked, but of actions which in all countries are considered praiseworthy; and men have never obtained a bad character by a course of good behaviour.

It is also important to observe, that the conduct of a people is not a fair test of the internal state of the mind, as it relates to morals. We know that individuals often pursue a course of conduct, which in their serious moments they condemn. Yet the power of temptation, and the habit of indulgence are such, that notwithstanding the convictions of conscience, they continue in a course of evil-doing. It would be a very inconclusive inference to determine from their habitual conduct, that they acted in accordance with the dictates of conscience. And what is true of individuals, may be true of nations and tribes. Those customs which they have received from their forefathers, may not meet with the approbation of their moral sense, and yet such is the force of an established custom, that they go on in the way in which they were brought up.

But a more satisfactory explanation of those facts, in which men seem conscientiously to go contrary to the fundamental principles of morals, is, that the principle on which they act is correct, but through ignorance or error they make an erroneous application of it.

When parents murder their own female children-a thing very customary in China-it is on the principle that they will be subject to more misery than happiness in the world; and therefore it is doing them a favour. Here, the general principle is correct-that parents should consult the best interests of their offspring-but the mistake is in the application. The same may be said of the practice of exposing aged parents, when they become incapable of enjoying the world.

As to those acts of cruelty which the Pagans perform in their religious services (the wife committing herself to the flames with the body of her deceased husband, children voluntarily thrown into the Ganges, or persons devoting their own lives by falling under the car of Juggernaut), they are performed on the principle that what God requires, or what pleases him, or what will secure happiness for ourselves or friends, should be done. It is true that the will of God should be obeyed, whatever sacrifice he may require; their error is in thinking that such sacrifices are required by Him. HOW FAR ALL MEN ARE AGREED IN THEIR MORAL

JUDGMENTS.

As the subject of morals is very extensive, and particular cases may be complicated, and as men are not only ignorant, but prejudiced by the errors received in their education, it is no more wonderful that they should adopt different opinions on these subjects than on other matters. That, however, which is true in regard to every department of human knowledge, is doubtless true in regard to the science of morals, There are certain self-evident truths, which are intuitively perceived by every one who has the exercise of reason, as soon as they are presented to the mind. In regard to these

Mr. Locke, in his zeal to disprove the existence of innate truths, attempts to render uncertain some of these first truths of morals.

When we go beyond these first principles, we may expect to find men falling into grievous error respecting moral duty; and this often appears in their application of general principles to particular cases. Most men either do not reason at all, or reason badly, and draw from sound principles incorrect conclusions. For the most part, they receive implicitly what they have been taught; or they are governed in their opinions by the common sentiment; or they adopt as true what is most for their interest, or most agreeable to their feelings. And as men are often under the influence of feelings or passions which produce perturbation of mind, and so bias the judgment, it is easy to see how errors of judgment respecting moral conduct, in many cases, may spring up. And yet it is true, that there are primary truths in morals, in which all men agree, so soon as they are presented to the mind. As in other cases, by pursuing a course of sophistical reasonings, conclusions may be arrived at which are contradictory to these first principles, and this will produce perplexity; or even a kind of speculative assent may be yielded to such conclusions of ratiocination; but whenever it is necessary to form a practical judgment, the belief of intuitive truths must prevail. Our assent in these cases is not a matter of choice, but of necessity. Bishop Berkeley thought he had demonstrated that there was no external world; and many others thought there was no flaw in his reasoning: but all these speculative sceptics were, nevertheless, practical believers in the real existence of external objects. Atheistical and infidel philosophers have often endeavoured to prove that there is no intrinsic difference between right and wrong, and some of them probably persuaded themselves that this opinion was true; but these very men, when an act of great injustice towards themselves or friends was committed, could not but feel that it was morally evil; and when they saw an act of disinterested benevolence performed, they could not but approve it as morally good.

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Instead of a", we may write a.

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1. Required the cube root of a3. Ans. a2.

2. Required the cube root of a or a1. Ans. a3, or3√ a. For a3 X as X or 3va ×3va ×3va=a.

3. Required the fifth root of ab. 4. Required the nth root of a2. 5. Required the seventh root of 2d-x. 6. Required the fifth root of (a—x)3. 7. Required the cube root of a3. 8. Required the fourth root of a1. 9. Required the cube root of a 10. Required the nth root of xm. 11. Required the third root of a". 12. Required the fourth root of x. 13. Required the second root of xn. 14. Required the fifth root of d3. 15. Required the eighth root of a3.

