TABLE II.

PRESENT VALUE of £1 due at the end of any Number of Years.

Yrs. 3 per cent. 3 per cent. 4 per cent. | 41 per cent. 5 per cent.

.4088377

32

26 .4636947 27 •4501891 -3950122 28 •4370768 ⚫3816543 ·3334775 29 •4243464 •3687482 •3206514 30 .4119868 •3562784 .3083187 31 -3999871 ⚫3442304 •2964603 •2555024 •388337 •3325897 •2850579 -2444999 33 -3770233 -3213427 •2740942 •2339712 34 •3660449 •3104761 •2635521 35 -3553834 -2999769 .2534155 36 -3450324 •2898327 ⚫2436687 •2050282 •1726574 37 ⚫3349829 •2800316 2312969 .1961992 •1644356 38 •3252262 •2705619 2252854 •1877504 •1566054 39 -3157536 -2614125 ⚫2166206 .1796655 •1491480 40 •3065568 -2525725 •208289 •1719287 -1420457 50 •2281071 -1790534

.1407126 •1107097 -0872037

•3606892

3184025

2812407

3468166

•3046914

2678483

-2915707

•2550936

•279015

.2429463

•267000 •2313775

⚫2203595

2098662

-1998725

•2238959 •1903548

TABLE III.

AMOUNT of £1 per annum in any Number of Years.

16

17

18

19

20

23

24

20.9710297 21.8245311 22.7193367 22.7050158 23.6975124 24-7417069 24-4996913 25.6454129 26-8550837 26-3571805 27-6712294 29.0635625 28.2796818 29-7780786 31-3714228 21 30.2694707 31.9692017 22 32.3289022 34-2479698 34-4604137 36-6178886 36.6665282 39.0826041

23.6574918

25.8403664

28-1323847

30.5390039 33-0659541

33-7831368 35.7192518 36-3033779 38-5052144

38.93703

41-4304751

41.6891963 44.5019989 44-5652101 47-7270988

36

37

38

39

80-724906

40

50

70.0076032 77-5983139 .86.1639658 95.8363227 73.4578693 81.7022464 91-0413443 101-6281388 77-0288947 85.9703363 96-1382048 107-7095458 90-4091497 101-464424 114-0950231

84-5502778 95.0255157 107-0303231 120-7997742

130-9979102 152-6670837 178-5030283 209-3479957

P

TABLE IV.

PRESENT VALUE of £1 per annum for any Number of Years.

18 13.1896817 12.659297 19 137098374

20

21

22

23:

26

15.6220799

16-8903523 15.9827692 15-1466115

13.1339394 14-2124033 13-5903263 13.0079365 14-6979742 14-0291599 13.4047239 15.1671248 14-4511154 13.7844248 15-6204105 14-8568417 14-1477749 24 16.0583676 15.2469634 14-4954784 25 16-4815146

12.5932936 12-0853209

12.4622103

12-8211527

13.1630026

13-4885739

13.7986418

14-8282089

14 0939446

14.3751853

TABLE V.

Amount of £1 in any Number of Days, &c. at Compound Interest.

Dys.3 per cent. [34 per cent. 4 per cent. | 4 per cent.[ 5 per cent.

