NOTE.-In many business transactions the year is regarded as 360 days, or 12 months of 30 days each.

153. The Calendar Months with the number of days they contain are as follows:

154. The Solar Year is the time between two consecutive returns of the sun to the vernal equinox. Its exact length is 365 da. 5 hr. 48 min. 50 sec. in mean solar time. For civil purposes, the year consists of 365 or 366 days.

In the calendar established by Julius Cæsar, B. C. 46, and thence called the Julian calendar, three successive years were made to consist of 365 days each; and the fourth, of 366 days. According to the Julian calendar, the average length of the year was 365 days, thus making an error of 11 min. 10 sec. each year; which in 400 years would amount to 73 hours, or about 3 days. In the sixteenth century, in consequence of the excess of the Julian year above the true solar year, the error in the calendar was 10 days. To correct the calendar, and to prevent any error in the future, Pope Gregory XIII. decreed that 10 days should be omitted in the month of October, 1582, and that all centennial years not divisible by 400 should be common years. Thus, the years 1700, 1800, and 1900, which according to the Julian calendar would be leap years, would according to the reformed calendar be common years. This

calendar is sometimes called the Gregorian calendar. It is now used in all civilized countries except Russia.

The Julian and Gregorian calendars are also designated by the terms Old Style and New Style. In consequence of the years 1700 and 1800 being com. mon years by the Gregorian calendar, the difference between the two styles is now 12 days. Thus, when it is July 4 in Russia, it is July 16 in other countries.

155. RULE FOR LEAP YEARS.-All years divisible by 4, except centennial years, are leap years.

All centennial years divisible by 400 are leap years.

LINEAR MEASURE.

156. Linear or Long Measure is used in measuring distances, also the length, breadth, and height of bodies, or their linear dimensions.

360000

In measuring length, the yard derived from the standard yard of England is the standard unit, the yards of the United States and England being identical. Theoretically, the yard is equal to 3999 of the length of a pendulum that vibrates seconds in a vacuum, at the level of the sea in the latitude of London; that is, a pendulum that vibrates seconds under the above conditions is 33.1393 inches in length. The standard yard is, in fact, the distance between two points on a brass bar, preserved at Washington, the distance to be taken when the bar is at a temperature of 62° Fahrenheit. This bar was obtained from England in 1827.

NOTES.-1. The inch is usually divided into halves, quarters, eighths, and sixteenths.

2. The foot and inch are divided by civil engineers and others into tenths, hundredths, thousandths, etc.

3. In measuring cloth, ribbon, and other goods sold by the yard, the yard is divided into halves, quarters, eighths, and sixteenths.

4. At the U. S. Custom Houses the yard is divided into tenths and hundredths.

5. The mile (5280 ft.) of the above table is the legal mile of the United States and England, and hence it is sometimes called the statute mile.

15%. Other Denominations.-The following denominations are also used:

1 Point

1 Line

1 Size

1 Hand

1 Fathom

1 Cable-length

1 Geographic Mile

1 Knot

60 Geo. Miles, or 69.16 Stat. Miles ( 360 Degrees

= 4 Inches.

6 Feet.

Used by shoemakers.

Used in measuring the height of horses. Used in measuring depths at sea.

120 Fathoms, or 240 yards.

1.15+ Statute Miles.

sea.

Used in measuring distances at

= 1 Geo. Mile. Used in determining the speed of vessels.

=

1 Degree

of latitude on a meridian, or of longitude on the equator.

the Circumference of the Earth.

SURVEYORS' LINEAR MEASURE.

158. Surveyors' Linear Measure is used in measuring land, roads, etc.

The unit of this measure is a chain, 4 rods or 66 feet in length, called Gunter's Chain. It is divided into 100 parts called links, each link being 7.92 inches in length.

NOTES.-1. Links are written decimally as hundredths of a chain.

3. Engineers for railroad and other purposes use a chain or tape 100 feet long, the feet being divided into tenths.

SQUARE MEASURE.

159. Square Measure is used in measuring surfaces.

The unit of square measure is a square bounded by lines of some known length. Thus, a square inch is a square whose sides are one inch long; a square foot, a square whose sides are one foot long; etc.

NOTE.-1 Rood = 40 sq. rds. = A. The rood has practically gone out

of use.

160. The Area of a surface is an expression for that surface in terms of square units.

3 feet.

4 feet.

In the diagram each small square represents a square foot. Since there are 3 rows, and 4 square feet in each row, there are 3 times 4 square feet, or 12 square feet in the rectangle. Hence, the area of any rectangle may be found by multiplying together the numbers denoting its length and breadth, in the same denomination; or, more briefly,

To find the area of a rectangle, multiply its length by its breadth.

SURVEYORS' SQUARE MEASURE.

161. Surveyors' Square Measure is used in measuring land.

NOTES.-1. 1 Pole or Perch = 1 sq. rd. = 16 sq. ch. =

2. The acre is the common unit of land measure. 3. In the vicinity of St. Louis, and in other parts of the Mississippi valley that were settled by the French, the old French arpent is still used as the unit of land measure. It contains about of an English acre.

162. U. S. Public Lands are divided by north and south lines run according to the true meridian, and by others crossing

them at right angles, so as to form townships of six miles square.

Townships are subdivided into sections, containing, as nearly as may be, 640 acres each, or 1 square mile.

Sections are subdivided into half-sections, quarter-sections, half-quarter-sections, and quarter-quarter-sections.

The following diagrams show the method of numbering the sections of a township, as also that of naming the subdivisions of sections.

163. Solid or Cubic Measure is used in measuring solids, or bodies, which have length, breadth, and thickness or depth; as boxes, earth, wood, stone, etc.

The unit of cubic measure is a cube, each of whose edges is a unit of some known length. Thus, a cubic inch is a cube, each of whose edges is one inch; a cubic foot is a cube, each of whose edges is one foot; etc.