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10th 6 11th 66 12th "
365 days, 5 hours, 48 minutes, 57 seconds, or 365.2423+ =1 solar year, 100 years =l century. Every 4th or leap-year has 366 days.
The year is also divided into 12 calendar months, as follows: 1st month, January, has 31 days. 7th month, July, has 31 days. 20 February, 28
August, 31 3d March, 31
30 4th April,
31 5th May, 31
Nov., 30 6th June, 30
Dec., 31 The diurnal motion of the earth on its axis is 171 miles per minute at the equator=1035 miles per hour. The earth moves in its orbit 68249 miles
April, June, and November;
All the rest have thirty-one.”
Note.-To know when it is leap-year, divide the years over even centuries by 4; if no remainder, it is leap-year; but if any remain, it is so many years after leap-year. (See the note at the close of the tables.)
Marked. 24 sheets, or 23.6 (sh.)
make 1 quire, qr. 20 quires
1 ream, 2 reams
1 bundle, bun.
Marked, 12 single things
make I dozen, doz. 12 dozen
gro. 12 gross (144 dozen)
1 great gross, g; gro. 20 single things (112 lbs.=1 quintal fish) 1 score, 5 scores (2 are 1 pair, or couple) 1 hundred, hund.
Marked 36mo, is when I sheet makes 36 leaves, or 72 pages, pp. 24mo. 1 24
48 1 8mo. 1 18
36 ] 2mo. 1
24 Octavo, or 8vo. I
16 Quarto, or 4to. 1
8 Folio, or fol. 1
Note. Extracts : The civil solar year of 365 days being short of the true year by 5h. 48m. 48sec., occasioned the beginning of the year to run forward through the seasons nearly 1 day in 4 years.
On this account Julius Cesar ordained that one day should be added to February every 4th year; by causing the 24th day to be reckoned twice ; and because this 24th day was the sixth (sextilis) before the Kalends of March, there were in this year two of these sextiles, which gave the name of Bissextile to this year, which being thus corrected, was thence called the Julian year.
Pope Gregory the 13th made a reformation of the calendar. The Julian calendar, or old style, had, before that time, been in general use all over Europe. The year, according to the Julian calendar, consists of 365 days and 6 hours; which 6 hours being one fourth part of a day, the common years consisted of 365 days, and every fourth year, one day was added to the month of February, which made each of those years 366 days, which are usually called leap years. This computation, though near the truth, is more than the solar year by eleven minutes which, in one hundred and thirty-one years will amount to a whole day. By this calculation, the vernal equinox was anticipated ten days from the time of the general council of Nice, held in the year 325 of the Christian era to the time of Pope Gregory, who therefore caused ten days to be taken out of the month of October in 1582, to make the equinox fall on the 21st of March, as it did at the time of that council. And to prevent the like variation for the future, he ordered that three days should be abated in every four hundred years, by reducing the leap-year at the close of each century, for three successive centuries, to common years, and retaining the leap-year at the close of each fourth century only. This was at that time esteemed as exactly conformable to the true solar year; but Dr: Halley makes the solar year to be 365 days, five hours, forty-eight minutes, fifty-four seconds, forty-one thirds, twenty-seven fourths, and thirty-one fifths ; according to which, in 400 years, the. Julian year of 365 days 6 hours, will exceed the solar year by three days, one hour, and fifty-five minutes, which is near two hours, so that in 50 centuries it will amount to a day, that is, the lh. 55m. in 400 years, would in 50 centuries=23h.57m. 30sec.; +3 days=3d. 23h.57m. 30sec.; which would be 22m. less than 4 days, and would be the true difference in 5,000 years. Though the Gregorian calendar, or new style, had long been used throughout the greatest part of Europe, it did not take place in Great Britain and America till the first of January, 1752 ; and in September following, the cleven days were adjusted, by calling the thiril day of that month the fourteenth, and continuing the rest in their order.
