6. Bought 3 bushels of nuts at $2 a bushel, and sold them at 10 cents a quart, liquid measure: how much was the gain? Ans. $5.17.

APOTHECARIES' FLUID MEASURE.

114. This measure is used in measuring liquids in preparing medicines.

TABLE.

60 minims or drops (m.) = 1 fluid drachm, f 3.

The minim is about equal to a drop of water. A pint of

water weighs nearly a pound.

Cong., from the Lat. congius, means gallon; and O., from the Latin octarius, means one-eighth.

Physicians write their prescriptions in the Roman notation, using the small j for small i when final. Thus, 1 scruple is written i.; 7 drams, 3vij.; 13 ounces, 3xiij.

In business transactions 30 days are considered a month, and

12 months a year.

116. The Solar Day is the interval of time between two successive passings of the sun across any given meridian.

117. The Mean Solar Day is the average length of all the solar days of the year. It is equal to 24 hours.

118. The Civil Day corresponds to the mean solar day, but begins and ends at 12 midnight.

119. A. M. denotes before noon; M., noon, and P. M., after noon.

120. The Solar Year is 365 days 5 hours 48 minutes 49.7 seconds in length.

The months of April, June, September and November have 30 days each. February has 28 days, except in leap-year, when it has 29. The other months have 31 days each.

Every year whose number is divisible by 4, except the centennial years not divisible by 400, is a leap-year.

Since the common year is almost 6 hours greater than 365 days, every fourth year is made a leap-year; but this makes more than the proper time, hence every hundredth year is considered a common year; this again makes less than the proper time, hence every centennial year divisible by 400 is made a leap-year; this makes a difference so small that almost 4000 years will elapse before the difference becomes a full day.

ORAL EXERCISE.

1. In 6 min. how many seconds? In min.? In min.? 2. How many minutes in 3 hr. 11 min.? In 1 hr.? In 480 sec.?

3. How many hours in a week? In 3 d. 11 hr.?

4. How many weeks in 49 d.? In 90 d.?

5. How many days from Jan. 1 to Feb. 28, inclusive?

6. How many days from March 28 to Aug. 16, inclusive? 7. What part of a day are 6 hr.? 10 hr.?

WRITTEN PROBLEMS.

1. Reduce 60000 sec. to hours, etc. Ans. 16 hr. 40 min. 2. How many seconds in a week?

Ans. 604800.

3. How many days from Jan. 1, 1875, to May 1, 1876, inclusive? Ans. 487. 4. A man was born Jan. 2, 1836, and he died Dec. 9, 1874: how old was he? Ans. 38 yr. 11 mo. 7 d. 5. If a note is given Jan. 1, 1876, for 90 days, when does it fall due? Ans. Mar. 31.

6. Point out the leap-years in the following: 1872, 1875, 1876, 1900, 1906, 1908, 2000, 1840, 1600, 1700, 1800, 1820? 7. How much time passes from 20 min. before 9 o'clock to 15 min. after 11 o'clock? Ans. 2 hr. 35 min. 8. How much time passes from 15 min. before 8 A. M. to 20 min. past 2 P. M.? Ans. 6 hr. 35 min. 9. How many leap-years in the nineteenth century?

CIRCULAR MEASURE.

121. Circular or Angular Measure is used in measuring angles and arcs of circles, and in determining latitude and longitude, including the location of places and vessels at sea. The unit of this measure is the degree, equal to part of the circumference of a circle.

Fig. 1.

cumference.

Fig. 2.

122. A Circle is a plane figure bounded by a curved line, every part of which is equally distant from a point within called the centre.

123. The bounding line is called the Circumference.

124. An Arc is any part of the cir

125. A Degree is part of the cir B cumference.

C

126. An Angle is the difference in the direction of two lines meeting at a common point called the vertex.

D Thus, DA C and C A B are angles.

A Fig. 3.

C

B

A

127. A Right Angle is one in which the two lines are perpendicular to each other, as in Fig. 3. The measure of an angle is the arc of a circle included between its two sides. Thus, in A B C the arc

A B is the measure of the angle C.

B

C

128. Any straight line extending from the centre to the circumference of a circle is called a Radius; and any straight line passing through the centre and limited by the circumference is called a Diameter.

90°

S.

C.

= 1 quadrant or right angle.

ORAL EXERCISE.

1. How many degrees in 600 min.?

2. How many minutes in 780 sec.? In 60°?

WRITTEN PROBLEMS.

1. What part of a circumference is 40°? 60°? 120°?

3. How many degrees in 7200"?

3. How many degrees in 890'?

Ans. 2°. Ans. 14° 50'.

NOTE.-Degrees of latitude vary but little, but increase slightly as we approach the poles. A degree of longitude at the equator equals 69.16 common miles; at 30 degrees north latitude, 59.81 common miles; at 60 degrees north latitude, 34.53 miles; and at the poles, nothing.

COUNTING.

The following Table is used in counting such objects as buttons, screws, etc.:

In printing books, large sheets are folded and named as follows: When the sheet is folded into

1. How many years are three score and ten?

2. How many eggs in 63 doz.?

3. How many screws in 14 gro.? In 1 gr. gro.?

4. How many sheets of paper in 6 quires.? In ream? 5. How many scores in 160 yr.?

6. How many sheets of paper will be required to make a quarto volume of 160 pp.?

7. How many sheets of paper will be required to make an 8vo of 240 pp.?

8. How many sheets of paper will be required to make a 12mo volume of 252 pp. .?

9. How many pages of a 16mo book will a quarto of 80 pp. make?