4. How many seconds more are there in the 3 spring months than in the 3 autumn months?

5. Reduce of a year to days.

6. Find the value of 0.375 yr. 0.142 dy. 0.27 min.

7. What part of a day are 12 hrs. 15 min. 25 sec.?

8. What part of 2 dys. 7 hrs. 18 min. are 1 dy. 3 hrs. 15 min.?

9. How much greater is the quotient of 100 yrs. 25 dys. 12 hrs. 27 min. 28 sec. divided by 4 than the product

of 4 yrs. 17 dys. 9 hrs. 12 min. 18 sec. multiplied by 5?

10. Find the number of days, reckoning from noon of the one to noon of the other, between Feb. 24 and

June 23, 1884; also between Dec. 25, 1884, and
May 25, 1885.

11. How many hours from noon of the 4th to midnight of the 7th of July, 1885?

12. Divide 11 wks. 6 dys. 18 hrs. by 9.

13. Divide 2 yrs. 135 dys. 17 hrs. by 72.

14. From 5 yrs. 17 hrs. take 2 yrs. 138 dys. 22 hrs.

15. Find the value of 3.1725 dys.

16. Find the value of 21.325 of a year.

17. Express 9 dys. 3 hrs. as the decimal of a week.

18. Express 13 hrs. 15 min. 17 sec. as the fraction of 6 dys. 1 hr. 48 min. 7 sec.

19. Express 3 dys. 20 hrs. 35 min. 33 sec. as the decimal of 27 dys. 13 hrs. 22 min. 30 sec.

20. Find the value of 5.58 yrs.

DIFFERENCE BETWEEN TWO DATES.

176. Find the difference between April 3, 1885 and dys. May 7, 1837.

yrs.

mos.

In finding the difference between long dates, 30 days are considered a month. As April is the fourth, and May the fifth, month, we write 4 and

-5 instead of the names of these months.

In finding the difference between short dates, the exact number of days is generally counted.

Ex. 121.

1. On the 1st of January, 1885, how much time had passed since the discovery of the Island of San Salvador, Oct. 12, 1492?

2. At the birth of Lafayette, Sept. 6, 1757, what was the age of George Washington, born Feb. 22, 1732? 3. If a note is dated March 5, 1885, and has 3 mos. 3 dys. to run, when is the note due?

4. If a note is discounted Feb. 1, and is due April 22, how many months and days has it to run?

5. Find the exact number of days from Sept. 23 to Jan. 11.

NOTE. In finding the difference of these dates, the 23d of September is not counted, but the 11th of January is.

6. Find the exact number of days between March 5 and July 4.

7. Find the exact number of days between June 3 and Nov. 1.

8. Find the exact number of days between Feb. 3 and June 3, of a common year.

9. Find the difference between June 7, 1885, and July 4,

1776.

ANGULAR MEASURE.

177. A circle is a plane figure bounded by a curved line called the circumference, all points of which are equally distant from a point within called the centre.

178. A line drawn through the centre and terminated by the circumference is called a diameter; and half the diameter is called the radius. Any part of the circumference is called an arc.

If a straight line fixed at one end is revolved, the other end will describe the circumference of a circle; and the difference in direction between the position of the straight line at the start and the straight line at any other position, is the angular magnitude described by the moving straight line. Thus, if OA revolve about O as a fixed point, the extremity A will describe the circumference ABC. When OA has

B

reached the position OB, the part of the circumference between A and B is described by A, and the part of the angular magnitude about the point O, between OA and OB, is A described by OA. The angle AOB is such a part of the angular magnitude about O as AB is of the circumference.

Ө

The circumference of every circle is divided

into 360 equal parts, called degrees, and corresponding to every one of these equal parts is an angle at the centre of the circle. Hence the whole angular magnitude about any point in a plane is divided into 360 equal parts called degrees, and the number of degrees in the angle formed by two lines drawn from the centre of a circle is the same as the number of degrees in that part of the circumference which is intercepted by these two lines.

179. An angle of 90°, as AOB, is called a right angle. An angle greater than a right angle is called an obtuse angle, and an angle less than a right angle is called an acute angle.

NOTE. A degree of the circumference of the earth at the equator contains 60 geographical miles, or 69.16 statute miles.

Ex. 122.

1. Reduce 49° 37' 29" to seconds. 2. In 13,978" how many degrees?

3. Find the value of 4 of 360°.

4. What part of the whole angular magnitude about a point is of a second?

5. Find the sum of 45.425°, 0.115', 0.255".

6. Change 0.471 of a minute to the decimal of a degree.

7. What part of 7° 35' 15" are 3° 20′ 45′′?

8. Divide 17° 27′ 13" by 5; multiply 8° 19′ 47′′ by 8; and find the difference between the results.

9. From 7° 0′ 18′′ subtract 3° 47′ 36′′.

10. The latitude of New York is 40° 42′ 43′′ North; the latitude of Boston is 42° 21' 30" North. Find their difference in latitude.

11. The latitude of New Orleans is 29° 57′ 46′′ North; the latitude of Rio Janeiro is 22° 56' South. Find their difference in latitude.

HINT. Their difference in latitude is found by taking the sum of their latitudes.

CURRENCY.

181. The coins of the United States are: 20-dollar, 10dollar, 5-dollar, 3-dollar, 24-dollar, and 1-dollar gold coins; 1-dollar, 50-cent, 25-cent, and 10-cent silver coins; 5-cent and 3-cent nickel coins; and 2-cent and 1-cent bronze coins.

182. As any sum of money can be expressed in United States currency as dollars and decimal fractions of a dollar, it is always best to treat United States money as a simple quantity.

183. The same is true of French, Italian, German, Russian, and Austrian currency.

1. How many shillings in 48d.? in 60 d.?

$0.453.

2. How many pence in 5s.? in 10s.? in a sovereign?

3. How many shillings in £31? in £24?