infinite number of parts, even when of the same kind, and no otherwise related to each other than that they are situated near to each other; whether they are at all in contact we do not know. If thought belonged to matter, each of these infinitesimal particles of matter would be a conscious boing, and his consciousness be independent of every other particle. By what medium of communication could these particles of matter agree on forming an organised body? But the pantheist does not believe that matter is endued with thought. His theory is, that in the world there exists not only external substance, but thought or intelligence in the same substance. But as this intelligence must have a subject in which it resides, and of which it is a quality, and as it cannot be an attribute of brute matter, there must exist a substance distinct from matter, of which it is a property. Matter being divisible, inert and extended, cannot have intelligence as an attribute, which is active, indivisible, and unextended. Extension and thought, therefore, cannot be properties of the same substance. If, then, the cause of the phenomena of nature which indicate design is in the world itself, the world must, besides the gross matter which we see and feel, be possessed of a soul, or spiritual substance, in which this intelligence resides. This would bring us to the old Pagan theory of the Soul of the World. Under the material part, but under this only, there is a spiritual substance, a soul; just as in a man, we can see and feel the body, but we know that within this case there exists a spiritual substance or soul. This theory, then, admits the existence of a great spirit, possessing the attributes necessary to account for all the appearances of wisdom in the world. It differs from the common theistical doctrine only in this, that it would confine this being to the world; but for this there could be assigned no valid reason. A being possessing such power over matter as to mould it into every organised form found in animals, vegetables and minerals, must have a complete control over matter, and be perfectly acquainted with all its most hidden properties and capabilities, and must be independent of matter, and must exist every where, to carry on the processes of nature. And as we do not know the extent of the material universe, we can set no limits to the presence of this spiritual, intelligent and omnipotent_being. The object of pantheism is to get clear of the idea of a personal God, who gives laws to creatures, and superintends and governs them according to their natures. But the hypothesis, if it could be established, does not answer the purpose for which it was devised. Still, even according to the hypothesis, we must have a personal God, who knows all things and rules over all. The only other atheistical method of accounting for the phenomena of the world, as indicating the most consummate wisdom, as well as the most omnipotent power, is the hypothesis, that the universe in its present form has existed from eternity, and that all the various species of animals and vegetables now observed have always existed, and have communicated existence to one another in an endless series. And as an eternal series has no beginning, it can have no cause. There is therefore no need of supposing any first cause, from whom every thing has proceeded. As we must suppose some being to exist from eternity, we may as well suppose that the world which we see is that eternal being.

This has always been the stronghold of atheism, and therefore deserves a more special attention. The only círcumstance, however, which gives an advantage to this theory is, that it carries us back into the unfathomable depths of eternity, where our minds are confounded by the incomprehensibility of the subject. It is also to be regretted that some truly great men, in attempting to refute this theory, have adopted a mode of reasoning which is not satisfactory. This, we think, is true with respect to Bentley, who possessed a gigantic intellect; and, as might have been expected, many are his followers. Dr. Samuel Clarke has also pursued a course in his reasoning on this point which, to say the least, is not entirely free from objection. The same may be said of many others, and especially of some, including the celebrated Stapfer, who have attempted a mathematical demonstration of the falsehood of an infinite series of living organised beings.

It will be an object, therefore, to free the subject as much as possible from intricacy and obscurity, and to present arguments which shall be level to any common capacity accustomed to attend to a train of reasoning. We may certainly assume it

as an admitted principle, that every effect must have not only a cause, but an adequate cause. If wise contrivance and evident adaptation of means to an end be found in the effect, to ascribe it to an unintelligent cause is as unsatisfactory as to assign no cause.

This, then, being assumed, we would take this position as incontrovertible, that if design manifest in one effect requires an intelligent cause, the same necessity requires the same kind of a cause for any number of similar effects; and the conclusion must be the same, whether the number is finite or infinite. This evident truth has been often and happily illustrated, by supposing a chain suspended before our eyes, but reaching beyond the sphere of our vision. The lowest link requires a support, and so does the second, and there is no less need of support for every successive link as you ascend the chain; and if you suppose as many links beyond your sight as there are atoms in the universe, still the same necessity of a support is presumed to exist. There must ultimately be a support for all these suspended links. But suppose some one to allege that the chain is of infinite length, and has no beginning, we immediately begin to experience some confusion of ideas. We attempt to grasp infinity, and finding ourselves baffled in the attempt, we are apt to lose sight of the proper logical conclusion in this case. The necessity of a supporting power has no dependence on the number to be sustained. If one, if one hundred, if one thousand require support, so do any number of links. The conclusion is not in the smallest degree affected by the number, except that the more links, the stronger must be the supporting power; but this has nothing to do with our present argument. The conclusion will be of the same kind, and will as necessarily follow, in the case of effects which have in them the marks of design. The number cannot affect the conclusion. If one such effect cannot exist without an intelligent contriver, an infinite number of great effects cannot. If multiplying one cipher, or zero, by any number in arithmetic, produces nothing, and the same is the result of multiplying a thousand ciphers, the conclusion is inevitable, that an infinite number of ciphers multiplied by any number cannot result in any positive quantity. Indeed, if all the individuals in the supposed infinite series are of the same kind, all are effects, and it is absurd to conceive of an effect without a cause. Cause and effect are correlative and imply each other; and if an effect cannot exist without a cause, much less can an infinite number of effects exist without an adequate cause.

