METHOD OF USING THE TABLE.-Suppose we wish to find the num ber 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 Februarv 28 days, the proper allowance must be made for leap year.

I. TERMS.-January is derived from Janus, the god of the year, to whom this month was sacred. February is from februa, the Roman fes tival 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, or sixth month. September, October, November, and 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.

II. The number of days in each month is easily remembered by the fol. lowing stanza :—

Thirty days hath September,
April, Jure, and November;
All the rest have thirty-one,
Excepting February alone;

To which we twenty-eight assign,
Till leap year gives it twenty-nine.

MENTAL EXERCISES.

1. How many seconds in 30 minutes? in 25 minutes? 2. How many minutes in 360 seconds? in 3 hours?

3. How many hours in 660 minutes? in 4 days?

4. How many days in 72 hours? in 4 weeks?

5. How many days in 3 common years? in 4 leap years?

6. How many common years in 730 days?

7. Name the months which have 30 days each; those which have 81 days each.

WRITTEN EXERCISES.

Ans. 86400 sec.

Ans. 604800 sec.

1. How many seconds in one day?

2. How many seconds in one week?

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

4. Reduce 56780 seconds to hours.

Ans. 7665 min.

Ans. 15 h. 46 min. 20 sec.

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

Ans. 8760 h.; 525,600 min. ; 31,536,000 sec. 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 February 21st, 1860, to September 10th, 1860? Ans. 202 days.

ADJUSTMENT OF THE CALENDAR.

297. A True or Solar Year is the exact time in which the earth revolves around the sun. It consists of 365 da. 5h. 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.

298. 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 others are common years.

NOTE.-The centennial years are 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 the time lost 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 5h. 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 2h. 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.

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 5th of October the 15th, and ordaining that henceforth only those centennial years should be leap years which are divisible by 400. This change was soon adopted by most Catholic countries, but Great Britain did not make the change till 1752, when the error amounted to 11 days. Some countries, as Russia, still adhere to the Julian Calendar, their dates being about 12 days behind ours. The dates are distinguished as Old Style and New Style.

MENTAL EXERCISES.

1. How many centuries is it since the birth of Christ?

2. When did the 18th century end and the 19th century begin? 3. How many leap years and how many common years in every century?

4. Which of the following are leap years: 1700? 1760? 1776? 1800? 1876? 1880? 1890? 1900? 2000?

5. My watch ticks 4 times in a second; how many times will it tick in a day?

MISCELLANEOUS TABLES.

299. The following tables are frequently used, the first in counting certain kinds of articles, and the second in the paper trade.

I. Two things of a kind are frequently called a pair and six a set. II. Paper is sold at retail by sheets, quires, and reams, and at wholesale by reams.

BOOKS.

300. In printing books large sheets of paper are used, which are folded into leaves according to the size of the book. The terms folio, quarto, octavo, etc., as applied to printed books, are based on sheets about 18× 24 in., about half the sizes now generally used, and indicate the number of leaves into which such a sheet is folded.

NOTE.-Printing paper is made of many sizes, according to the require ments of the printer. In book printing 24 X 38 inches, called Double Medium, is perhaps used most largely.

301. Clerks and copyists are often paid by the folio for making copies of legal papers, records, and documents.

72 words make 1 folio, or sheet of common law.

90 ""

66 "1"

66 "chancery.

MENTAL EXERCISES.

1. How many dozens in a gross? In 2 gross? In a great gross?

2. How many pairs in 40? Scores in 60? Scores in 70? Sets in 48? 3. How many sheets in 3 quires? In 24 quires? In a ream? In ream?

4. How many eggs in 2 dozen? In half a dozen? In a dozen and a quarter?

5. How many years in 3 score? In 3 score and 10? In 4 score and a half?

6. How many sheets of paper will be required to make a 12mo. book of 360 pages? Of 480 pages?

7. How many sheets will be required to make an octavo book of 320 pages? Of 400 pages?

8. How many octavo books will the paper for a quarto book make, of the same number of pages?

WRITTEN EXERCISES.

1. How many fine black crayons are there in 42 boxes, each containing 1 gross? Ans. 6048.

2. Sold 63 boxes of Maynard's writing ink, each box containing 3 dozen bottles; how many gross?

Ans. 15 gross, 9 dozen.

8. What would be the cost of 3240 sheets of foolscap at 36 cents a quire?

Ans. $48.60

4. A lady copied in one month 795.5 chancery folios at 129 per folio; what did she receive?

Ans. $95.46.

5. A printer used 3 reams 5 quires 19 sheets of paper for printing half-sheet posters; how many did he print, allowing 1 quire to a ream for waste? Ans. 3000.

6. How much paper would it require to print 5000 copies of a 12mo book of 424 pages, allowing 1 quire to each ream for waste?

REDUCTION OF COMPOUND NUMBERS.

302. Reduction is the process of changing a number from one denomination to another without altering its value. 303. There are Two Cases: Reduction Descending and Reduction Ascending.

These two cases have been considered in the examples under the tables, but we will present a few more problems under their proper heads.

REDUCTION DESCENDING.

304. Reduction Descending is the process of reducing a number to a lower denomination.

1. Reduce £6 5 s. 3 d. to pence.

SOLUTION.-In 1 pound there are 20 shillings, and in £6 there are 6 times 20 shillings, or 120 shillings; 120 shillings plus 5 shillings are 125 shillings; in 1 shilling there are 12 pence, and in 125 shillings there are 125 times 12 pence, or 1500 pence; 1500 pence plus 3 pence are 1503 d. Therefore, etc.

OPERATION.

£ 8. d.
6 5 3
20

125 s.

12

1503 d., Ans.

Rule.-I. Multiply the number of the highest denomination given, by the number of units of the next lower denomination which equals one of this higher, and to the product add the number given, if any, of this lower denomination.

II. Multiply this result as before, and proceed in the same manner until we arrive at the required denomination.

WRITTEN EXERCISES.

2. Reduce 15 lb. 4 oz. 3 pwt. 15 gr. to 8. 17 lb. 73 53 19 18 gr. to gr.

gr.

Ans. 88407 gr. Ans. 101618 gr.

4. 3 cable lengths 100 fathoms to feet.

Ans. 2760 ft.

5. In 18 T. 13 cwt. 75 lb. 14 oz. how many ounces?

Ans. 598014 oz.