1.000081
1.000162

3 1.000243

5

7

1.0000943 1·0001075 1-0001206 1·0001337 1.0001885 1.0002149 1·00024121 1·0002674 1.0002828 1.0003224 1 0003618 1-0004011 4 1.0003240 1.0003771 1.0004299|1-0004825 1.0005348 1.0004050 1.0004714 1-0005374 1-0006031 1.0006686 61.000486 1.0005657 1:0006449 1:0007238 1:0008023. 1:000567 1:000660. 1·0007525|1 0008445 1-0009361/ 8 1:0006481 1.0007543 1.000860 1:00096521-0010699 9 1.0007291 10008486 1:00096751 0010859 1-0012038 10 1.0008102 1-00094291-00107511-0012067 1.0013376 20 1-001621 1:0018868 1-0021514 1-0024148 1002677 301-0024324 1:0028815 1.0032288 1.0036244 1.0040182 40:1-0032446 1.00377711-0043074 1-0048354 1.0053612 501-0040574 1:0047236| 1-0053872 1.0060479 1.006706 601-00487081-005671 1.0064681 1.0072619 1.0080525 701-0056849 1-0066193 1-0075501 1-0084773 | 1 0094009 801-0064997 1-0075685 1.0086334 1.0096942 1.0107511 90 1.0073151 | 1-0085186 1-0097178 1 0109126 1.0121031 100 1.0081312 1.0094696 1.0108033 1-0121324 | 1·0134569 1201-0097653 1-0113743 1-012978 1.0145765 1.0161699 1·0170265 | 1·0188902

140 1-01140211-0132825 1 0151573 160 1-0130416 1.0151944 1-0173413 1-0194824 1.0216178 180 1 0146837 10171098 1.01953 1-0219443 1.0243527 2001.01632851-0190289 1-0217234 1·024412.1-0270949

220

240

1-01797591-02095161-0239215 1:0268858 1-0298444.

1.019626 1-02287791-0261244 1·02936551-0326013 2601-0212788 1:02480781-028332 1.0318512 1.0353656

280

1-0229343 1-0267414 1·0305443 | 1·0343429 | 1·0381373 300 1-0245924 1.02867871-0327614 1.03684071 0109164 3201-02625331-0306196 1.0349833 1.0393444 1.043703 340 1-0279168 1·0325641 | 1·0372099 | 1·0418542 1.046497 1.029583 1.0345124 1.0394414 1-0443701 1-0492985

360

1.003466

1.002871 1-0032737 1.0036751-004074 1-0074171 1-0086374 1-0098534 1.011065 1.0122722 1.0148892 1-0173495 1.0198039 1.0222524 1-0246951 | 1-0224166 | 1·02613681-02985241-0335636 | 1-0372704)

SECT. III.

DUODECIMAL MULTIPLICATION,
AND ARTIFICERS' MEASURING.

Duodecimal Multiplication is a method of multiplying similar to multiplication of decimals, with this difference, that the scale of notation in the former decreases in a twelvefold proportion, whereas in the latter it decreases in a tenfold proportion.

RULE. Under the multiplicand write the corresponding_denominations of the multiplier, that is, feet under feet, inches under inches, &c. Multiply each term of the multiplicand, beginning with the lowest denomination, by the feet in the multiplier, and write the several products under the respective terms of the multiplicand from which they arise; observing to carry 1 for every 12 from each lower denomination to the next higher. Then multiply by the inches of the multiplier (if any,) in the same manner, and write the products each one place to the right hand, carrying as before at 12. Next, multiply by the parts, (if any,) writing each product another place to the right; and so on: the sum of the several lines of products is the answer.

Note 1. When the number of feet in the multiplicand is great, first multiply by the feet of the multiplier, and then, instead of multiplying by the inches and parts, take such aliquot parts of the multiplicand as they are of a foot.

2. When the number of feet in both factors is great, first multiply the feet of the multiplicand by the feet of the multiplier, then take parts of the multiplicand for the inches, &c. of the multiplier: and for the inches, &c. of the multiplicand, take parts of the feet only of the multiplier.

EXERCISES.

1. Mult. 9 ft. 3 in. by 3 ft. 5 in. 2. Mult. 6 ft. 8 in. by 5 ft. 9 in. 3. Mult. 12 ft. 7 in. by 4ft. 11 in. 4. Mult. 15 ft. 9 in. by 8 ft. 5 in. 5. Mult. 14ft 8 in. by 9ft. 10 in. 6. Mult. 15 ft. 6 in. by 7 ft. 9 in. 7. Mult. 19 ft. 1 in. by 6 ft. 2 in.