How many

1. Pints in 16gal. 3qt. 1pt. of wine? 2. Gallons in 7635 gills of vinegar?

3. Pints in 26bu. 3pk. 7qt. 1pt. of berries? 4. Bushels in 37891 pints of clover seed?

5. What cost 5gal. 3qt. 1pt. of vinegar at 3 cents a pint? 6. What cost 217bu. 3pk. 5at. of canary seed at 183 cents a quart?

APOTHECARIES' FLUID MEASURE.

197. Apothecaries' Fluid Measure is used for measur ing liquids in preparing medical prescriptions.

60 minims (m.) equal 1 fluidrachm,

fz.

fz.

0.

Cong.

NOTE. Cong. is the abbreviation of congiarium, the Latin for gallon. O. is the initial of octans, the Latin for one-eighth, the pint being oneeighth of a gallon.

199. The year is divided into 12 calendar months, three of which constitute a division called a Season. The seasons, months, and number of days in each, are exhibited in the fol lowing table:

NOTES.-I. January is derived from Janus, the god of the year, or janua, a gate, because this month opens or begins the year. February is from februa, the Roman festival of propitiation, 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. July was named by Mark Antony after Julius, the surname of Caius Cæsar, who was born in this month. It was previously called Quintilis. August was named after Augustus Cæsar. It was formerly called Sextilis, the sixth month. September, October, November, December, are respectively named from the Latin numerals, Septem, Octo, Novem, and Decem.

II. The unit of time is the day. 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 reckoned from noon, and consists of 24 hours. The Civil day is the average length of all the solar days of the year; it begins and ends at 12 o'clock, midnight, and consists of two periods of 12 hours each.

III. The number of days in each month is easily remembered by the following stanza :--

Thirty days hath September,
April, June, and November;
All the rest have thirty-one,
Except the second month alone;
To which we twenty-eight assign,
Till leap year gives it twenty-nine.

It is often necessary to determine the number of days from one date to another, for which we give the following

TABLE

200. SHOWING THE NUMBER OF DAYS FROM ANY DAY OF ONE MONTH TO

THE SAME DAY OF ANY OTHER MONTH IN THE SAME YEAR.

90

59

FROM ANY

DAY OF

To THE SAME DAY OF

Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. Oct. Nov. Dec.

January 365 31 59
February 334 365 28

March

306 337 365 31

June July

31

August 153 184 212 243 273 304 334 365
61 92 122
September 122 153 181 212 242 273 303 334 365 30 61 91
October 92 123 151 182 212 243 273 304 335 365 31 61
November 61 92 120 151 181 212 242 273 304 334 365 80
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 allow ance must be made for leap year.

1. How many minutes in 5da. 7h. 45min. ?

2. How many seconds in one day?

3. How many seconds in one week?

4. Reduce 56780 seconds to hours.

Ans. 604800.

Ans. 15h., etc.

5. In one year how many hours; how many minutes; how many seconds?

Ans. 8765 hours+.

6. How many days from May 8th to October 19th?

Ans. 164 days.

7. How many days from March 28th to December 16th?

Ans. 263 days. 8. How many days from Feb. 21st, 1860, to Sept. 10th, 1860?

Ans. 202 days.

201. ADJUSTMENT OF THE CALENDAR.

A True or Solar Year is the exact time in which the earth revolves around the sun. It consists of 365d. 5h. 48min. 49.7sec. 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.

The calendar is reckoned according to the following rule :

nial

RULE.-Every year that is divisible by 4, except the centenyears, 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 which when expressed in figures end in two ciphers.

EXPLANATION.-I. If we reckon 365 days as 1 year, the time lost in the calendar in one year is 5h. 48min. 49.7sec., and in 4 years is 23h. 15min. 18.8sec., that is one day, lacking only 44min. 41.2sec.; 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 4th year be reckoned as leap year, since we add 44min., etc., too much, the time gained in the calendar in 4 years is 44min. 41.2sec., and in 100 years it will be 18h. 37min. 10sec., that is one day, lacking 5h. 22min. 50sec.; hence the second error may be corrected by deducting one day from each centennial leap year, thus calling each centennial 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 5h. 22min. 50sec., and in 400 years it will be 21h. 31min. 20sec.; hence the time lost in 400 years will be 1 day, lacking 2h. 28min. 40sec., 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.

NOTE. The reckoning of time by the ancients was very inaccurate. The calendar was reformed by Julius Cæsar, 46 B. C., who made the year to consist of 365 days, adding one day every fourth year. In 1582, Pope Gregory corrected the error which resulted from the above correction, by striking out 10 days from the calendar, calling the 4th of October the 14th. Some countries, as Russia, still adhere to the Julian Calendar, their dates being about 12 days behind ours. The dates g distinguished as Old Style and New Style.

CIRCULAR OR ANGULAR MEASURE.

202. Circular Measure is used to reckon angles and directions, latitude and longitude, difference of time, etc.

203. A Circle is a plane surface bounded by a curve line, every point of which is equally distant from a point within called the centre.

204. The bounding line is called the circumference; the distance from the centre to the circumference is called the radius, and the line through the centre, with both ends in the curve, the diameter. The circumference is divided

into equal parts for the purpose of measuring angles, according to the following

NOTES.-I. The unit is the degree, which is go of the circumference of a circle. One-fourth of a circumference, or 90°, is called a quadrant. A minute of the earth's circumference is equal to a geographical mile.

II. The divisions of the circumference are not of absolute length, they are merely equal parts, used to indicate the size of angles; thus, & quadrant, whether the circle is large or small, measures a right angle.