(3.) If the answer will be more or less, place more or less in the middle term.

A bankrupt paid 13s. 6d. in the £, and his assets realised £3124, 10s.; what were his liabilities?

What quantity of carpet 27 in. wide will cover a room 18 ft. 6 in. long by 12 ft. 4 in. wide ?

How many yards of paper 20 in. wide will cover the walls of a room whose length is 24 ft. 6 in., width 16 ft. 9 in., and height 12 ft?

1. If a man walks 44 miles in an hour and a half, how long will he be in walking 28 m.?

2. If land be bought at £83 per acre, how much is that per square mile?

3. Of a certain kind of goods, 170 lbs. now cost as much as 204 lbs. did at this time last year, and an order has just been given for the same quantity as cost £47, 10s. last year; what will be the amount of the bill?

4. If 12 yds. of cloth cost £17, how much can be purchased for £8, 16s.?

5. The carriage of a parcel of goods weighing 3 tons 2 cwt. 3 qrs. cost £3, 17s.; what will be the cost of 9 other parcels weighing each 6 cwt. 2 qrs. 18 lbs.?

6. If eleven things cost 15s., what will nineteen things cost at the same rate?

7. If 7 men spend £3, 10s. in three months on tobacco, what does each man spend per week on the average (allowing 13 weeks for 3 months)?

8. A sum of £6725, 4s. yields an annual income of £305, 12s. 6d.; what would £10621, 17s. 2d. yield at the same rate?

9. If 17 yds. of cloth cost £6, 12s. 84d., what will 110 yds. cost? 10. What is the income corresponding to an income-tax of £59, 1s. 3d., at the rate of 5d. in the pound?

11. A bankrupt's assets are £613, 2s. 8d., his debts £3698, 16s.; how much can he pay in the £?

12. A sets out from a certain place and walks at the rate of 3 m. per hour; B follows on horseback 20 minutes later, at the rate of 84 m. an hour; how soon will he overtake A? (The question is, if in one hour he gains 44 m., how long will he take to gain 14 m.?) 13. If a lb. of standard gold were worth £46, 14s. 6d., how much should 5 sovereigns weigh?

14. If of of 2 of 40 lbs. of beef cost 1d., how many pounds may be bought at the same rate for 6s. 74d.?

15. If the property in a town be assessed at £1875, 10s., what must be the rate in the £ to raise £915, 7s. 6d.?

16. A bankrupt owes A £72, 6s. 8d.; B £118, 5s. 9d.; C £103, 6s. 5d.; his assets are £205, 7s. 6d.; how much can he pay in the pound?

17. If a ton of coals cost £1, 18s. 8d., what weight can I get for 14d.?

18. A pair of blankets, each measuring 6 ft. 9 in. by 5 ft. 3 in., cost 10s. 6d., what will be the cost of a pair of like thickness and quality, each measuring 9 ft. 9 in. by 8 ft. 3 in.?

19. 40 yds. of silk are purchased for £14, 1s. 7d.; for what amount of money may 44 yds. be purchased at the same rate?

20. How much will 3 nls. of cloth come to at 4s. 7d. for 2 yds.? 21. How many yards of cloth, worth 18s. 34d. per yard, must be given in exchange for 937 yds., worth 3s. 74d. per yard?

22. An income of £150 per annum pays a tax of £4, 7s. 6d.; what will the tax be on an income of £586, 1s.?

23. If a piece of plate that weighs 7 oz. 9 dwts. 15 grs. cost £11, 12s. 2d., how much of it cost £1, 13s. 2d.?

24. By selling goods at £3, 14s. 6d. per cwt., which cost me 50s. the hundredweight, I gained two guineas; what quantity did I buy? 25. Paid £43, 15s. for 35 sacks of oats, each weighing 20 stones; what must I give for 4 cwt. 42 lbs.?

COMPOUND PROPORTION.

Two more methods to solve Compound Proportion problems are first given, and then a few examples for practice.

Cause and Effect.-This method is the most mechanical of all methods of teaching Double Rule of Three, but is good and effective. In every Compound Proportion sum there is a supposition consisting of three terms; the supposition always begins with such words as "if," "suppose," etc. The supposition may be divided into Cause and Effect. Take the following supposition so common in Rule of Three problems: "If 7 men reap 12 acres in 3 days." Here "12 acres reaped" is the effect produced by 7 men (the cause) in 3 days. We know from the principles of ratios previously laid down, that as causes are to causes, so are effects to effects; hence this gives a startingpoint for working out Double Rule of Three. To solve questions according to this principle, the following example will serve as an illustration, which is first worked out by a FOURTH METHOD for contrast: If 7 men reap 12 acres in 3 days, how long will 9 men take to reap 20 acres?