Our next argument will leave out of view altogether the idea of infinity, which is so apt to confound the mind. It is this. Every effect must not only have a cause, but that cause must be in existence and operation; for it would be absurd to think of a cause operating, when it no longer had an active existence. Let us, then, take that individual of a series of organised beings which came last into existence. Let it be an animal-a dog or horse. This individual we know came recently into being; when produced there must have been an adequate cause in existence and in operation. What was that cause? The hypothesis confines us to the preceding series of animals of the same species, supposed to have come down in uninterrupted succession from eternity. But whether the series be long or short, finite or infinite, is of no consequence as it relates to our present argument. What we are inquiring after is a cause in existence at the time this curiously organised and animated being came into existence. Now at that time the individuals of the series had all ceased to exist, except the immediate progenitors. Whatever cause existed, cannot therefore be looked for in them; and if the effect is such as manifestly to be beyond any power and skill which they possessed, the contriving and efficient cause cannot be found in the series. There must be a higher cause.

But lest some persons should have a vague notion that some hidden power might be communicated through the series, although not found in the progenitors of the animal under consideration, we will lay down a principle which is admitted in mechanical powers, and is equally applicable to all causes. It is this. In all cases where any power is communicated through a series of individuals, the whole power necessary to produce the effect, must not only be communicated to the first, but to every single thing in the series, until it reach the last, which is intended to be affected by the original power.

Or we may reason thus: Since £1.98 (amount) requires £1 principal for the given time, £756 (amount) will require as many pounds as £1.08 is contained times in £756; and £756 £1.08 £700, the same as before.

PROOF.-£700 X 08= £56, interest for 1 year and 4 months; and £700+56= £756, the sum whose present worth is required. Hence,

To find the present worth of any sum, payable at a future time without interest.

First find the amount of £1 for the time, at the given rate, as in simple interest; then divide the given sum by this amount, and the quotient will be the present worth.

The present worth subtracted from the debt will give the true discount.

This process is often classed among the problems of interest, in which the amount (which answers to the given sum or debt), the rate per cent., and the time are given, to find the principal, which answers to the present worth.

2. What is the present worth of £424-83, payable in 4 months, when money is worth 6 per cent.? What is the true discount? Solution.-£424.83 £1.02= £416·50= £416 10s., present worth; and £424·83 — £416-50 = £8.33 £8 6s. 74d., the true discount.

3. What is the present worth of £1,000, payable in 1 year, when the rate of interest is 5 per cent.?

4. What is the present worth of £1,645, payable in 1 year and 6 months, when the rate of interest is 5 per cent.?

5. What is the true discount on a bill for £2,300, payable in 6 months, when the rate of interest is 5 per cent.?

6. What is the true discount, at 6 per cent, on £4,260, payable in 4 months?

7. What is the present worth of a bill for £4,800, due in 3 months, when the rate of interest is 6 per cent. ?

8. What is the present worth of a bill for £6240, payable in 1 month, when the rate of interest is 4 per cent.?

9. A man sold his farm for £3,915, payable in 24 years: what is the present worth of the debt, at 6 per cent. discount? 10. What is the present worth of a bill for £10,000, payable at 30 days' sight, when interest is 5 per cent. per annum? 11. What is the difference between the true discount of £8,000 for 1 year, and the interest of £8,000 for 1 year, at 5 per cent.?

BANK DISCOUNT. CASE I.

[on the given sum from the time it is discounted to the time it becomes due. Hence, in ordinary business transactions, discount is the same as simple interest paid in advance. Thus, the usual discount on a bill for £105, payable in 1 year, at 5 per cent., is £5 5s., while the true discount is only £5.

The difference between ordinary discount and true discount, is the interest of the true discount for the given time. On small sums for a short period this difference is trifling, but when the sum is large, and the time for which it is discounted is long, the difference is worthy of notice. Ordinary discount is always supposed to be meant, unless the word "true" is prefixed. It is usual to charge interest for the 3 days' grace.

