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The French government have adopted such a system of weights and measures, graduated on the decimal scale of notation.

In multiplication, the multiplicand being repeated a certain number of times, or a certain fraction of a time, when the multiplier is a fraction, it follows that the multiplier, considered as a multiplier, must always be regarded as a simple or abstract number. And since the product is a repetition of the multiplicand, it must be like the multiplicand; that is, if the multiplicand is an abstract number, the product will be an abstract number; if the multiplicand is a denominate number, the product will be a denominate number of tne same kind.

In division, the quotient showing how many times the divisor is contained in the dividend, or what fraction of a time when the divisor is greater than the dividend, it follows that the quotient must be regarded as an abstract number; and that the divisor and dividend must be alike.

Note.—In many cases, however, the process of division is rather the dividing of a dividend into as many equal parts as are indicated by the divisor ; in which case, the quotient, expressing the units in one of those parts, is of the same kind as the dividend, while the divisor is to be regarded as an abstract number. See Example, Art. 86.

What is a simple number? What is a denominate number? What kind of numbers are all our different weights and measures ? What is said of the French measures ? In multiplication, can the multiplier ever be a denominate number? Are the product and multiplicand always alike? What is said of the quotient? What is said in the note ?

The following are some of the most important tables of weights and measures at present employed in this country.

ENGLISH MONEY. " 65. The denomination of English money are Farthings, Pence, Shillings, and Pounds.

The pound sterling, which was not a coin, but a bank

note of 20 shillings, has now gone into disuse, and a gold coin, called a Sovereign, supplies its place; but the name pound is still given to 20 shillings.

TABLE.*
4 farthings, far. make 1 penny, d.
12 pence

6 1 shilling, so
20 shillings « 1 pound, £.

far. d.

4= 1 s.
48= 12.= 1 £

960=240=20=1 NOTE.-Farthings are sometimes expressed in fractions of a penny, as follows: 1 farthing=1 d., 2 farthings=} d., 3 farthings = d.

What are the denominations of English money? Which denomination is never coined ? What gold coin is equivalent in value to one pound? Repeat the Table. How are farthings sometimes expressed ?

TROY WEIGHT. 66. The original of all weights used in England was a grain or corn of wheat, gathered out of the middle of the ear; 32 of these, well dried, were to make one pennyweight, 20 pennyweights one ounce, and 12 ounces one pound. But in latter times, it was thought sufficient to divide the same pennyweight into 24 equal parts, stis called grains, being the least weight now in common use.

Coins, precious metals, jewels, and liquors, are weighed by Troy weight.

* The Pull weight and value of English gold and sil rer coin are as in the succeeding table, note.

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What was the original of all weights used in England ? How was the grain ob tained ? Is it still used as a weight? What substances are weighed by Troy weight ? Repeat the Table.

APOTHECARIES' WEIGHT.

67. This weight, as its name would imply, is used in weighing medicines in small quantities, as for prescriptions. But drugs and medicines in gross are bought and sold by Avoirdupois Weight. The pound and ounce Apothecaries' Weight are the same as in Troy Weight.

Name of Coin.

VALUE. WEIGHT

£ 8. d. pot. gr. FA guinea,

1 1 0 5 9
Half guinea, 0 10 6 2 167
Gold.

Quarter guinea, 0 5 3 1 8}
Sovereign, 1 0 0 5 3;3

Half sovereign, 0 10 0 2 13,1
LA crown,

0 5 0 18 4,4
Silver.

Half crown, 0 2 6 9 2 i
Shilling,

0 1 0 3 15,3
Sixpence,

0 0 6 1 191 * This scale of weights is said to have been borrowed originally from Troyes in France--hence its name. Some, however, contend that the name has reference to the monkish title given to London, of Troy Novant

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68. By this weight are weighed all things of a coarse or drossy nature, as bread, butter, cheese, flest., groceries, and some liquids; all metals, except gold and silver.

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The pound Avoirdupois contains 7000 grains.

From the preceding table, it will be seen that 112 pcrunds instead of 100, are called one hundred weight. In most cases however the hundred weight is taken equal tc 100 pounds, and 25 pounds, instead of 28, is called a quarter. Coal merchants in buying coal receive 112 pounds for a hundred weight, and 20 hundred weight for a ton, making 2240 pounds ; but they retail it at 2000 pounds for a ton.

What substances are weighed by Avoirdupois Weight? Repeat the Table. By this weight how many pounds make one hundred weight? In most cases how many pounds make a hundred weight? How is coal usually bought and sold ?

LONG MEASURE.

LATITUDES.

LENGTH IN INCHES.

69. It is usual, at the present time, to derive the meas. ure of length from that of a pendulum vibrating once in a second of time. The length of such pendulums will vary for different latitudes, as here given.

PLACES.
Equator, 00 0' 0" 39.01612
Cape of G. H., 33 55 15 39.07815
New York, 40 42 43 39.10120
Paris, 48 50 14 39.12929
London, 51 31 8 39.13929

The Pole, 900 0 39.21820 The French government derive their linear unit of measure from one quarter of the circumference of a great circle of the earth passing through the poles. Having determined by actual surveys the length of that portion of such a circle comprised between the parallels of Dunkirk

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