If £100 in twelve months gain £6, in what time will £75 gain £3 7s. 6d. ? Ans. 9 months.

If £75 in 9 months gain £3 7s. 6d., what will £100 gain in 12 months?

Ans. £6.

If a regiment of soldiers, consisting of 1360 men, consume 351 quarters of wheat in 108 days, how much will 11232 soldiers consume in 56 days?

If 50 men can do a piece of work in 100 days, working 8 hours per day, in what time will 120 do it, working 6 hours per day? Ans. 555 days.

Note. The two statements are in inverse proportion; in one, more requires less, and in the other, less requires more.

The pupil having now learned to state with readiness sums of five given numbers to find a sixth, and being told that inverse statements require the right, and direct statements the left, figures, to be taken for a divisor, will, I trust, fully understand the statements of the few sums it will be necessary for me to insert in the Chain Rule; and for the purpose let us take, as our example, the last sum of five numbers, and add a couple more terms to it, by giving dimensions to the work supposed to be done, and that which is to do.

If 50 men can build a wall 180 yards long in 100 days, working 8 hours per day, in what time will 120 build a wall 205 yards long, working 6 hours per day?

The first and second statements, as before described, are inverse; the third is direct, as it will require longer to build 205 yards than 180; the answer is 6322 days.

F 5

We can increase it two terms more, by taking the height of the wall: thus

If 50 men can build a wall 180 yards long, and 7 feet high, in 100 days, working 8 hours per day, in what time will 120 men build a wall 205 yards long and 10 feet high, working 6 hours per day?

The last statement is direct, as in proportion it must

take longer to build ten than seven feet.

Ans. 901055

2268

If we add two more terms, the principle is still the

same.

If 50 men can build a wall 180 yards long, 7 feet high, and 13 inches thick, in 100 days, working 8 hours per day, in what time can 120 men build a wall 205 yards long, 10 feet high, and 10 inches thick, working 6 hours per day?

to build a ten inch wall, than a thirteen inch one.

*

Having now shewn the pupil how in one statement eleven terms are easily worked, I wish to remark the expedition that is acquired by this rule. The above sum worked by proportion, as it must be if not done by the chain rule, would require five statements, three direct

and two inverse, the fourth proportional of one becoming the centre term of the next; and each centre term having a fraction, the work would necessarily be complicated. And I wish here to impress upon the pupil's mind that Arithmetic cannot be kept too simple; for a momentary dulness, or a stray thought crossing the mind, will often lead the cleverest calculator into error. Tradesmen knowing this have adopted a rule, which, from being almost always in use, and from the readiness with which it can be applied to almost every calculation, is called Practice.

PRACTICE.

FOR Practice there can be no settled rule, as every person that has goods or any other commodity calculates their amount in the shortest possible manner; and the more extensive the person's business is, the less time he can afford to lose, and the shorter his method is likely to be. And I would here take an opportunity to advise the pupil to follow an example so good, and use all diligence to attain the knowledge useful to his station in life, and never to neglect the duties of that station to acquire knowledge which perhaps can never be useful to him.

But to shew the great dispatch that this rule, if I may so call it, enables us to use in calculation, we will work the following sum.

Bought 267 stone of oatmeal at 2s. per stone, how much did it cost?

The person knowing that part of Arithmetic already taught, would proceed as I have done in the sum on the right, viz. multiply it by 2,

and divide the product by 20; but

267

2

2,0) 53,4

£26. 14s.

the person knowing Practice, at once knows that 2s.

is the of a pound, and that to divide by ten we have only to cut off the right-hand figure, thus ;

26,7. He then has £26, and he knows that the seven cut off is seven stone; at 2s. is fourteen shillings.

If such is the expedition that is gained in calculation by this Rule, I am certain the pupil will, to make himself master of a rule so useful, study with attention the following tables, as an hour or two will make him sufficiently acquainted with them.

When the Price is less than a Penny.

At åd. per yard what will 264 yards of tape cost?

Here, if the price was 1d., the answer would be 264d.; but being d., the answer

will be of 264d., which is found by the example to be Gs. 6d.

farth.

264

2 =

132

1

66

12) 198d.

16s. 6d.

Bought 149 yards of ribbon at d. per yard, what did Ans. 3s. 1d.

it cost?

Bought 168 yards of rope at d. per yard, what did

Ans. 7s.

it cost? What will 240 red herrings cost at d. each?

When the Price is less than a Shilling.

Ans. 15s.

What will 2004 lbs. of lard cost at 3d. per pound?

Three pence is the of a shil

ling, and the first line 501 is the amount in shillings at 3d.

d.

2004

3 =

501

=

831

2,0) 58,4

£29 4s. 6d.

pound. Both sums added together, and the total divided by twenty, is the answer in pounds and shillings.

amount?

What will 3257 ounces of coffee cost at 4d. per ounce ? Ans. £54. 5s. 8d. Bought 5752 yards of rope at 41d., what is the Ans. £107. 17s. What is the price of 5272 lbs. of bees-wax at 9d. per lb. ? Ans. £197 14s. Bought 7921 loaves of bread at 10 d. per loaf, what did it amount to ? Ans. £326. 11s. 6d.

What is the price of 3752 lbs. of meat at 4 d. per lb. ? Ans. £70. 7s.