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MISCELLANEOUS EXAMPLES. 329. 1. Maurice H. Decker, bought of Silas Kingsbury & Co., Elmir, M. Y., July 5, 1888, 1760 ft. pine, at $29 per M; 40 cedar posts, at $12.50 per O; nails and hardware, $6.21; 11248 ft. stringers, at $4.75 per M. What was the amount of the bill ?

2. Geo. W. Banning, bought of E. B. Henry & Co., Syracuse, N. Y., June 13, 1888, on account, 2 doz. carpet stretchers, at $3; 10 grindstones, at $2.25; 5 doz. steelyards, at $9; 15 blacksmith drills, at $7; 12 clothes wringers, at $1.50; 6 doz. wrought wrenches, at $12. 25; 3 copying presses, at $5; 7 doz. cow bells, at $8.50; 15 doz. cast steel axes, at $12. Find the amount of the bill.

3. Wm. J. Howard, bought for cash of Howe & Collins, carpet dealers, Rochester, N. Y., July 1, 1888, 100 yd. Moquette, at $1.75; 250 yd. body Brussels, at $1.50; 325 yd. tapestry Brussels, at $1.00; 500 yd. 3-ply ingrain, at 750; 275 yd. 2-ply ingrain, at 654; 300 yd. matting, at 254; 200 yd. lining. at 121¢. How much money was required to pay the bill ?

4. Henry R. Smith, bought of 0. L. Warren, Waverly, N. Y., Dec. 15, 1888, terms, 60 da.; 2% off, in 10 da.; 3 doz. Eagle wash boards, at $1.75; 5 doz. Novelty wash boards, at $2.25; 5 M. No. 4 paper bags, at $1.75; 3 doz, butter bowls, at $2; 5 doz. 0. C. trays, at $4; 11 doz, feather dusters, at $18; 10 gro. Gates' matches, at $2.75; 15 broom racks, at $2.25; 5 doz. wood shovels, at $7.50; doz, oil tanks, at $16. What was the amount of the bill ?

5. Jeffrey & Co., bought of Perry & Co., Buffalo, N. Y., Sept. 1, 1888: 10 pc. F. of L. cotton, 50 601 653 51 6010 pc. M. shirting, 40 41 46 34 51 45 50 55 52 62 61 56, at 8%.

43 52 42, at 54. 5 doz. C. silk, at 80%

15 pc. crash, 600 yd., at 5. 4 pc. A. F. cashmere, 622 513 55 60, at| 6 pc. C. jeans, 503 451 50 55 51% 46, at 19€.

54. 5 pc. A. L. L. cotton, 40 462 512 55 10 doz. M. L. thread, at 59€. 421, at 44.

10 R. print, 41 55 45 51 46 50 40 56 500 lb. W. S. warp, at 15%.

42 52, at 414. Find the amount of the bill.

6. W. C. Blanchard, bought of M. C. Wood, Utica, N. Y., July 15, 1888: 10 pc. R. gingham, 60 612 501 603 51|4 pc. N. sateen, 553 55 50 603, at 514. 613 61 50 55 513, at 84.

5 gross T. Braid, at $7.621. 10 doz. F. E. braid, at 234.

3 doz. L. shirts, at $7.20. 10 pc. B. checks, 45 41 551 42 52 402 6 pc. T. R. print, 25 35 303 31 21 251, 50 55 513 452, at 244.

at 44. 15 gro. G. buttons, at $1.121.

10 cases E. Batts, at $6.00. 2 pc. T. A. flannel, 65 60, at 30°. 20 gro. S. P. buttons, at 49€. 6 pc. E. lining, 40 551 452 52 41 501, 4 pc. V. barege, 20, 23 25 25, at 1634. at 5%.

7 pc. W. Print, 453 51 45 50 462 55 50 5 doz. L. L. gloves, at $3.05.

at 544. What was the amount of the bill ?

pc.

7. I. F. Hoyt, bought of Mann & Moore, Sept. 4, 1888, terms 30 da. : 10 pe. N. sateen, 552 51 503 541 56 55 20 pc. R. Gingham, 50 521 51 512 55 522 53 513 50, at 544.

603 621 612 58 552 561 533 51 553 15

pc. T. A. flannel, 623 651 61 582 55 612 61 581 56 542 511, at 644. 631 653 62 602 63 563 601 58 622 651 10 pc. B. checks, 45 521 412 40 553 503 at 3334

45 511 42 503, at 25°. What was the footing of the bill ?