To find the discount on a bill or promissory note. Calculate the interest of the bill or promissory note for three days more than the specified time, and the result will be the discount. The discount subtracted from the sum named in the bill or note will give the present worth required.

Note.-Interest should be computed for the three days' grace in each of the following examples.

13. What is the discount on a bill for £465, payable in 6 months, at 6 per cent.?

14. What is the discount on a bill for £972, payable in 4 months, at 5 per cent.?

15. What is the discount on a bill for £1,492, payable in 3 months, at 7 per cent.?

16. What is the discount on a bill for £628, Į ayable at 60 days' sight, at 5 per cent.?

17. What is the present worth of £2,135, payable in 8 months, at 7 per cent.?

18. What is the present worth of a bill for £2,790, payable in 1 month, discounted at 6 per cent. at a bank?

19. What is the discount, at 5 per cent., on a bill for £1,747, payable at 90 days' sight?

20. What is the discount, at 44 per cent., on a bill for £3,143, payable in 4 months?

21. What is the discount on £5,126, payable in 30 days, at 8 per cent.

22. What is the discount on £3,841, payable in 60 days, at 6 per cent.?

23. What is the present worth of a bill for £6,721, payable in 10 months, discounted at 6 per cent. at a bank?

24. What is the present worth of a bill for £1,500, payable in 12 days, at 7 per cent. discount?

25. What is the discount on £10,000, payable in 45 days, at 6 per cent. ?

26. What is the discount on £25,260, payable in 90 days,

27. What is the difference between the true discount and ordinary discount on £5,000 for 10 years, at 6 per cent. ?

:

CASE II.

28. A man wishes to make a bill payable in 1 year, at 6 per cent., the present worth of which, if discounted at a bank, shall be just £200 for what sum must the note be made? Analysis. The present worth of £1, payable in 1 year, at 6 per cent. discount, is £1 - £To £; that is, the present worth is of the principal or sum discounted. The question then resolves itself into this: £200 (present worth) is of what sum? Now, if £200 is of a certain sum, is of £200; and £20094 £2·12766, and 188 = £2·12766 × 100, which is £212-766 £212 15s. 3d. Ans.

=

=

Or we may reason thus: Since £ present worth requires £1 principal or sum to be discounted for the given time, £200 present worth will require as many pounds as £ is contained times in £200; and £200 ÷ £·94 = £212·766, or £212 15s. 3d.

PROOF.-£212-766 X 06 = £12.7659, the discount for 1 year; and £212-766 £12.7659 £200, the given sum Hence,

To find what sum, payable in a specified time, will produce a given amount, when discounted at a bank, at a given per

cent.?

29. How large must I make a bill, payable in 6 months, to raise £400, when discounted at 7 per cent, discount?

30. What sum, payable in 4 months, must be discounted at a bank, at 5 per cent., to produce £950?

31. What sum, payable in 60 days, will produce £1,236, if discounted at a bank, at 8 per cent.?

32. For what sum must a bill be drawn, payable in 34 days, the proceeds of which, at 6 per cent. bank discount, will be £2,500 ?

33. For what sum must a bill be drawn, payable in 90 days, so that the proceeds, at 7 per cent. bank discount, may be £3,755?

34. A man bought a farm for £4,268 cash: how large a bill, payable in 4 months, must he take to a bank to raise the money at 6 per cent. discount?

35. A man wishes to obtain £6,324 from a bank at 6 per cent. discount: how large must he make his note, payable in 1 month and 15 days?

36. What sum, payable in 8 months, if discounted at a bank, at 6 per cent., will produce £1,000?

37. What sum, payable in 4 months, will produce £5,000, if discounted at 7 per cent. at a bank?

38. A man received £4,625 as the proceeds of a bill, payable in 60 days, discounted at a bank at 5 per cent.: what was the

amount of the note?

39. A merchant wished to pay a debt of £8,246 at a bank, by getting a bill payable in 30 days discounted, at 8 per cent.: how large must he make the bill?

INSURANCE.

Insurance is security against loss or damage of property by fire, storms at sea, and other casualties. This security is usually effected by contract with insurance companies, who, for a stipulated sum, agree to restore to the owners the amount insured on their houses, ships, and other property, if destroyed or injured during the specified time of insurance.

Insurance on ships and other property at sea is sometimes effected by contract with individuals.

The insurers, whether an incorporated company or individuals, are often termed underwriters.

The written instrument or contract is called the policy. The sum paid for insurance is called the premium. The premium paid is a certain percentage on the amount of property insured for 1 year, or during a voyage at sea, or other specified time of risk.

