22. If you should, on June 20th, buy a note dated January 20th, drawn for $40, on 8 months, what should you pay for it, money being worth 2 % a month? Ans. $37.52.

23. A, B, and C join their capitals, which are in the proportion of 1, 3, and 4; at the end of 4 months A withdraws of his capital, and at the end of 9 months more they divide their profits, $2840; what should each receive?

Ans. $1020, $1040, and $780.

24. If 100 liters of wine cost 250 francs, what must be the price per gallon, in United States money, to gain 20 per cent.?

25. If 3 lb. of tea be worth 4 lb. of coffee, and 6 lb. of coffee be worth 20 lb. of sugar, how many pounds of sugar can be had or 9 lb. of tea? Ans. 40 pounds.

26. An express train leaves Chicago for a point 120 miles west, at 2 o'clock, and goes at the rate of 25 miles per hour; at what time must a slow train, which goes 15 miles in 50 minutes have left, so as not to be overtaken by the express train? Ans. 12 hours 8 minutes.

27. The merchandise balance of an account is $200 due by averaging the account from June 11; what will be its cash value, if payment be delayed till Sept. 11, or for 3 months, allowing interest at 6% ? Ans. $203.

28. A guardian paid his ward $6460 for $5000 which he had in his hands 4 years; what rate of interest did he allow him? Ans. 73% %.

29. How many square feet of 1 inch boards may be sawed from a beam 24 feet long, and whose rectangular ends are 16 inches by 12 inches, if no allowance is made for the thickness of the saw? Ans. 384 sq. ft.

30. If the weight of a hectoliter of wheat is 75 kilograms, what weight of wheat will fill a bin 2 meters long, 1.4 meters broad, and 1 meter deep? Ans. 2100 kilos.

REVIEW QUESTIONS. What is a Power? (385) A Root? (388) Invotion? (386) Evolution? (390) Square Root? 391) Cube Root? (396)

31. In a mixture called coffee, of the whole plus 25 pounds is coffee, and part less 5 pounds is chiccory; what per cent. of the whole is chiccory? Ans. 29 per cent.

32. A has due him $144, payable in 7 months, but the debtor agrees to pay down, and in 4 months; in what time. should he pay the balance?

33. What must be the face of a 60 days' note, when money is worth 6 %, to allow of taking $3958 from a bank?

34. If the specific gravity of iron in bars is 7.8 times that of water, and a liter of water weighs a kilogram, what is the weight of a bar of iron 4 meters long, 1 decimeter broad, and 3 centimeters thick? Ans. 93.6 kilos.

35. If a pipe 6 inches bore will discharge a certain quantity of water in 3 hours, in what time will 3 pipes, each 3 inches bore, discharge 3 times that quantity? Ans. 12 hours.

36. If the merchandise balance of an account is $600, due April 21, what was its cash value, interest at 7 %, on the preceding January 1st? Ans. $587.17.

37. A cat watches a mouse which is distant 24 feet, and stealing towards it, advances 5 feet every quarter of an hour, while the mouse goes away 3 feet in the same time; now, allowing the cat the last quarter of an hour to advance 7 feet, how many hours will she be in catching the mouse? Ans. 23 h.

38. A park in the form of a rectangle is 40 rods long and 36 rods wide; what is the length of a straight walk between its opposite corners? Ans. 53.81+ rods.

39. A circular garden, containing one acre and forty-one square rods, has a graveled walk of uniform width just within the circle, that takes up 12 square rods of the ground; what is the diameter of the garden, and the width of the walk? Ans. Diameter of garden, 16 rd. nearly; width of walk, 4+feet

REVIEW QUESTIONS. What is Mensuration? (409) A Point? (401) A Line? (402) A Plane Figure? (407) When are figures or volumes similar? (431) What is a Series? (441) An Arithmetical Series ?(443) A Geometrical Series? (448) An Annuity? (452)

APPENDIX.

INTEREST FOR DAYS.

458. Computations of interest for days may often be abridged, by observing for what time at the given rate, the interest is equal to one hundredth of the principal.

459. The interest is one hundredth of the principal.

RULE. Remove the decimal point in the principal two orders to the left, for the interest at 4 per cent. for 90 days, at 5 per cent. for 72 days, etc. For the interest for any other number of days, at 4 per cent. multiply the interest for 90 days by the number of days and divide by 90, at 5 per cent. multiply the interest for 72 days by the number of days and divide by 72, etc.; or, when more convenient take multiples or aliquot parts of the interest that is a hundredth of the principal.

Examples.

1. What is the interest of $7000 at 5 % for 18 days?

2. What is the interest of $64.50 at 7 % for 60 days?

Ans. $.74.

3. What is the interest of $9600 at 71% for 63 days?

Ans. $126.

4. What is the interest of $9360 at 9 % for 120 days?

Ans. $280.80.

5. What is the amount of $375 at 8 % for 105 days?

Ans. $383.75.

VERMONT RULE FOR PARTIAL PAYMENTS. at annual interest with payments in

460. The process

Art. 316, is,

Find the interest on the principal and on the unpaid annual interests to the end of the year in which the first payment is made; apply the payment or payments made, with interest to the end of the year, to liquidate, first, the simple interest on the unpaid annual interests: second, the annual interests; third, the principal itself.

NOTE 1. "To the end of the year," is understood to be reckoned from the time that the note begins to draw interest. The last computation is reckoned to the time of settlement.

NOTE 2. Interest is never to be made a part of the principal, except at the time of settlement.

NOTE 3. Simple interest on unpaid annual interests draws no interest.

Example.

$1000.

St. Albans, Vt., January 1, 1874. For value received, I promise to pay A. W. Holt, or order, one thousand dollars, on demand, with interest annually.

James G. Arthur.

INDORSEMENTS. July 1, 1875, $2; Sept. 1, 1876, $300;

Amount of 1st pay't to Jan. 1, 1876, 2.06

VERMONT INTEREST RULE.

461. The following will furnish additional applications that rule. (Art. 316.)

Examples.

1. A note for $1000 was given July 1, 1864.

INDORSEMENTS. January 1, 1865, $100; September 1,

1866, $223.99; December 25, 1866, $12.

How much was due, by simple interest, January 1, 1867.

Ans. $803.12.

2. A note for $700 was given February 4, 1864.

INDORSEMENTS.

December 18, 1864, $164; June 24, 1865,

$200; September 11, 1865, $120; July 5, 1866, $60.

What was due on this note, by annual interest, Nov. 28, 1866?

3. A note for $625.50 given October 1, 1864.

Ans. $233.50.

INDORSEMENTS. January 1, 1865, $200; November 1, 1865, $20; January 1, 1866, $300.

How much was due, by simple interest, May 1, 1866?

Ans. $143.79.

4. A note for $1000 was given January 1, 1866. INDORSEMENTS. April 1, 1866, $24; August 1, 1866, $4; December 1, 1866, $6; February 1, 1867, $60; July 1, 1867, $40.

What will be due by annual interest, June 1, 1870.

Ans. $1130.62.

462.

The New Hampshire Interest Rule is the same as that of Vermont with the exception

If at the date of any payment there be no interest except the accruing annual interest, and the payment or payments do not exceed such annual interest, deduct the payment or payments at the end of the year without interest.