H. B. Smith, bought of Jones Bros. & Co., Dec. 3, 1888: 19 pc. M. gingham, 472 36 413 491 393 441 443 51 402 392 373 35 382 35 41%

41 323 34 361 423 46 353 381 45 50 463 492 381 413 382 361, at 6 & 483 332 391 36, at 114.

10 pc. B. D. velvet, 212 273 25 262 293 20 pc. P. B. sheeting, 323 321 372 40 222 243 21 203 232, at $6.50.

Find the footing of the bill.

9. Drown Bros. & Ço., bought of W. B. Adams & Co., for cash, June 18, 1888: 20 pc. L. gingham, 582 461 413 381 462 372 34 362 423 48 432 531 381 42, at

453 512 55 382 35 373 493 402 513 44 514. 442 40 371 333 462, at 8.14.

20 pc. E. lining, 45 541 392 483 462 382 24

pc. W. print, 441 463 512 393 412 45 471 372 453 463 424 443 453 431 352 483 51 343 372 35 362 413 343 491 542 343 422 532 441, at 444. What sum of money was required to pay the bill ?

10. Find the amount of the following inventory: 25 pc. M. gingham, 462 482 391 472 41 39 432 472 42 362, at 84.

50 393 503 42 442 362 34, 361 492 15 pc. E. lining, 47 413 49 502 46 451 403 413 392 401 492 45 383 33 382 383 36 412 381 453 33 402 391 45, at 462 321, at 1044.

314. 40 pc. L. gingham, 35 362 323 411 38 10 pc. L. plaid, 462 481 381 358 401

401 353 382 46 482 43 343 46 39 331 383 41 322 363 35, at 104. 373 342 48 362 32 383 471 50 482 411 4 pc. C.denims, 392 611 483 362 at 1214. 351 39 423 44 412 451 48 433 36 331

DENOMINATE NUMBERS.

330. Denominate numbers may be either simple or compound.

331. A Simple Denominate Number is a unit or a collection of units of but one denomination.

332. A Compound Denominate Number is a concrete number expressed in two or more different denominations; as 5 lb. 4 oz. 12 dr.; 4 yr. 7 mo. 12 da.

REMARK. Compound denominate numbers are sometimes called compound numbers.

333. Compound Numbers express divisions of time, and of the money, weights, and measures of the different countries.

REMARK. – Most denominate scales are varying, but the uniform decimal scale is used throughout the metric system, and, except in Great Britain, in the money of most civilized countries. The units of all denominate numbers are treated by the decimal scale.

334. A Denominate Fraction is a fraction expressing one or more of the equal parts of a denominate or concrete unit; as of a ton, of a yd., $ of a gal.

335. Reduction of Denominate Numbers is the process of changing them from one denomination to another, without altering their value. It is of two kinds, Reduction Descending and Reduction Ascending.

336. Reduction Descending is the process of changing a denominate number to an equivalent number of a lower denomination; as the change of barrels to an equivalent in gallons, quarts, pints, or gills.

337. Reduction Ascending is the process of changing a denominate number to an equivalent of a higher denomination; as the change of gills to an equivalent in pints, quarts, gallons, or barrels.

MEASURES OF TIME.

338. Time is the measure of duration; its computations, being based upon planetary movements, are the same in all lands and among all peoples.

339. The Solar Day is the unit of time; it includes one revolution of the earth on its axis, and is divided into 24 hours, counting from midnight to midnight again.

340. Noon, marked M. for Meridian, is that moment of time at which a line, called a Meridian, projected from the centre of the earth to the sun, would pass through the point of observation.

341. A. M. (Ante-Meridian) denotes the 12 hours before noon.

342. P. M. (Post-Meridian) denotes the time between noon and the following midnight.

REMARKS.—1. For astronomical calculations, the day begins at 12 o'clock doon, but for civil affairs, it begins at 12 o'clock midnight.

2. In banking business, the law fixes the end of the day at the hour appointed for closing the bank.

343. The Solar Year is the exact time required by the earth to make one complete revolution around the sun. It is equal to 365 days, 5 hours, 48 minutes, 49.7 seconds, nearly 3654 days.

