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3. How many bushels in 78954 pints of timothy seed ?
Ans. 1233 bu. 2 pk. 5 qt. 4. What cost 8 gal. 3 qt. 1 pt. of kerosene at 3 cts. a pint ?
Ans. $2.13. 5. What cost 7 bu. 3 qt. 1 pt. of strawberries at 124 a pint?
CIRCULAR MEASURE. 396. Circular Measure is used to measure angles and directions, latitude and longitude, etc.
397. A Circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the centre.
398. The Circumference of a circle is the bounding line; any part of the circumference, as BC, is an arc. An arc of one-fourth of the circumference is called a quadrant.
399. For the purpose of measuring angles, the circumference is divided into 360 equal parts, called degrees; each degree into 60 equal parts, called minutes; each minute into 60 equal parts called seconds.
400. Any angle having its vertex at the centre, is measured by the arc included between its sides; thus, COB is measured by the arc BC. A right angle is measured by 90 degrees, or a quadrant; half a right angle, by 45 degrees, etc.
60 seconds ("').
1 minute 60 minutes
1 degree 30 degrees
1 sign .
S. 12 signs, or 360°
1 circumference. C. C.
12 360 21600 1296000
I. TERMS.-The division of the circumference of the circle into 360 equal parts, took its origin from the length of the year, which (in round numbers) was supposed to contain 360 days, or 12 months of 30 days each. The 12 signs correspond to the 12 months. The term minute is from the Latin minutum, which signifies a small part. The term second is an abbreviated expression for second minutes, or minutes of the second order. Signs are used in astronomy as a measure of the zodiac.
II. UNIT. --The unit is the degree, which is to of the circumference of a circle. A quadrant is one-fourth of a circumference, or 90°. A minute of the earth's circumference is called a geographic mile.
III. DIVISIONS.—The divisions of the circumference are not of absolute length, but are merely equal parts, indicating the size of angles. Thus, a quadrant, whether the circle is large or small, measures a right angle.
MEASURES OF TIME. 401. Time is a portion of duration. The measures of time are fixed by the revolution of the earth on its axis and around the sun.
402. A Day is the time of the revolution of the earth upon its axis; a Year is the time of the revolution of the earth around the sun
1 week .
wk. 4 weeks
1 lunar month mo. 12 calendar months, or 13 lunar months, 1 da., 6 h.,
yr. yr. mo.
da. h. min.
365 8760 525600 = 31536000 1 = 12
366 8784 527040 = 31622400 1
7 168 10080 604800 1 24 1440
3600 Scale.--Ascending, 60, 60, 24, 7; descending, 7, 24, 60, 60.
I. TERMS. - Second and minute are parts of an hour, corresponding to the parts of a degree in Circular Measure. Hour is derived from the Latin hora, originally a definite space of time fixed by natural laws; a day, derived from the Saxon daeg, is the time of the revolution of the earth upon its axis; a week is a period of uncertain origin, but which has been used from time immemorial in Eastern countries ; a month, from Saxon monadh, from mona, the moon, is the time of one revolution of the moon around the earth ; a year, from Saxon gear, is the time of the earth’s revolution around the sun; a century comes from the Latin centuria, a collection of a hundred things.
II. UNIT.— The unit of time is the day; it is determined by the revolution of the earth on its axis. The Sidereal Day is the exact time of the revolution of the earth on its axis. The Solar Day is the time of the apparent revolution of the sun around the earth. The Astronomical Day is the solar day, beginning and ending at noon. The Civil Day is the average length of all the solar days of the year; it begins at 12 o'clock midnight, and consists of two periods of 12 hours each.
THE CALENDAR. 403. The Calendar is a division of time into periods adapted to the purposes of civil life.
404. The Year is divided into 12 calendar months, three of which constitute a period called a Season.
405. The seasons, months, and number of days in each, are given in the following table: NO. OF Mo. MONTH. .
No. of LAYS. 1 January,
28 or 29
31 I. NAMES. -January is derived from Janus, the god of the year, to whom this month was sacred. February is from februa, the Roman festival of expiation, celebrated on the 15th of this month. January and February were added to the Roman calendar by Numa, Romulus having previously divided the year into 10 months. March is from Mars, the god of war and reputed father of Romulus. It was the first month of the Roman calendar. April is probably from the Latin aperire, to open, from the opening of the buds or the bosom of the earth in producing vegetation. May is from Maia, the mother of Mercury, to whom the Romans offered sacrifices on the first day of this month. June is from Juno, the sister and wife of Jupiter, to whom it was sacred. July was named by Mark Antony after Julius Cæsar, who was born in this month. It was previously called Quintilis. August was named after Augustus Cæsar, who entered upon his first consulate in this month. It was formerly called Sextilis, the
sixth month. September, October, November, December, are respectively named from the Latin numerals, Septem, Octo, Novem, and Decem, as, when the year began in March, they were the seventh, eighth, ninth, and tenth months, as their names indicate. It will be noticed that we have derived our names of the months directly from the Romans, as have most of the nations of modern Europe, while the days of the week in English are derived from the Saxons.
