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The lowest denomination being mills, we may consider the sum 185627 as representing a number of mills. Now, in dividing this sum by the number of mills in a unit of any of the other denominations, it is evident that we may read it in any or all of those denominations; but, as accounts are kept in dollars and cents, it is usual to consider the dollars as whole numbers, and the inferior denominations as decimals; therefore, as 1000 mills make a dollar, we divide by 1000, in separating, by a comma, three figures on the right, and read 185 dollars and 627 thousandths, or (as 10 m. make 1 c.) 185 dollars 62 cents and 7 mills.

Hence, we see that the calculation of Federal Money is the same as that of abstract decimals.

Examples. 1. Find the sum of $5,16; $29,457; $347,20, and $1,627.

Answer, $383,444. 2. From $1000,50 subtract $597,237.

Answer, $403,263. 3. Multiply $35,637 by 1,25.

Answer, $44,54625, or $44,55—. 4. Multiply $379,23 by 25. Answer, $9480,75. 5. Divide $35,84 by 6,25.

Answer, $5,7344. 6. Divide $12125 by 31,25.

Answer, $388. 279. Gold, silver, jewels, and very costly articles are weighed by Troy Weight, the denominations of which are as follows:

Troy Weight
24 grains, gr., make...... 1 pennyweight, dwt.
20 pennyweights 1 ounce, oz.

1 pound, 16. We refer the student to what is said in Art. 4, from which he will understand that the grains here spoken of are wheat grains, taken from the middle of a full-grown ear.

280. By the following weight apothecaries mix their medicines, but buy and sell by Avoirdupois :

Apothecaries' Weight.
20 grains, gr., make...... 1 scruple, >
3 scruples...

1 drachm,
8 drachms..

1 ounce,
1 pound, Ib

12 ounces ......

12 ounces....

Apothecaries' Wine Measure.
1 minim.
60 = 1 fluidracbm =

,2254 c. in.
480 8 1 f. 02. =

1,8047 7680 = 128

28,875 61440=1024=128=8=1 gal. 231 cubic inches.


16=1 pt.

- 1 pt.

Imperial Measure.

Gr. Troy. 1 minim

,91 60 1 A. dr. =

54,7 480 8 1 fl. 02.

437,5=1 oz. 9600 160 20

8750 =1,251b. 76800 = 1280 = 160 8

pts. 1 gal. = 70000 =10 lb. Tea-cup

4 fluid ounces.
Wine-glass 2


Tea-spoon =Î fluidrachm = i. oz. 281. By the following weight are weighed things of a gross and drossy nature, groceries, chandlers' wares, and metals, except gold and silver.

Its name, Avoirdupois, is derived from the French words avoir, to have, du, of the, and poids, weight; that is, to have great weight.

Avoirdupois Weight.
16 drachms, dr., make ......... 1 ounce, oz.
16 ounces

1 pound, 16.
28 pounds.....

1 quarter, qr: 4 quarters, or 112 lbs...... 1 hundredweight, cut. *20 hundredweight, or 2240 lbs. 1 ton, T. A hundredweight is sometimes called a quintal.

The pound Avoirdupois consists of 7000 grains Troy, and is to the pound Troy very nearly as 17 to 14.

282. We have already noticed that 3 barley-corns, placed lengthwise in contact, make 1 inch, and 12 inches, i foot. The foot, thus constituted, is, however, differently divided to suit different kinds of measurement. In Carpentry, it is divided into inches, and these into halves, quarters, eighths, and sixteenths. In Civil Engineering, for the sake of the convenience of decimal calculation, it is divided into tenths and

* By some a short ton is sometimes used, consisting of 2000 lbs, and a short cwt., consisting of 100 lbs.

3 feet.... 6 feet....

hundredths; and, in philosophical investigations, it is frequently divided into inches and lines, as in the following Table :

Long Measure.
10 lines Eng., or 12 lines Fr., l., make... 1 inch, in.
12 inches

1 foot, ft.
1 yard, yd.

1 fathom, fath. 5.1 yards, or 164 feet.

1 rod or pole, P. 40 poles, or 220 yards....

1 furlong, fur. 8 furlongs, or 1760 yards.

1 mile, M. 3 miles ..

1 league, L. A hand, by which horses are measured, is 4 inches. Though the league and fathom are chiefly confined to maritime* affairs, they are, by some nations, and particularly the French, often used to denote distances on land.