344. The Common Year consists of 365 days for 3 successive years; and every fourth year, except it be a centennial year, contains 366 days, one day being added for the excess of the solar year over 365 days; this day is added to the month of February, which then has 29 days, and the year is called Leap Year. The slight error still existing after this addition, is again corrected by excluding from the leap years the centennial years which are not divisible by 400. Thus 1900, 2100, 2200, while divisible by 4, are not divisible by 400, hence will not be leap years; while 2000, 2100, 2800, being divisible by 400, will be leap years.

REMARKS.—1. The correction last named was made by a decree of Pope Gregory XIII., in 1685, and is known as the Gregorian calendar. It is used in all civilized countries except Russia, and is so nearly correct that an error of one day will not be shown for 4000 years, hence it is practically correct.

2. The calendar in general use previous to 1685 was known as the Julian calendar, having been established by Julius Cæsar, 46 B. C. This calendar is still in use in Russia, and as the difference in the two calendars is now 12 days, the current date in Russia is 12 days behind that of the other civilized countries of the world; thus when it is Jan. 1 in Russia, it is Jan. 13 in all other countries.

3. The Julian and the Gregorian calendars are sometimes designated by the terms Old Style (O. S.), and New Style (N. S.)

345. Rule for Leap Years.-I. All years divisible by 4, except centennial years, are leap years. II. All centennial years divisible by 400 are leap years.

Table.
60 seconds (sec.)
= 1 minute

min.
60 minutes
= 1 hour

hr.
24 hours
= 1 day

da.
7 days
= 1 week

wk.
4 weeks
= 1 lunar month ...

mo.
30 days

=l commercial month..
365 days
= 1 common year

yr.
= 1 leap year-

yr.
12 calendar months = 1 civil year

yr.
= 1 decade
= I'century

C.
Scale, descending, 12, 30, 24, 60, 60; ascending, 60, 60, 24, 30, 12.

REMARK.-In most business transactions 30 days are considered a month, and twelve such months a year.

mo.

366 days

10 years 100 years

66

28-29 66

346. The Calendar Months are as follows: 1st. January (Jan.) having 31 days. 7th. July (July) having 31 days. 2nd. February (Feb.)

8th. August (Aug.)

31 3rd. March (Mar.)

31

9th. September (Sept.) 30 4th. April (Apr.)

30
10th. October (Oct.)

31 5th. May (May)

31

11th. November (Nov.)30 6th. June (June)

12th. December (Dec.)

31

66

66

66

30

347. The year begins with the first day, or First, of January, and is divided into four seasons of three months each.

348. The Seasons are Winter, Spring, Summer, and Autumn, or Fall.
The Winter months are December, January, and February.
The Spring months are March, April, and May.
The Summer months are June, July, and August.
The Autumn months are September, October, and November.

REMARK.—The ancient Roman year began with March 1, and thus September, October, November, and December ranked, as their Latin derivation indicates, as the 7th, 8th, 9th, and 10th months respectively of the Roman year.

REDUCTION OF TIME. 349. The reduction of expressions of time from higher to lower denominations, or the reverse, may be accomplished in the same manner as the reduction of United States money heretofore explained, the only difference being that the scale in the latter is uniform, while that in the former is varying.

36 mo. ng mo.

350. To Reduce Time from Higher to Lower Denominations. EXAMPLE. —Reduce 3 yr. 7 mo. 11 da. 7 hr. 25 m. 38 sec. to seconds. OPERATION.

EXPLANATION.-Since one year 3 yr. 7 mo. 11 d. q hr. 25m. 38 sec. equals 12 months, 3 years equal 36 12

months, and 7 months added gives

43 months; since one month equals OPERATION CONTINUED. 30 days, 43 months equal 1290 days, 31231 hr.

and 11 days added gives 1301 days; 43 mo.

60

since one day equals 24 hours, 1301 30 1873860 m.

days equal 31224 hours, and 7 hours 1290 da.

added gives 31231 hours; since one 11 da.

hour equals 60 minutes, 31231 hours 1873885 m.

equal 1873860 minutes, and 25 min1301 da.

60

utes added gives 1873885 minutes; 24 112433100 sec.

since one minute equals 60 seconds, 31224 hr.

1873885 minutes equal 112433100 ny hr. 112433138 sec.

seconds, and 38 seconds added gives

112433138 seconds. 31231 hr.

25 m.

38 sec.

REMARK.—The reduction descending of any compound denominate number can be accom. plished as above, by observing the scale of the table to which it belongs.

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