(1.) First place the numbers in the same order that they come in the question on the left-hand side of the page or slate, and bracket them together, so as to find the odd term. Place this odd term in the third place, and write over what it is, days, etc.

(2.) Mark the demand by a line, as the perpendicular line on the extreme left hand; and ask the questions about the numbers in the demand, i.e., will 9 men take more days or less days than 7 men to do the work? Ans. Less; therefore put less (7) in the middle, and the 9 in the first place. Next, will 20 acres take more days or less days to reap than 12 acres? Ans. More; therefore put more or 20 in the middle.

(3.) Finish in the usual way.

To work out this sum according to the principles of cause and effect:

(1.) Put in the third place the effect contained in the supposition, which is 12 acres, and the cause in the first and second, 7 men in 3 days.

The blank falls

(2.) Put the corresponding terms under this first statement, 9 men under men, 20 acres under acres. under days, hence days is to be the answer.

(3.) Put a X in the second space; this will link the cause of one supposition with the effect of the other, and it will be found that the cause of the supposition multiplied by the effect of the demand, will equal the cause of the demand multiplied by the effect of the supposition. Hence the two terms linked with the blank will be the divisor, and the other three terms the dividend, thus:

If £1000, put out to interest for 6 years, realised £250, how much must be invested to bring in £375 in 4 years.

If it cost £517, 11s. 6d. to board 39 pupils in a training institution for 10 months, what would be the additional expense of boarding 15 other pupils for 13 weeks?

The rules, as usually given for solving Double Rule of Three on the cause and effect principle, are as follow:

(1.) Set down the terms expressing the supposition in one line, taking care to separate the cause from the effect.

(2.) Under these terms set the corresponding terms of the demand, marking the term sought or wanting by a dash, thus

(3.) Join the cause terms of the one line with the effect terms in the other.

(4.) Multiply the three terms that come together, and divide by the two terms.

EXERCISES.-L.

1. A farmer lends another 500 qrs. of wheat at 496 lbs. to the quarter; how many quarters of 480 lbs. must be paid back? 2. If the carriage of 5 cwt. cost 19s. for 15 m., what will the carriage of 13 cwt. cost for 70 m.?

3. If 5 men or 8 boys can dig 56 cub. yds. of earth in 14 dys. of 10 hrs. long, in how many days of 9 hrs. long will 14 men and 6 boys dig 240 cub. yds., the soil in the latter case being one-fourth less difficult to dig?

4. If 14 oxen can plough 13 6625 ac. in 48 dys., in how many days can 7 oxen plough 2.140625 ac.?

5. How many days of 12 working hours each should 17 men take to do a piece of work similar to one which 10 men finished in 19 dys. of 11 hrs. each?

6. How long will 17 men take to earn £50, if 12 men in 64 dys. can earn 13 guineas?

7. If 18 horses eat 37 qrs. 7 bush. 3 pks. of corn in 45 dys., in what time will 50 horses eat 25 qrs.?

8. If 30 ac. be mown by 6 men in 5 dys., how many acres can be mown by 50 men in 20 dys.?

9. If £3, 10s. are given for the loan of £100 for a year, how much ought to be paid for the use of £312, 10s. for 1 yr. 35 wks. 5 dys.?

10. How many days will 10 men require to manufacture 47 reams of paper, working 12 hrs. a day, when 15 men take 9 days, working 11 hrs. a day, to make 52 reams?

11. If 204 men build a wall 306 ft. long, 8 ft. high, and 3 ft. thick, in 42 dys. of 6 hrs. each, in how many days of 8 hrs. each will 188 men build a wall 6 ft. high and 18 in. thick round a rectangular enclosure, whose length is 319 ft. and breadth 97 ft.?

12. If a beam which is 10 in. wide, 8 in. deep, and 5 ft. 6 in. long, weigh 8 cwt. 1 qr., find the length of another beam the end of which is a square foot, which shall weigh a ton.

13. If 14 men can mow 168 ac. in 12 dys. of 84 hrs. each, how many can be mowed by 20 men in 11 dys. of 7 hrs. each?