3. The time at St. Louis is 1 hr. 4 min. 564 sec. earlier than that of New York, whose longitude is 74° 1′ 6′′. What is the longitude of St. Louis?

4. The time at Louisville is 5 hr. 16 min. 38 sec. earlier than that of Dublin, whose longitude is 6° 20′ 30′′ west. What is the longitude of Louisville?

REM. When it is 9 A.M. at New York it is 10 A.M. 15° east of New York and 15° west of New York the time is 8 A.M.

What is the difference in

5. The difference in time of Washington and St. Petersburg is 7 hr. 9 min. 194 sec. longitude?

Ans. 107° 19' 48" = difference in longitude.

6. The longitude of Cincinnati is 84° 24' west.

When

it is 10 o'clock A.M. at Cincinnati, it is 22 min. 8 sec.

past 10 at Buffalo.

What is the longitude of Buffalo?
Ans. Longitude of Buffalo 78° 52'.

RATIO.

Two fractions can be formed of any two integral num. bers, the one a proper fraction, the other an improper fraction. These fractions are also called Ratios.

As the product of any number multiplied by the proper fraction is less than the number itself, the fraction is called a Diminishing Ratio; and as the product of any number multiplied by the improper fraction is greater than the number itself, it is called an Increasing Ratio.

PROBLEMS.

1. If 5 lbs. sugar cost 50 cents, what will 9 lbs. cost? It is evident that 9 lbs. will cost more than 5, and just as much more as is indicated by the increasing ratio formed by the two like terms, 5 lbs. and 9 lbs.

10

If 5 lbs. cost 50 cts., 9 lbs. will cost 50 cts. x 90 cts.; this may be further demonstrated thus,

In a problem of ratios, the one ratio is given, and one of the terms of the other ratio, to get the second term; thus, in the above:

The ratio of the money will be the same as of the sugar. As the required sugar is more than the given, the ratio must be increasing; that is, f... 50 ×

of the required money to the gain, of the sugar.

EXAMPLES.

= 90, the ratio 8, the same as

=

1. If 5 bushels of wheat cost $6.25, what will 8 bushels cost?

The ratios of the wheat and of the money is the same. REM.-Ratios can only be formed by two like terms.

2. If 5 bushels of oats cost $1.50, what will 21 bushels cost?

21

=

f88 = 21; the ratio is the same.

Given
Required,

5 bu. and $1.50. 21 bu. and

$1.50 × 1 = $6.30.

REM.-Write the given terms in a line and the like term of the required immediately under that of the given. One term of the required is wanting, and the given like term may be called the term of demand, and should be placed first and multiplied by the ratio, having for its numerator the required term of the ratio, and for its denominator the given term.

As a general thing, an increase in the required term of the ratio will take more of the unknown to accomplish it; an increased amount of goods will cost a greater sum of money; an enlarged piece of work, an additional sum of money; and the greater the work, the longer time to perform it, etc. In examples of this kind, the ratios are direct, and the required term of the ratio holds the place of the numerator and the given term that of the denominator, and the product of the ratio and the odd given term is the term required.

3. If a man travel 40 miles in 8 hours, how many miles will he travel at that rate in 18 hours?

4. If 15 bushels of wheat yield 3 barrels of flour, how many bushels will yield 10 barrels of flour?

5. If a man travel 30 miles in 2 days, how long will it take him to travel 240 miles?

6. If a staff 4 feet long cast a shadow 3 feet, what is the height of a steeple which casts a shadow 90 feet?

7. If the interest of $100 for one year is $5, what would be the interest of $500 for the same time?

8. If of a barrel of flour cost $4, what will 4 barrels cost?

REM. 4 is a multiplier, and is a divisor; the must be inverted.

9. If 4 bushels of wheat cost $5.40, what will 83 bu. cost? 9 bu.? 23? 31? 471? 391? 58? 974? 1064? 10. If 8 bushels of wheat cost $10, what will be the cost of 9 bu.? 10 bu.? 15 bu. ? 374 bu.? 95% bu.? 1253 bu.? 1504 bu. ? 279 bu.?

11. If 5 acres of land

cost $230, what is the cost of 6 acres? 7 acres? 12 acres? 131 acres? 17? 183? 194? 205? 37? 493?

12. If 2 acres of land cost $110, what will of an acre cost? acre? acre? acre? acre? acre? acre? 1 acres? 1 acres?

13. If of a yard of cloth cost of a dollar, what will of a yard cost?