less than it would have been if there had been only a daughter; what would have been the mother's portion had there been only a son? Ans. $1750.

(13.) At $11,76 per hundred weight, what will hundred weight of sugar come to?

of a

Ans. $1,47.

(14.) How long must a laborer work, at the rate of $0,62 per day, to earn $25?

Ans. 40 days. (15.) Traveling at the rate of 43 miles an hour, in how many hours will a footman go 34 miles?

Ans. 7,5 hours. (16.) If 85 yards of cloth be bought for 191,25 dollars, and sold at 2,87 dollars per yard, how much is the whole profit? Ans. $53,123. (17.) How much butter at 9 cents a pound, will pay for 12 yards of cloth at 2,19 dollars per yard?

Ans. 292 pounds. (18.) At 45 dollars per acre, what is the value of of an acre of land? Ans. $9,10.

(19.) The loss of merchandize by a fire was estimated at 11372,75 dollars, of which was insured; how much was the loss after deducting the insurance?

Ans. $4549,10.

(20.) A benevolent individual whose income was 5000 dollars, devoted,12 of it to charitable objects; how much did he give away annually?

Ans. $600. Ans. 70,785.

tea, the first con

(21.) How much is of of 7863 ? (22.) A merchant buys three chests of tains 60 and one thousandth pounds; the second, 39 and one ten thousandth pounds; the third, 26 and one tenth pounds: how much did he buy in all?

Ans. 125,1011 pounds. (23.) B has 936 dollars, and A has 1 dollar 3 dimes and 1 mill: how much more money had B than A ?

Ans. $934,699. (24.) A merchant buys 37,5 yards of cloth at 1,25 dollar per yard: how much does the whole come to?

Ans. $46,875.

(25.) A farmer sells to a merchant 13,12 cords of wood at 4,25 dollars per cord, and 13 bushels of wheat at 1,06 dollar per bushel he is to take in payment 13 yards of broadcloth at 4,07 per yard, and the remainder in cash: how much cash did he receive? Ans. $16,63.

PART III.

DENOMINATE FRACTIONS.

§ 102. 1. MONEY, weight, measure, &c., have each an accepted unit or whole, taken as a standard of estimation, peculiar to itself, the subdivisions of which have a constant relation to each other; the unity or single part of one subdivision being a fraction of the next above it; the denominators to which are conventional, and always understood.

2. These subdivisions vary with each separate class of quantities; and, in consequence, a different number in each makes the unit or whole.

3. The relation of these subdivisions to each other in each class of expressions is also irregular; that is, it is not from one to another by the same number or denominator. Hence, in each separate class of such expressions, the increase from right to left is by a distinct number for each place.

4. Numbers expressing quantities whose subdivisions thus form fractions with conventional denominators are called denominate.

5. The only difficulty in operations on such numbers consists in the attention necessary to be paid to the irregular system of subdivision, or the conventional denominators, to know how many units of each subdivision make a whole or a unit of a higher subdivision, which determines the principles of carrying. All the other operations on them are precisely like the same operations on simple numbers.

6. The subdivisions in the denominate quantities are so many and various, that it is necessary to have tables to recall them to memory.

Such tables we subjoin, to be thoroughly committed to memory, by the pupil, before proceeding further.

I. ENGLISH, OR STERLING MONEY.

The denominations of English or Sterling Money, are the pound, the shilling, the penny, and the farthing.

This is the currency of Great Britain and her dependencies; and when the United States were Colonies of Great Britain, was their currency. More of this hereafter.

II. TROY WEIGHT.

The denominations of Troy Weight are the pound, the ounce, the pennyweight, and the grain.

By this weight are weighed gold, silver, jewels, and all liquors.

III. AVOIRDUPOIS WEIGHT.

The denominations of Avoirdupois Weight are the ton, the hundred weight, the quarter, the pound, the ounce, and the dram.

cwt. 1=

T. 1=4=

112= 1792= 28672.

1=2080 = 2240 =35840=573440.

By this weight are weighed all things of a coarse or drossy nature, as corn, bread, butter, cheese, flesh, grocery wares, and some liquids; also all metals, except silver and gold.

In this weight the words gross and nett are used. Gross is the weight of the goods, with the boxes, casks, or bags, in which they are contained. Nett is the weight of the goods only; or what remains after deducting from the gross weight, the weight of the boxes, casks, or bags.

A hundred weight is 112 pounds, as appears from the Table. But at the present time, the merchants in our principal cities, buy and sell by the 100 pounds. For the state of New-York, the statute provides, that "the hundred weight shall consist of one hundred pounds avoirdupois, and twenty such hundreds shall constitute a ton."

Note, that 1 lb. Avoirdupois

1 oz. 1 dr.

=

oz. pwt. gr.

14 11 15 Troy. = 0 18 54

= 0 1 31/

Hence it appears that the pound Avoirdupois contains 6999 grains, and the pound Troy 5760; the former of which augmented by half a grain becomes 7000, and its ratio to the latter is therefore very nearly as 700 to 576, that is, as 175 to 144; consequently 144 pounds Avoirdupois are very nearly equal to 175 pounds Troy; and hence we infer that the ounce Avoirdupois is to the ounce Troy as 175 to 192.

The unit of weight is the pound, of such magnitude that a cubic foot of water at its maximum density, weighs sixty-two and a half pounds, or one thousand ounces.

IV. APOTHECARIES' WEIGHT.

The denominations of Apothecaries' Weight are the pound, the ounce, the dram, the scruple, and the grain.

This is the same as Troy Weight, only having some different divisions. Apothecaries make use of this weight in compounding their medicines; but they buy and sell their drugs by Avoirdupois Weight.

V. DRY MEASURE.

The denominations of Dry Measure are the chaldron, the bushel, the peck, the gallon, the quart, the pint, and the gill..

By this measure are measured corn, seed, fruit, salt, and coal.