thus, for example: if it be asked how many times will a wheel, which is 16 feet in circumference, turn in 184 miles?

Here the pounds whose number of farthings answers to the number of feet in a mile, is 5; therefore, the multiplier will be ; and the operation may be

54 16

or

11 32

performed mentally, step by step, in the following order.

of 184 of 23=43=£63 5s. 60,720 farthings and consequently the answer.

EXAMPLES.

How many times will the wheel of a coach, that is 16 feet in circumference, turn in 1,131 miles?

Here, to bring miles to feet. we must multiply by 5; and, we see that the divisor is 16 feet; which, as it happens, is 3 times 5; for

5

1

16

Then 1,131-3=£377=361,920 times the answer.

How many times will the wheel of a coach, that is 17 feet in circumference, turn in 150 miles?

Answer, 46,588

times.

Here multiply the miles by 5, and divide by 17; which the reader ought to do in one line.

The following question is inserted to show what method of reasoning should be adopted when questions are propounded where the dividend end with ciphers.

Suppose the globe of the earth to be 25,000 miles in circumference, how many guineas, each of an inch in diameter, will reach round it?

Here, by cutting off the thousands we have 25.

And, 25334 thousands.

Also, 3366(6×11)=2,200.

Now, annex the three ciphers struck off above (for thousands) and we have £2,200,000=2,112,000,000 farthings answer.

The following example is a beatiful specimen of the use and value of fractions, as compared with the common method of calculating.

There are two wheels, the one is 18 feet, and the other 24 feet in circumference, how many times will one of them turn round more than the other in 153 miles?

Also 14 of 153=¦ of 17=4=£11 13s. 9d=11,220

It may not, perhaps, be useless to illustrate how questions may be made, and their answers quickly given by the means of fractions.

When the divisors are in yards, feet, inches, &c., let the £. sterling, whose number of farthings represent yards, feet, inches, &c., in the integer be put as a numerator, and the divisor in the question a denominator.

The denominator of this fraction will represent the miles, and the numerator brought to farthings will, in numbers, be

the answer.

EXAMPLE.

5

17

Let the circumference of a wheel be 17 feet; then will shew that it will turn round as many times as there are farthings in £5, or £5 10s.; namely, 5280; and this may be carried on in the form of a fraction ad infinitum.

In a similar manner may the difference in the number of times two wheels will turn round in any number of miles be found.

Thus let 15 and 18 feet be the circumference of each.

Then

18-15 3

1

=

=

18 X 15 270

their difference; and, which 90

also shews that one wheel will turn round more than the other in 90 miles (see denominator,) as many times as there are feet in 1 mile, (see numerator.)

And

1X5

90

11 180

This shews that their difference in 180 miles will be as many times as there are farthings in £11.

EXAMPLES.

How many crowns, each 14 inches in diameter, will reach 150 miles ? Answer, 7,603,200.

How many crowns pieces, each 1 inches in diameter, will reach 560 miles? Answer, 23,654,400.

SQUARE MEASURE.

To reduce acres to poles.

Rule. Divide the given number of acres by 6; because there are 160, or 9° square poles to an acre.

EXAMPLES.

In 76 acres, how many poles ?

Here 76÷6 £12 13s. 4d.=12,160 answer.

How many poles in 184 acres?

Answer, 29,440.

In 186 acres, how many poles?

Answer 29,760.

To reduce acres to yards.

Rule. Multiply the number of acres by 54, or £5 Os. 10d., the farthings in which will be the answer; because the product of 160, (the poles in an acre,) and 30 the square yards in a pole is 4840, which, being considered as farthings, are equal to £5, as above.

EXAMPLES.

How many square yards in 56 acres?

Here 56×5 £282 6s. 8d.=271,040 answer.

In 96 acres, how many yards?

Answer, 464,640.

Answer, 580,800.

In 120 acres, how many square yards?

If acres are to be brought to square feet, multiply them by 45, (5X9, the square feet in a yard,) the farthings in number, will be the answer.

In 48 acres, how many square feet?

Here 45X48=2,178=2,090,880 answer.

Answer, 2,439,360

How many square feet in 56 acres?

In 72 acres, how many square feet?

Answer, 3,136,320.

WINE MEASURE.

To reduce pipes to gallons, quarts, and pints.

Rule. For gallons, divide the given number of pipes by 8; for quarts, by 2; and for pints, by unity; the quotient considered as guineas, and brought to farthings will, in numbers, equal the answers respectively.

EXAMPLES.

In 76 pipes, how many pints?

Here 76×8=608; which, being put to the right of 76, becomes 76,608 answer.

In 128 pipes, how many quarts?

Answer, 64,512.

How many gallons in 864 pipes?

Answer, 108,864.

How many gallons, quarts, and pints, are there in 341 pipes, and of each an equal number?

Answer, 31,248.

To reduce puncheons to gallons, quarts, and pints.

Rule. Multiply the given number of puncheons by 672, (7 times 96,) that is by 7, doubling the right hand figure in the product for shillings; which, being brought to farthings will equal, in numbers, the answer in pints.

Note. Proceed, as above, to find gallons, quarts, &c.

P