The rule in the preceding article may be applied to

The index of a power or root may be exchanged for any every case in evolution. But when the quantity whose root other index of the same value.

Instead of as we may put að.

For in the latter of these expressions, a is supposed to be resolved into twice as many factors as in the former; and the numerator shows that twice as many of these factors are to be multiplied together. Hence the value is not altered.

From the preceding article it will be easily seen, that a fractional index may be expressed in decimals.

7. Thus aao, or 20-5; that is, the square root is equal to the fifth power of the tenth root.

at

8. Express a in decimals.

3

9. Express a in decimals.

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The process of resolving quantities into equal factors, is called Evolution.

In subtraction, a quantity is resolved into two parts. In division, a quantity is resolved into two factors. In evolution, a quantity is resolved into equal factors. Evolution is the opposite of involution. The former is finding a power of a quantity, by multiplying it into itself. The other is finding a root, by resolving a quantity into equal factors. A quantity is resolved into any number of equal factors, by dividing its index into as many equal parts.

From the foregoing principles we deduce the following

GENERAL RULE FOR EVOLUTION.

Divide the index of the quantity by the number expressing the

root to be found. Or,

Place the radical sign belonging to the required root over given quantity.

the

If the quantities have co-efficients, the root of these must be extracted and placed before the radical sign or quantity. Thus,

To find the square root of d1, divide the index 4 by 2, i. e. d. So the cube root of do, is d3 = d2.

6

is to be found, is composed of several factors, there will frequently be an advantage in taking the root of each of the factors separately.

This is done upon the principle that the root of the product of several factors is equal to the product of their roots.

Thus Vaba xvb. For each member of the equation if raised to any power, will give the same result.

When, therefore, a quantity consists of several factors, we may either extract the root of the whole together, or we may and the root of the factors separately, and then multiply them

into each other.

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SIGNS.-(1.) An odd root of any quantity has the same sign as the quantity itself.

(2.) An even root of a positive quantity is ambiguous. (3.) An even root of a negative quantity is impossible.

But an even root of a positive quantity may be either positive or negative. For the quantity may be produced from the one, as well as from the other.

Thus the square root of a2 is+a, or — a.

An even root of a positive quantity is, therefore, said to be ambiguous, and is marked with the sign. Thus the

square root of 36 is V36. The 4th root of x is +2.

The ambiguity does not exist, however, when from the nature of the case, or a previous multiplication, it is known whether the power has actually been produced from a positive or from a negative quantity.

But no even root of a negative quantity can be found. The square root of a2 is neither a nora. For+a+a+a2. And -ax +a2 also. An even root of a negative quantity is, therefore, said to be impossible or imaginary.

The methods of extracting the roots of compound quantities need not be considered here. But there is one class of them, the squares of binomial and residual quantities, which it will be proper to attend to in this place. The square of a + b, for instance, is a2 + 2ab + b2, two terms of which, a2 and b2, are complete powers, and 2ab is twice the product of a into b, that is, the root of a2 into the root of b2.

Whenever, therefore, we meet with a quantity of this description, we may know that its square root is a binomial; and this may be found by taking the root of the two terms which are complete powers, and connecting them by the sign. The other term disappears in the root. Thus, to find the square root of x2 + 2xy + y2, take the root of 22, and the root of y2, and connect them by the sign+. The binomial root will then be x + y.

In a residual quantity, the double product has the sign prefixed, instead of +. The square of ab, for instance, is a2 — 2ab+b2. And to obtain the root of a quantity of this description, we have only to take the roots of the two complete powers, and connect them by the sign Thus the square

2xy + y2, is x

--

y. Hence,

root of x2
To extract the square root of a binomial or residual.

Take the roots of the two terms which are complete powers, and connect them by the sign which is prefixed to the other term.

1. To find the root of 2+ 2x + 1.

The two terms which are complete powers, are x2 and 1. The roots are x and 1. Then + 1. Ans. 2. Find the square root of 22

2x + 1.

3. Find the square root of a2 + a + 1. 4. Find the square root a2 + ja +1.

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out any alteration of its value. For n√ an = an = a. 2. Reduce 4 to the form of the cube root. 3. Reduce 3a to the form of the 4th root.

4. Reduce tab to the form of the square root.

5. Reduce 3 X (ax) to the form of the cube root.

6. Reduce a2 to the form of the cube root.

N.B. In cases of this kind, where a power is to be reduced to the form of the nth root, it must be raised to the nth power, not of the given letter, but of the power of the letter.