283. The scholar has seen (211) that a compound fraction is the product of two or more simple fractions. But (188) every fraction is a ratio; wherefore, substituting the word ratio for the word fraction, we say that a compound ratio is the product of two or more simple ratios. Hence, every compound fraction is a compound ratio.

A unit of any of the lower denominations of a compound number is a fraction of that of the next higher, and a compound fraction of a unit of any order higher than the next. For example, a farthing compared with a penny is }, which is a simple fraction. But

, as the penny is of a shilling, the farthing, compared with the shilling, is of in, which is a compound fraction. Compared with a pound, it is į of 12 of 20; which is also a compound fraction.

As į is the ratio of a farthing to a penny, and 1 the ratio of a penny to a shilling; and as as, the ratio of a farthing to a shilling, is formed by multiplying 1 and is together, the ratio of a farthing to a shilling is said to be compounded of the ratio of a farthing to a penny, and of that of a penny to a shilling. The ratio of a farthing to a pound is a ratio compounded of the ratio of a farthing to a penny, of the ratio of a penny to a shilling, and of that of a shilling to a pound. Thus, į of l'z of ab=ix 12 = oo; that is, te is a ratio compounded of the ratios į 12, and 20

* Maritime, belonging to the ocean.

The ratio of 1 inch to 1 mile is 633.0; of what ratios is it compounded ?

284. By the following measure are measured cloths, laces, ribbons, &c. :

Cloth Measure. 21 inches, in., make..

1 nail, n. 4 nails....

1 quarter, qr.
4 quarters ....

1 yard, yd.
2 quarters, or 10 nails...... 1 ell Hamburgh, E. H.
3 quarters...

1 ell Flemish, E. F.
5 quarters.

1 ell English, E. E. 6 quarters..

1 ell French, E. Fr. The ratio of 1 inch to 1 E. Fr. is 34 ; of what seven ratios is it compounded? What is the value of each ratio ?

285. The scholar has already been informed (110) that the space contained in any surface, called its content, is estimated in squares, and that the content of any right-angled figure of four sides is found by multiplying its length, taken in any measure, by its breadth, taken in the same measure. The units of the following Table are those chiefly used for measuring surfaces; and, as some of them refer solely to the measurement of land, the table is called

Land or Square Measure. 100 Eng. or 144 Fr.square lines, s.l., make 1 square inch, 144 square inches.

1 square foot, s. f. 9 square feet...

1 square yd, s. yd. 304 square yards, or 2724 s. f......... 1 pole, or perch, p. 40 poles in length, and one in breadth.. 1 rood, r. 4 roods, or 160 poles......


acre, a. 4840 8. yds., or 43560 s. f.....

1 acre. 640 acres.

1 square mile, s.m. In the actual measurement of land an instrument is usually employed, called the

Surveyor's or Gunter's Chain. 7,92 inches make...

1 link.
25 links ..

1 rod, pole, or perch.
100 links, 22 yds., or 66 ft. 1 chain 4 rods.
80 chains.....

1 mile. 10 square chains--that is, 10 chains in length, and 1 in breadth-make....

1 acre. 100000 square links..

1 acro.


The length, 10 chains, is 1000 links, and the breadth, 1 chain, is 100 links, and 1000 x 100=100000, the content of an


links. 286. To find the content of any right-angled piece of ground with Gunter's Chain, multiply the length in links by the breadth in the same, and divide by the number of square links in an acre; that is, point off, in the product, five figures on the right for decimals. The figures on the left of the comma will be acres. Multiply the decimals by 4, pointing of five, as before, and the figures on the left of the comma will be roods, or quarters of an acre. Again, multiply the decimals by 40, pointing off as before, and, on the left of the comma you have the poles.

For example, the length of a piece of ground is 30 chains, 57 links, and the breadth 20 ch. 23 links; what is its content?

3057 2023 9171 6114 6114 61,84311

4 3,37244


14,89760 The content is, therefore, 61 A. 3 R. 15 P., very nearly. If

you have not Gunter's Chain, multiply the length in yards, by the breadth in yards, and divide the product by 4840; or, for greater accuracy, the length in feet by the breadth in feet, and divide the product by 43560. In the above example the length being 2017,6 ft., and the breadth 1335,2 ft., I proceed thus : 2017,6 x 1335,2 =2693900 — Then,

61 A. 3 R. 15 P., very nearly, as before. The ratio of a square Fr.line to a square mile is 678080502700; of what ratios is it compounded ? What is the value of each ?

287. We have shown the application of the preceeding measure to surfaces, or figures which have only two dimensionsnamely, length and breadth, (for, however irregular or various

269 3900
4 3 5 60

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