The American Student's Guide

12. If a pipe of Canary wine cost 40£ what will one pint of it cost? Ans. 9+96 remainder. 13. How many yards of cotton cloth, that is 3 quarters of a yard wide, will line a coverlet that is 9ft. long and 7ft. wide? Ans. 9 yds. 14. If 1 pennyweight of gold be worth 89 cents, what are 8ozs. 10pwts. 16grs. worth? Ans. $151.893 cents. 15. What is the weight of a pea to a steelyard, which, being suspended 39 inches from the center of motion, will equipoise 208lbs. suspended at the draught end 3 quarters of an inch from the said center of motion? Ans. 4 pounds.

16. What weight, suspended 3 quarters of an inch from the fulcrum, will be equipoised by the pea of a steelyard that weighs 4lbs. suspended 39 inches from the said fulcrum, at the other end? Ans. 208 pounds.

17. A lady very fair did herself betake,

Of nice needle work, a carpet rare to make,
With silk and silver wrought most curiously,
With elegant pictures, pleasant to the eye;
Fifteen yards in length the carpet did extend,
Seven quarters wide it was from end to end;
But she's desirous, before the carpet's seen,
To line it with silk five quarters wide, and green.
Now this lady fair desires of you to know
How many full yards will line the carpet so.
Now, sir, only grant the lady-fair's desire,
And she will your talents very much admire.

Answer. Dear Miss, the question is quite easy done,
It requires yards exactly twenty-one.

18. As I was hunting on the forest grounds,

Up starts a hare before my two gray-hounds;
The dogs being swift on foot did fairly run
Unto her fifteen rods just twenty-one.
The distance that she started up before
Was four-score, sixteen rods just, and no more.
Now this I'd have you unto me declare,

Hov far they ran before they caught the hare?

21-15-6; then, as 6: 21 :: 96 336 rods, answer.

This question may be proved by Simple Addition, in the following

manner:

96+15+15+15+5+15+15+15+15+15+15+15+15+15+15+15+15—336
00+21+21+21+21421+21+21+21+21+21+21+21+21+21+21+21=336

Or thus: 15× 13+96=336, and 21 × 16=the same.

N. B. Sound; that is tot interrupted, moves about 1150 feet in one second of time.-See Vyse's Arithmetic, page 68. Mr. Nicholas Pike says it moves about 1142 feet in a second. See Pike's Arithmetic, page 370.

19. How long after the firing of a cannon at Newburyport will the sound be heard at Ipswich, estimating the distance to be 10 miles? feet. SPC. feet. Answer.

10 miles 52800ft., then: As 1142: 1 :: 52800 46sec.+268 rem. 20. If I see the flash of a cannon 1 minute and 3 seconds before I hear the report, how far is she off, supposing the sound to move 1150 feet in a second. Ans. 24150 yards.

21. One evening fair I did espy

A Mediterranean ship pass by,
Whose gallant gunners quickly sped,
And fired a volley from her head.
Now from the time the flash appear'd
Until the sound I plainly heard,
Was minutes two and seconds four,
What was her distance from the shore?

As ls. 1142ft. :: 124sec... 26min.

1442yds. 2ft. Answer..

The following question is inserted by the request of a friend:
22. A Maypole there was whose height I would know,
The sun shining quite straight, to work I did go;
The length of its shadow, upon level ground,
Was sixty-five feet, when measur'd, I found.
A staff I had by me just five feet in length,
Which gave out a shadow four feet and one tenth..
The height of the Maypole I would gladly know,
And that is the thing you are required to show.

Answered poetically by Mr. JAMES BROWN.
Sir, your question to solve I did puzzle my brain,
I read it and tried it, and read it again;

I thought it was sure some profound mystery,
Till at length it turn'd out the plain Rule of Three.
Suppose that a shadow of four feet and one-tenth
Requires a staff which is just five feet in length,
The Maypole, whose shadow was sixty-five feet,
Will be twenty-six yards perpendicular height.
The remainder is full fifteen inches and more,
Which I probably might have mentioned before;
But I thought if Goliah would want such a rod,
When we cut it we'd leave a good stump on the sod.
Now, sir, if my answer does please you aright,
I am your humble servant, and bid you good night..

THE DOUBLE RULE OF THREE DIRECT.

The Double Rule of Three Direct is composed of five terms, which are given in the question to find the answer; three of them are called the terms of supposition, and the other two the terms of demand.

A RULE FOR STATING THE QUESTIONS, &c.

1. Set down the term of supposition in the first place, which is the principal cause of gain or loss, interest or demand, increase or decrease, action or passion.

2. Set down the term of supposition in the second place, that signifies the time in which the gain is acquired, the loss sustained, the action performed, or the distance from one place to another.

3. Set down the term of supposition in the third place; that designates the gain or loss, interest or action performed, which must be of like name with the answer required.

4. Place the two terms of demand in a line with the terms of supposition, so that the first and fourth terms of the stating may be of like name; also, the second and fifth, and the stating will be completed.

5. If the first and fourth terms of the stating be of different denominations, reduce them both to the same, and do likewise by the second and fifth terms.

6. Reduce the middle term to the lowest denomination mentioned in it, or lower, if the nature of the question require it.

7. When all the terms of the stating are reduced as above directed, (if necessary,) then multiply the first and second terms together for a divisor, and the three remaining terms for a dividend; the quotient thence arising will be the answer required to the question, and of like name with the middle term, or whatever denomination it was reduced to.

8. Questions may be wrought by two single statings in direct proportion, which may serve as proof to the compound stating; or, the operation may be proved by changing the order of the compound stating and working backward, which will produce the middle term of the first stating for the answer, if the work in both be right.

9. When a question is wrought by two single statings, the answer to the first will be the middle term of the second one.

10. The operation, in many questions, may be contracted by working with the aliquot parts instead of the whole terms. The aliquot parts are found by dividing a multiplying term by a dividing term, or a dividing term by a multiplying term.

EXAMPLES.

1. If 24 bushels of provender serve 16 horses 12 days, howmany bushels will serve 48 horses 32 days?

H. D.

If 16×12: 24 :: 48x32

H. D.

H. D. B.

H. D.

If 48 x 32: 192 :: 16× 12

192