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(1) What principal at Int. for 8 years at 5 per cent. a year, will amt. to $840? Ans. $600 100X05 $5.00×8=40+100-$140 amt. of $100 at rt. Then, as $140: 100 :: 840: $600 Ans. for, 840×100÷÷ $600.600X05-30.00X8=240+600 $840. proof. (2) A lent B his money for 6 years at 4 pr. ct. a year, and rec'd. $1240;-what was the principal? Ans. $1000. CASE 8. When the principal, amt. and time are given to find the rate.

RULE 1. Subtract the principal from the amt. and the remainder will be the Int.

2. As the principal is to the whole Int. so is 100 to the Int. of 100 for the whole term, which, divided by the time will give the rate. Thus:

(3) At what rate per cent. will $600. amt. to $744. in 4 years? Ans. at 6 per cent? 744-600 $144 Int. then as 600: 144 :: 100: 24-46 Ans. (4) A lent B $834 for 2 1-2 years and rec'd. $927.825; what per cent. did he charge? Ans. 4.1-2. CASE 9. When the principal, amt. and rate are given to find the time.

RULE. Divide the Int. on the principal for the whole time, by the Int. of the principal for 1 year, the quotient will be the answer Thus:

(1) In what time will $400 amt. to $520 at 5 per ct. a year?

520-400-$120 Int. for the whole time, and 400X0520.00 Int. for 1 year, then, 120÷20=6 Ans.

(2) $1000 at 4 1-2 pr. ct. a year amt. to $1281.25; what Ans. 61-4 years. was the time?

FALSE SYNTAX.-LESSON 32.

RULE 7. Every adjective refers to some noun expressed or implied, in qualification;-As Mary writes a long letter. He lived in a manner agreeably to the dictates of reason. This sentence is faulty, for the adverb, agreeably, is employed to qualify the noun, dictates, to which it refers; in violation of rule 7: hence, agreeably, should be agreeable. Thus:-He lic ed in a manner agreeable to the dictates of reason.

He adressed an exhortation suitable to the occasion.
The reproof was suitably to the offence.

They wandered about solitarily and distresedly.

The study of Grammar should be attended to previously to that of punctuation.

OBS. 1. Some adjectives do not admit of comparison, and can be used only in the positive state.

A method of attaining the rightest happiness.

His is the perfectest copy. Theirs is the universalist profession.

OBS. 2.

Double comparatives and superlatives should be carefully avoided.

A more serener temper. The most strictest sect. A more superior work. It is more easier to build two chimnies than support one. This apple is the best of the two, is bad language, for the superlative degree can be applied only when three or more things are compared: it should be the better. The boy wore a new cap, and a new pair of boots;-the boots were new and not the pair: hence, a pair of new boots is better language.

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Application of the the Inflections to the exclamation point. RULE. When this point follows a phrase or sentence, which, otherwise pointed, would require the rising or falling inflection, then the appropriate slide is adopted. Thus:

Whither shall I turn?` wretch that I am!' to what place shall I betake myself? Shall I go to the capitol?' Alas! it is overflowed by my brother's blood! or shall I go to my house? There I behold my mother, plunged in misery, and weeping in despair!`

Oh the dark days of vanity! when here, how tasteless! and how terrible when gone!` gone!' they ne'er go: when past they haunt us still!

NOTE. The exclamation point is generally applied to strong and pas sionate language, and generally adopts the falling inflection, but to this rule there are many exceptions.

SIMPLE INTEREST ON PARTIAL PAYMENTS.--LESSON 35.

RULE 1. Find the Int. on the principal to the time of the first payment, which subtract from the payment, and the rcInainder from the principal.

2 Find the Int. on the residue of the principal from the 1st to the 2d payment, and subtract as before.

3 If at any time the payment is less then the Int. for the time being-then place the payment on one side in the form of a memorandum.

4

Continue to find the Int. on the principal, until the amt. of the partial payments, exceed the amt. of Int. and then subtract as in the first instance.

5 Proceed through all the payments, and what is left after the deduction of the last payment, will be the true balance. (1) Thus:-B holds C's note for $300 bearing date Mar. 4, 1820, on Int. at 6 per cent. on which are endorsed the following payments.

Sept. 16, 1820, $46.50 time 6 mo. 12 ds. Int. $20.35.

Jan. 4, 1821, $50

Mar. 22, 1822, $162.56

What was due Mar. 4, 1824?

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18 ds. do 10.98.

20 ds. do. 41.86. Ans. $127.48.

1 prin. $300; pay't. 46.50-Int. $20.35=26.15 & 30026.15

$273.85.

2 prin. $273.85; do 50-10.98=39.12. & 273.85-39.12 =$234.73.

3 prin. $234.73; do 162.56---41.86

120.70

$114.03.

120.70 &234.73

4 prin. $114.03;--time 23 mo. 18 ds. Int. $13.45. X11403 $127.48. Ans.

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(2) D holds A's note fo: $520. dated May 6, 1825, Int. at 6 per cent. after 3 mo. on which were endorsed the following payments. Aug. 9, 1825, $87.375;-Feb. 25, 1826, $100,-May 12, 1826, $102:-What was due Oct. 1, 1827. Ans. $270.93.

NOTE. This is the only equitable mode of casting Int. on partial payments; and this is equitable only when the payments are promptly made. If made too early, it works a loss to the borrower; but if too late, the loss falls to the lender.

FALSE SYNTAX.-LESSON 36.

RULE S. Adverbs refer to verbs, participles, adjectives, and other adverbs, in modification,-As, Sophia writes daily, &c. Joseph's brother acted noble though unsuccessfully.

This sentence is faulty, because the adjective, noble, is employed to modify the verb, acted, in violation of the 8th rule. Noble, should therefore be nobly. The sentence amended will read thus:-Joseph's brother acted nobly though unsuccessfully.

We may live happy though we are not rich. He awards just, and deals honourable. Joseph rights the matter entire clear.

OBS. 1. The adverb requires an appropriate situation in the sentence in which it is employed;--generally as near the word which it is designed to modify as possible. It is usually put before the adjective, but after the verb, and between the helping verb and the principal verb.

These things should be never separated in the sentence. We always should prefer our duty to our pleasure. Not only he found her employed but pleased also. OBS. 2. Two adverbial negatives in the same sentence, perverts the meaning, and it becomes an affirmative.

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I do not want no more;-implies I want more.
We need not, nor do not limit him.

This man does not

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Application of the Inflections to the parenthesis.

RULE. When the parenthesis has no associate pointing or is accompanied by the comma, the rising inflection is applied both before and at the close of the parenthesis. Thus:

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