II. The number of days in each month is easily remembered by the following stanza :
Thirty days hath September,
Till leap year gives it twenty-nine. 406. The time from any day of one month to any day of another month in the same year is readily found by the following table:
SHOWING THE NUMBER OF DAYS FROM ANY DAY OF ONE MONTH TO
THE SAME DAY OF ANY OTHER MONTH IN THE SAME YEAR.
TO THE SAME DAY OF
Jan. Feb. Mar Apr May J'ne July Aug Sep. Oct. Nov Dec
January 365 31 59 90 120 151 181 212 243 273 304 334 February 334 365 28 59 89 120 150 181 212 242 273 303 March 306 337 365 31 61 92 122 153 18+ 214 245 275 April 275 306 331 365 30 61 91 122 153 183 214 244 May
245 276 304 335 365 31 61 92 123 153 184 214 June 214 245 273 304 334 365 30 61 92 122 153 183 July 184 215 243 274 304 335 365 31 62 92 123 153 August 153 154 212 243 273 304 334 365 31 61 92 122 September 122 153 181 212 242 273 303 334 365 30 61 91 October 92 123 151 182 212 213 273 304 335 365 31 61 November 61 92 1201 151 181 212 242 273 304 334 365 30 December 31 62 90 121 151 182 212 243 274| 304 335 365
METHOD OF USING THE TABLE.—Suppose we wish to find the number of days from March 10th to November 16th. We find March in the vertical column, and November at the top, and at the intersection we find 245, to which adding 6 days we have 251, the number of days required.
The table being constructed for February 28 days, the proper allowance must be made for leap year.
ADJUSTMENT OF THE CALENDAR. 407. A True or Solar Year is the exact time in which the earth revolves around the sun. It varies a little as given by different authorities, but Laplace, Herschel, and some others, reckon it at 365 da. 5 h. 48 min. 49.7 sec. Now since it is inconvenient to reckon the fractional part of a day each year, it is necessary to arrange a correct calendar in which each year may have a whole number of days. This is done by causing some years to consist of 365 days and others of 366 days. The former are called common years, the latter Bissextile or Leap years.
408. The Calendar is reckoned according to the following rule:
Rule.—Every year that is divisible by 4, except the centennial years, and every centennial year divisible by 400, is a leap year ; all the other years are common years.
NOTE.—The centennial years are the hundredth years, or those whose expressions in figures end in two ciphers.
EXPLANATION.-I. If we reckon 365 days as one year, the time lost in the calendar in one year is 5 h. 48 min. 49.7 sec., and in four years is 23 h. 15 min. 18.8 sec., that is, one day, lacking only 44 min. 41.2 sec.; hence the first error can be corrected by adding one day every four years, making the year to consist of 366 days.
II. If every fourth year be reckoned as leap year, since we add 44 min., etc., too much, the time gained in the calendar in four years is 44 min. 41.2 sec., and in 100 years it will be 18 h. 37 min. 10 sec., that is, one day lacking 5 h. 22 min. 50 sec.; hence the second error may be corrected by deducting one day from each centennial leap year, thus calling each centennial year a common year of 365 days.
III. Again, if every centennial year be reckoned as a common year, since we do not add enough, the time lost in 100 years will be 5 h. 22 min. 50 sec., and in 400 years it will be 21 h. 31 min. 20 sec.; hence the time lost in 400 years will be 1 day lacking 2 h. 28 min. 40 sec., and this error may be rectified by making every 4th centennial year a leap year.
In the same way we may make the calendar correct for any number of years.
NOTES.–1. The reckoning of time among the ancients, owing to their ignorance of astronomy, was very inaccurate. The calendar adopted by Romulus consisted of only ten months, but Numa added two more, and arranged a system of intercalations, which, had it been adhered to, would have made the year to average 3654 days. But changes were frequently made for political reasons, and the calendar fell into such confusion that the civil equinox, in the time of Cæsar, differed from the astronomical by three months. The calendar was reformed by Julius Cæsar, 46 B. C., who decreed that the year should consist of 3651 days, and since it was not convenient to count the 4 of a day every year, every 4th year was made to consist of 366 days. This extra day, called the inter-calary day, was introduced by counting the 24th of February twice. This day, being the sixth before the kalends of March, the years containing it were called bissextile (bis-sextile), having two sixths. With us it is called Leap Year, because it leaps, as it were, over a day.
2. The correction of Cæsar assumed the year to consist of 365 days, 6 hours, which is 11 min. 10.3 sec. too much; hence his correction introduced a slight error, which in 1582 had amounted to 10 days--the civil