45°

29. On the plane face of the hemisphere suggested above (Art. 1287), draw diameters AD and FG at right angles; and 45° from G, a chord NM parallel to FG. (This chord will not bisect AC) As MCG

N

W

A

450

M

1289. The pupils have already learned that the volume of a rectangular prism is equal to the area of the base multiplied by its altitude; these problems are intended to show that the same is true of all prisms and of the cylinder (6).

1292. 8. The volume of the frustum is obtained by deducting the volume of the part cut off from the volume of the whole pyramid (Problem 7). The rule is given later.

10. Fig. 49 gives the method of calculating the slant height. The illustration shows a sec

5 in.

A

B

12 in.

5 in.

from A will fall on CD at a

X

FIG. 49.

point X, 5 in. from C. In

the right-angled triangle AXC, AX= altitude = 12 in. AC2 = AX2+ XC2 = 144+25 169; AC= √169 = 13.

XX

NOTES ON THE APPENDIX

1306. A person that contracts to receive a rate of interest greater than is permitted by law, is liable to a penalty, except in Connecticut. In Delaware, Minnesota, etc., the penalty is the forfeiture of the contract; in New York, the forfeiture of the contract, $1000 fine, and 6 months' imprisonment; in Indiana, Kansas, Kentucky, Maryland, Michigan, Mississippi, Ohio, Pennsylvania, Tennessee, Vermont, Virginia, and West Virginia, the forfeiture of the excess of interest; in North Carolina, the forfeiture of double the amount of interest; in Georgia and New Hampshire, the forfeiture of three times the excess of interest; in Alabama, Delaware, Florida, Illinois, Iowa, Louisiana, Missouri, Nebraska, New Jersey, South Carolina, Texas, and Wisconsin, the forfeiture of all interest; in Arkansas and Oregon, the forfeiture of principal and interest.

1307. 3. Amount of $1000, June 1, 1896, to June 1, 1897 Amount of $150, Sept. 16, 1896, to June 1, 1897, 8 mo..

Due June 1, 1897

Interest to settlement, Apr. 16, 1898, 10 mo.

Amount Apr. 16, 1898

Amount of $50, Sept. 16, 1897, to Apr. 16, 1898, 7 mo.

$1,060.00

156.37

$903.63

47.44

$951.07

51.75

Balance due

$899.32

4. Amount of $500, July 25, 1896, to Apr. 1, 1897, 8 mo. 6 da.

$520.50

Amount of $100, Sept. 18, 1896, to Apr. 1, 1897,

6 mo. 13 da.

$103.22

Amount of $200, Feb. 5, 1897, to Apr. 1, 1897, 1 mo.

26 da.

201.86

305.08

Balance due

$215.42

5. Amount of $870.50, Jan. 2, 1894, to March 18, 1896, 2 yr.

Interest March 18, 1896, to Jan. 2, 1897, 9 mo. 14 da.

Amount

Amount of $250, Aug. 24, 1896, to Jan. 2, 1897, 4 mo. 8 da.

Due at maturity

$985.99 235.

$750.99

35.54

$786.53

255.33

$531.20

Below will be found answers to the partial payments examples of Chapters XIII and XIV, according to the Connecticut rule. NOTE. Although the legal rate in Connecticut is 6%, the rates given in the examples should be used.

5. $899.32 (see Art. Art. 1015. 7. $700.50.

Art. 1008. $70.51. Art. 1009. 1. $224.22. 2. $261.21. 3. $1278.15. Art. 1011. 4. $771.24. 1307, 3). Art. 1013. 5. $1088.31. Art. 1023. 7. $1232.26. Art. 1051. 7. $77.07. Art. 1090. 3. $649.13. 4. $224.64: Art. 1107. 2. $1089.64.

The time in each of the preceding examples was found by compound subtraction, taking 30 days to each month. In the examples in Art. 1110, the Connecticut rule has been followed. In these, the time is taken in days. (See Art. 1111.)

Due Oct. 15, 1899

Amount of $80, Feb. 15, 1897, to June 15, 1897

New principal June 15, 1897

Interest to Oct. 15, 1899, 2 yr. 4 mo.

Interest for 1 yr. 4 mo. on $40.98, unpaid interest.

Interest for 4 mo. on $40.98, unpaid interest .

Amount Oct. 15, 1899

Amount of $15, Sept. 15, 1898, to Oct. 15, 1899

NOTE. — If four places of decimals are used, the answer to 6 is $367.6442,

or $367.64+; to 7, $766.7658, or $766.77 -.

81.60 103.50

$683.02

95.62

3.28

.82

$782.74

15.98

$766.76

The teacher that wishes other examples of this kind can use 9 and 10 of Art. 1309, and 12, 14, and 15 of Art. 1310, the answers to which are as follows: Art. 1309. 9. $1734. 10. $738.29. Art. 1310. 12. $1901.18. 14. $3432.20. 15. $1010.95.

1309. Pupils in New Hampshire should not be taught the preceding method, but should be confined to the rule laid down by the courts of their own state.

An examination of 8 will show the manner of ascertaining the balance. The interest for 1 year is $36. As no interest is due except that which accrued during the year, and as the sum paid is less than the interest due, no interest is allowed on the payment of $30, made during the year. This payment being $6 less than the interest due at the end of the year, the interest on $6 is added to the interest on the principal at the end of the next year, making a total of $642.36 then due less the amount of $100 for 11 months. Interest is allowed on the $100 payment because it is in excess of the interest then due.

NOTE. — The amount of the payment of March 14 canceled the $3 interest on interest and $7.48 additional, leaving $ 102.52 interest still unpaid Jan. 3, 1897 on which two years' interest is taken to Jan. 3, 1899. Two years' interest on the principal is also taken, and one year's interest on the annual interest due Jan. 3, 1898 and unpaid. It will be noticed that no interest is taken on the interest upon interest, $3 and $6.15. See 14 of Art. 1310, as calculated by the N.H. rule:

As additional examples, the teacher may use 7 of Art. 1308, and 12, 14, and 15 of Art. 1310. The answers by the N.H. method are 7, $767.60; 12, $1901.27; 14, $3435.80; 15, $1011.40.

$1465.80

1030.00

435.80

$3435.80