The American Student's Guide

XIII. OF MOTION OR CIRCLE MEASURE.

AN EXAMPLE.

In half a year's time the sun makes his progress through 6 signs of the zodiac. How many degrees, minutes, and seconds does the progress amount to? Ans. 180 deg. 10800 min. and 648000 sec.

4. A goldsmith has 3 ingots of silver, each weighing 2 lb. 2 oz. 13 pwts. 8 grs. He intends to make them into spoons of 2 oz., cups of 5 oz., salt-cellars of 1 oz., and snuff-boxes of 2 oz., wants an equal number of each sort. Please to inform him how many to make. Ans. 8 of each sort..

and

5. How many teaspoons will 4560 grains of silver make, allowing each spoon to weigh half an ounce? Ans. 19 spoons.

6. A butcher cut 780 pounds of beef into pieces of 12, 3, 4, 5, and 6 pounds, and had an equal number of each weight. How many were there? Ans. 40 pieces of each weight.

7. How many bags, each holding 43 bushels, can be filled out of a garner containing 190 bush. of wheat? Ans. 42 bags, and 1 b. over.. 8. How many casks, which will hold 33 gallons.each, may be filled out of 5 pipes and 1 hogshead of rum? Ans. 21 casks.

9. A vintner is desirous of drawing off a pipe of Canary wine into bottles containing pints, quarts, and pottles, and of each sort an equal number. How many will he have?

Ans. 144.

10. A tract of land containing 1299600 square perches is to be divided into 25 equal parts. How many acres, &c. will there be in each part? Ans. 324A. 3r. 24 perches.

THE SINGLE RULE OF THREE DIRECT.

The Single Rule of Three Direct is composed of three terms, which are always given in the question, to find the fourth term or answer; two of them are called the terms of supposition, and the other one, the term of demand.

A RULE FOR STATING THE QUESTIONS AND THE OPERATION. 1. Set down the term of supposition in the first place; that always moves the question, and is the principal cause of gain or loss.

2. Set down the term of supposition in the second place, that is of the same denomination as the fourth term or answer required. 3. Set down the term of demand, that is, whatever you wish to find the value of, in the third place, and the stating will be completed. 4. If the first and third terms of the stating are of different names, they must be reduced into the same denomination.

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

6. When all the terms of the stating are reduced as above directed, (if necessary)-then multiply the second and third terms together, and divide the product by the first term-the quotient will be the fourth term or answer to the question, and of like name with the middle term or whatever denomination it was reduced to.

7. If there should be any remainder, reduce it to the next denomination below the name of the quotient now obtained, and divide the product by the same divisor as before, and the quotient will be so many of this last denomination-proceed in the same manner with all the remainders, till you have reduced them to the lowest denomination that the middle term admits of, and the several quotients, properly connected, will be the answer.

8. The questions must be proved by reversing the order of the stating, and working it back again, which will produce the middle term of the first stating for the answer, if the work in both statings be correct.

A POETICAL RULE.

This Golden Rule has places three,
The first and third must so agree,
That of one name they may remain,
If to the truth you would attain;
The second by third, then multiply,
And divide by the first ingeniously,
Then will your quotient be the same,
That you in second place did frame;
Which by Reduction may be brought
Into whatever name is sought.

Change the stating and backward work,
And that will prove the given quirk.

EXAMPLES.

1. If 8 yards of linen cost 5 dollars, what will 2 yards cost at the same rate?