It is worthy of remark here, that the bringing tons to lb. may be performed by the same operation (with a very slight exception,) as the bringing cwt. to lb.; and here it will be seen that the one is as easy as the other, that is to say, it is as easy to multiply by 2240 as 112; so that a person remembering one can remember the other; as the following will shew, with this only difference, that instead of doubling the right hand figure and the fraction of the one, you double the whole of the other.

LONG MEASURE.

To reduce miles to yards.

Rule. Multiply the miles given by for pounds sterling; the farthings will, in numbers, be the answer.

Rule. Multiply the miles by 5, or its equaly, (for y multiplied by the feet in a yard is,) for pounds sterling; the farthings in this product will, in numbers, equal the

answer.

EXAMPLES.

Reduce 79 miles to feet.

Here 79×5

£434)=417,120 answer.

The best way, perhaps, to multiply by 5, is to suppose a cipher on the right of the given number of miles, and divide by 2; and, if you add to this quotient all the figures except the right hand figure, the product of 5 will be obtained.

If the number of miles be odd, after dividing by 2, the figure in the unit's place will be 5; for which add, thus; for example, 71X5=395; and 395 × 39-434.

But, the above plan is not wanted, if the miles be even because they are divisible by 2; and 11 times this quotient will be the product of 5.

Reduce 56 miles to feet.

In 745 miles, how many feet?

Answer, 295,680.

Answer, 3,933,600.

To reduce miles to inches.

Rule. Multiply the given number of miles by 66, (12 times 52,) which consider as pounds; the farthings in which will, in numbers, be the answer.

Note. The reader will, perhaps, find it best first, to multiply by 6, (for, should there be of a mile, it will be found to be much easier,) and then by 11, thus, let 13 be multiplied by 66.

13

6

81

11

891

But the following method may not be amiss.

13

6

81

81

891

In 156 miles, how many inches?

Here 156 × 66(6×11)=10,296=9,884,160 answer.

If the miles are divisible by 3, it may be the best to divide them by it, and proceed with the quotient as though you would reduce them to barley corns.

Note. When it is required to reduce furlongs to inches, make the furlongs the fractional part of a mile, and multiply it by 66.

EXAMPLES.

In 6 furlongs, how many inches?

Here 6 furlongs mile.

And 66x=£49 10s. =47,520 answer.

To reduce miles to barley corns.

Rule. Multiply the given number of miles by 198; the product of which, brought to farthings, will be the answer. Note. The best method to find the product of a number to be multiplied by 198 is, (what has before been given in multiplication,) to multiply first by (for 200), and then repeating the same figures again, leaving two right hand figures to stand alone in the manner following.

The above note is here repeated because, in multiplication the author has not laid down the method for shewing the product in one line.

Multiply 137 by 198.

137X2=274.

274

27,126-137x198.

Now, this product might have been obtained without the above process, by observing the following plan.

First, it is evident that 137 X2, produces 274; and, because there are figures on the right of the 2, 3 is deducted from the right hand figure 4, and there remains 271.

Lastly, the 74 taken from 100 and annexed to the 271, makes 27,126, as may be seen above.

EXAMPLES.

How many barley corns will reach 246 miles?

Here 246 × 198, as above directed, produces 48,708 for pounds=46,759,680 barley corns the answer.

In 76 miles, how many barley corns ?

Answer, 14,446,080.

How many barley corns in 547 miles ?

Answer, 103.973,760.

In 16 poles, how many barley corns?

First, 16 poles==% of a mile.

And, 198-20=£9 18s.=9,504 answer.

Note. If there be furlongs given with the miles, then

£24 15s. must be added to the product of the miles for each furlong; because, 18=£24 15s.; and this sum may again be continually divided by the several denominations in each name, till you come to barley corns, which will end with a farthing for each.

How many barley corns will reach round the world which is 360 degrees, each degree 691⁄2 miles?

First, 360×70=25,200; this being the half of 360, or 180 too much, we may deduct it easily from the above; for it may be seen that it will not alter the thousands, and we have 25,020; which sum is equal to the product of 360 × 691.

And 25,020 X 2=50,040.

50040

50040

4,953,960=4,755,801,600 barley corns the answer.

Note. If 501 had been deducted from 50,040; and lastly, the difference between 40 and 100 placed to the right of those figures, we should have had the same difference

as above.

BEAUTIFUL ILLUSTRATIONS OF DIVISIONAL PROCESSES.

There are no particular rules for a divisional process; it depends greatly upon a person's ingenuity, thus, for instance, in common arithmetic, let it be asked how many times a wheel, that is 17 feet in circumference will turn round in 119 miles? We must know that the number will be as many times as there are feet in 7 miles; for 4=7; and thus, by making use of the divisor first, a considerable number of figures will be saved. The same, also, obtains here; but where this cannot be done, recourse may also be had to another contrivance by placing the multiplier as a numerator, and the divisor in the question a denominator.