Rates of insurance on dwelling-houses and furniture, stores and goods, shops, manufactories, etc., vary from to 2 per cent. per annum on the sum insured, according to the exposure of the property and the difficulty of moving the goods in case of casualty. It is a rule with most insurance companies not to insure more than two-thirds of the value of a building or goods on land.

Coasting vessels are commonly insured by the season or year. In time of peace, the rate varies from 4 to 7 per cent. per annum; in time of war it is much higher. Whale ships are generally insured for the voyage, at a rate varying from to 8 per cent. on the sum insured.

5

When the general average of loss is less than 5 per cent., the underwriters are not liable for its payment.

CASE I.

To compute insurance for 1 year, or a specified time. Multiply the sum insured by the given rate per cent., as in interest. Ex. 1. A man effected an insurance on his house for £1,500, at 1 per cent. per annum: how much premium did he pay? Solution.-£1500 × 0125 (the rate) = £18·75. Ans.

2. What is the premium for insuring a store to the amount of £2,760, at per cent. ?

3. What premium must I pay for insuring a quantity of goods, worth £6,280, from Liverpool to New York, at 1 per cent.?

4. What is the annual premium for insuring a stock of goods, worth £10,200, at per cent.?

5. What is the annual premium for insuring a coasting yessel, worth £1,600, at 6 per cent. ?

6. A bookseller shipped a quantity of books, valued at £4,700, from London to Dublin, at 1 per cent. insurance: what amount of premium did he pay?

7. A merchant shipped a cargo of flour, worth £4,500, from Liverpool to New York, at 2 per cent.: how much premium did he pay?

8. What is the insurance on a cargo of teas, worth £7,500, from Canton to London, at 2 per cent.?

9. What is the annual insurance on a factory, worth £6,500, at per cent.?

10. A powder mill was insured for £1,945, at 124 per cent.: what was the annual premium?

11. A ship embarking on an exploring expedition was insured for £4,536, at 8 per cent. per annum: what did the insurance amount to in 5 years?

12. A policy of insurance for £1,500 was obtained on a whale ship, at 7 per cent. for the voyage: what was the amount paid for insurance? CASE II.

13. If a man pays £16 annually for insuring £800 on his shop, what per cent, does he pay?

per cent.

Analysis. If £800, the amount insured, costs £16 premium, £1 will cost of £16; and £16 £800 = .02, which is 2 PROOF.-£800 X 02 £16, the premium paid. Hence, To find the rate per cent., when the sum insured and the annual premium are given.

will be the rate per cent. required. Divide the given premium by the sum insured, and the quotient

Note. This case is similar in principle to Problem II. in Interest.

14. If a man pays £60 annnally for insuring £2,400 on his house and shop, what per cent. does it cost him?

15. A merchant pays £200 per annum for insuring £8,000 on his goods: what per cent. does he pay?

16. A merchant paid £122 10s. premium on a cargo of flour, worth £12,250, from Charleston to Portland: how much per cent. did he pay?

17. An importer paid £35 insurance on a quantity of cloth, worth £2,800, from London to New York: what per cent. did he pay?

CASE III.

18. A man pays £45 annually for insuring his library, which is 3 per cent. on the amount of his policy: what is the sum insured?

Analysis. Since £18 will insure £1 at the given rate for a year, £45 will insure as many pounds as 18 are contained times in £45; and £4503 £1,500. Ans.

PROOF.-£1500 X 03 £45, the given premium. Hence, To find the sum insured, when the premium and the rate per cent. are given.

Divide the given premium by the rate per cent., expressed in decimals, and the quotient will be the sum insured.

Note.-This case is similar in principle to Problem III. in Interest.

19. An importer paid £650 premium on goods from London to New York, which was 1 per cent. on the amount insured: how much did he insure?

20. A merchant paid £1,640 premium on goods from London to Constantinople, which was 2 per cent. on the worth of the goods insured: how much did he insure?

21. A premium of £487 10s. was paid on a cargo of cotton from Liverpool to New Orleans, which was per cent. on its value: what amount was insured on the cargo?

22. When the rate of insurance is 1 per cent., what sum can you get insured for £860 premium?

23. At per cent. per annum, what amount can a man get insured on his house and furniture for £20 10s. per annum? CASE IV.

To find what sum must be insured on any given property, so that, if destroyed, its value and the premium may both be recovered.

24. If a man owns a vessel worth £1,920, what sum must he get insured on it, at 4 per cent., so that, if wrecked, he may recover both the value of the vessel and the premium?

Analysis. It is plain, when the rate of insurance is 4 per cent. on a policy of £1, the owner would receive but £8% towards his loss; for he has paid £1 for insurance. Since, therefore, the recovery of £ requires £1 to be insured, the recovery of £1,920 will require as many pounds to be insured