(3.) Take the root denoted by the common denominator.
9. Reduce a✶ and to a common index.
ist. The indices

and reduced to a common denominator are and.

2nd. The quantities a and b raised to the powers expressed by the two numerators are a3 and 62.

3rd. The root denoted by the common denominator is the th. The answer, then, is (a3) 11⁄2 and (b2)14. The two quantities are thus reduced to a common index, without any alteration in their values. For aal, which (a3)TM. =

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CASE III. To reduce a quantity to one with a given index. Divide the index of the quantity by the given index, place the quotient over the quantity, and set the given index over the whole. This is merely resolving the original index into two factors. 17. Reduce a to one with the index.

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18. Reduce a2 aid to others with the common index §. 2× 3 = 6, the first index.

2

+1 = 4×3, the second index. )

Therefore (a)

and (2) are the quantities required.

19. Reduce 4 and 3 to others with the common index . 20. Reduce x and y1 to others with the common index . 21. Reduce a and b3 to others with the common index . 22. Reduce c2 and d1 to others with the common index.

1

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23. Reduce am and bm to others with the common index 7. 24. Reduce a, b, and to others with the common index. CASE IV..To reduce a radical quantity to its most simple terms; i. e. to remove a factor from under the radical sign.

Resolve the quantity into two factors, one of which is an exact power of the same name with the root; find the root of this power, and prefix it to the other factor, with the radical sign between them.

This rule is founded on the principle, that the root of the product of two factors is equal to the product of their roots.

It will generally be best to resolve the radical quantity into such factors, that one of them shall be the greatest power which will divide the quantity without a remainder.

N. B. If there is no exact power which will divide the quanthe reduction cannot be made.

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CASE V. To introduce a co-efficient of a radical quantity under the radical sign.

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Present.

Raise the co-efficient to a power of the same name as the radical || Mi dólgo or dóglio, I grieve part, then place it as a factor under the radical sign.

35. Thus, a n1b= "√ anb.

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1. Reduce 5/6 to a simple radical form.

2. Reduce √5a to a simple radical form.

3. Reduce 5 and 6 to others with the common index.

ti duóli, thou grievest

si duble or dóle, he grieves

ci dogliamo, we grieve

vi doléte, you grieve

si dólse, he grieved
ci dólémmo, we grieved
vi doléste, you grieved
si dólsero, they grieved
Future.

Mi dorrò, I shall or will grieve

si dólgono or dógliono, they ti dorrái, thou wilt grieve

zgrieve

Imperfect.

Mi doléva or doléa, I grieved ti dolévi, thou grievedst

si doléva or dolea, he grieved ci dolevámo, we grieved vi doleváte, you grieved si dolévano, they grieved Indeterminate Preterite. Mi dólsi, I grieved

ti dolésti, thou grievedst

si dorrà, he will grieve

ci dorrémo, we will grieve
vi dorréte, you will grieve
si dorránno, they will grieve
Conditional Present.

Mi dorréi or dorria, I should or would grieve

ti dorrésti, thou wouldst grieve si dorrébbe, he would grieve ci dorrémmo, we would grieve vi dorréste, you would grieve si dorrebbero, they would grieve

IMPERATIVE MOOD.

[No first Person.] Duóliti, grieve (thou)

4. Reduce a2 and a to others with the common index.si dólga, let him grieve

5. Reduce

98 to its simplest form.

6. Reduce 243 to its simplest form.

7. Reduce

54 to its simplest form.

8. Reduce 780 to its simplest form. 9. Reduce 9381 to its simplest form.

10. Reduce xax to its simplest form. 11. Reduce √198 a to its simplest form. 12. Reduce √3— a2x2 to its simplest form.

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Present.

dogliamoci, let us grieve dolétevi, grieve (ye or you) si dólgano, let them grieve

SUBJUNCTIVE MOOD.

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che si dólgano or dógliano, that che si doléssero, that they might

grieve

they may grieve

So conjugate

Condolérsi to complain. | Ridolére, to lament again. Observation.-Dolére signifies, also, to ache, and then it is used impersonally. Examples:

Mi duble la tésta, my head aches, or I have the headache. Mi dólgono i dénti, my teeth ache, or I have the toothache.

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Present: dovere, to owe

Past avére dovuto, to have owed

Present Gerund: dovéndo, Past Gerund: avendo dovuto,

Present.

Caglia, it may matter,

Imperfect.

Calésse, it might matter.

owing Past Participle: dovuto, owed

having owed

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