A just and equal measure of the year is called the periodical year, as being the time of the earth's period about the sun, in departing from any fixed point in the heavens, and returning to the same again. The Zodiac is a great circle of the sphere, containing the twelve signs, through which the sun passes.
There are two kinds of Reduction, termed simple and compound, by which we are taught how to change a sum or quantity of one denomination to another, whether it be greater or less, still retaining the same value ; when the sum consists of only one denomination, and that is to be changed, or reduced to another, it is called Simple Reduction. The operations are all performed either by multiplication or division; when by multiplication, it is called reduction descending ; when by division, reduction ascending; for instance, to reduce pounds (avoir.) to drams, multiply by 16,
which will reduce it to ounces, then by 16 again, and it will be sin drams; then take those drams and divide by 16, and it will be ounces;. then divide again by 16, and it will be pounds, because 16 ounces make 1 pound, and 16 drams 1 ounce, &c.
By the above process, sums in reduction will reciprocally prove each other; and it would be well for the teacher to require it of the pupil.
1. Multiply the sum or quantity by that number of the next lower denomination which it requires to make one of its own.
2. If there be one or more denominations between the de. nomination of the given sum or quantity, and that to which it is to be reduced, first reduce it to the next lower than its own, and then to the next lower, &c.
3. When low denominations are to be brought to higher denominations, as for example, drams to pounds, cents to dollars, inches to miles, &c., divide hy as many of the lower as make one of the higher, and set down what remains (if any) at the right ; so proceed till you have brought it into that denomination which your question requires. See example.
Example. Bring 2cwt. to drams. 2 cwt.
Explanation: First multiply thu 2cwt. 4xqr.=1 cwt. by 4, and this will reduce it to quar
ters, because 4 quarters = lcwt, 8 qr.=2 cwt. then multiply the quarters by 28, and 28 x lb.=l qr. this will reduce it to pounds, because
28 lb.=l.qr. ; then multiply by 16 224 lb.=8 qr.
which will reduce it to 16 x oz.=1 lb.
because 16 ounces = 1 lb.; then
multiply the ounces by 16, which 1344
will reduce it to drams; because 16 224
drams 1 ounce, &c. Then to
prove it, take the sum of the drams, 3584 oz.=224 lb. and divide by the same denomina16 X drams=1 oz. tions by which you multiplied, and
this will bring back the 2 cwt. 16)57344 drams=3584 oz.
17920. 80 lbs. 4 oz.
Ans. 180. 115200. 16800.
Avoirdupois Weight. 1. In 120 pounds, how many ounces ? 2. Bring 1 cwt. to ounces. 3. Bring 10 cwt. to ounces. 4. Bring 1284 ounces to pounds. 5. Bring 1642 quarters to cwts. 6. Bring 184 drams to ounces. 7. Bring 1674 drams to pounds. 8. Bring 1 ton to drams.
Troy Weight. 9. Reduce 15 lbs. to ounces. 10. Bring 20 lbs. to grains. 11. Bring 35 ounces to grains. 12. Bring 1476 ounces to pounds. 13. Bring 34 lbs. to ounces. 14. Bring 97 lbs. to grains. 15. Bring 1796 grains to ounces. 16. Bring 1100 ounces to pounds.
Apothecaries' Weight. 17. Bring 72 ounces to drams. 18. Bring 10 pounds to grains. 19. Bring 17 pounds to ounces. 20. Bring 57 ounces to scruples. 21. Bring 27 drame to grains. 22. Bring 480 scruples to pounds.
Long Measure. 23. Bring 40 yards to seet. 24. Bring 74 poles to feet. 25. Bring 120 furlongs to poles. 26. Bring 27 yards to inches. 27. Bring 1 mile to yards.
Cloth Measure. 28. Bring 5 yards to quarters. 29. Bring 10 yards to nails. 30. Bring 72 quarters to nails. 31. Bring 144 quarters to nails.
Land or Square Measure. 32. Bring 18 roods to poles.
Ans. 576. 57600,
204. 1368. 1620.
1221. 4800. 972.