APPENDIX.

The following subjects are presented in an appendix, not because they are unimportant, but for the reason that thus placed they may more distinctly constitute a supplementary course which the pupil may elect to study or not, as circumstances may incline him.

1. Duodecimals.

2. Metric System.

3. Specific Gravity.

4. Foreign Exchange.

5. Arithmetical Progression.

6. Geometrical Progression.

9. Circulating Decimals.

10. G. C. D. and L. C. Dd. of Fractions.

11. Thermometer.

12. The Clock.

13. Work.

7. Compound Interest (Table). 14. Averaging of Accounts. 8. Annuities.

15. Miscellaneous Exercises

and Problems.

DUODECIMALS.

Duodecimals (Latin, duodecim, twelve) are fractions of which 12 of any order equal one of the next higher order.

The unit is the foot, which is divided into 12 equal parts called primes ('), each prime (') being divided into 12 equal parts called seconds (''), each second ('') in the same manner into 12 thirds ('/'), and each third (/) into 12 fourths ('''').

Duodecimals are employed principally by artisans in the measurement of lines, surfaces, and solids.

The adding and subtracting of duodecimals differ in no respect from the adding and subtracting of other compound numbers.

EXERCISES.

1. What is the sum of 12 ft. 7' 10, 17 ft. 8' 9', and 35 ft. 5' 8'? 2. Add 7 ft. 1' 3" 6', 1 ft. 3" 6' 1, 7 ft. 8' 7'' 9'/', 8 ft. 10' 6'.

8'', and 352 ft. 7′ 9′′ 4'/'. 4''' 3'''', and 7'//'.

3. Add 123 ft. 5' 6' 8', 217 ft. 9' 10' 4. Add 6 ft. 4' 2, 15 ft. 4' 3'', 8' 9' 5. What is the sum of 186 ft. 5′ 9′′ 4' 5////, 218 ft. 7' 10'' 10///

8', and 235 ft. 6′ 9/ 7/ 10.

6. From 9 ft. 1' 3' take 2 ft. 6' 1" 3".

7. From 18 ft. 3' 9'

8. From 275 ft. 5' 6' 8'

9. From 225 ft. 0' 2' 5'

take 10 ft. 2' 2'' 6'''.

take 127 ft. 8' 4" 5".

7'//' subtract 117 ft. 5' 9′′ 8′′// 5////.

10. From a board 15 ft. 7' 6" in length, 3 ft. 8' 11" were sawed off. What was the length of the piece left?

MULTIPLICATION.

What is the product of 8 ft. 5′ 4′′′ and 5′ 3′′?

Adding the two partial products, we have 44 ft. 4' 0'' 0''.

NOTE. and, etc., are called indices. Since a product has as many indices as both its factors, by the use of the indices the multiplication may be performed, in practice, without the fractions.

PROBLEMS.

1. A board is 7 ft. 5' 8" in length and 2 ft. 4' 7" in breadth. What is its area?

2. How many cubic feet in a wall 80 ft. 9' long, 3 ft. 4′ high, and 1 ft. 8 in. wide?

3. Find the surface to be plastered in a room 18 ft. 3′ long, 15 ft. 2' wide, and 10 ft. 3′ high, allowing 8' for the width of the baseboard.

4. A pile of wood is 255 ft. long, 4 ft. 6′ high, and 8 ft. 4' wide. Find the number of cords in it.

5. What are the solid contents of a block of stone 3 ft. 2′ long, 2 ft. 3' 6" wide, and 4 ft. 2′ high?

6. What would it cost to plaster a wall 32 ft. 8′ long and 9 ft. high at 17 cents per square yard?

7. How many loads of earth must be taken out in digging a cellar that is to be 45 ft. 6 in. long, 25 ft. wide, and 10 ft. 9 in. deep?

1. A floor contains 216 sq. ft. 5′ 10′′ 6', and is 10 ft. 6' wide. How long is it?

2. The square contents of a quilt are 14 ft. 6 in.; it is to be lined with stuff 2 ft. 7 in. wide. Find the length of the lining.

3. A stick of timber is 3 ft. 2 in. wide, and 2 ft. 9 in. thick; it contains 176 cu. ft. 4' 1" 6'. Find its length.

4. Find the cost of carpeting a room 15 ft. long, 12 ft. wide with carpet 27' wide, at 75 cts. a yard.

5. A plank is 5′ thick, 20 ft. 2′ long, and contains 14 cu. ft. 8'. How wide is it?

THE METRIC SYSTEM.

The Metric System is a decimal system of weights and measures; the fundamental unit is the metre. The Standard Metre is a bar of very hard metal, whose length, as determined by French scientists, is 10000000 of a quadrant of a meridian, and is equal to about 39.37 inches.

This system was first adopted in France in 1795, and is now used also in Germany, Spain, Portugal, Belgium, and Greece, as well as in Mexico, Brazil, and most of the other States of South America. Its use is allowed by law in Great Britain and in the United States, but as yet it finds small favor, except among scientists.

The principal units of the Metric System are:

1. The Metre (m), for lengths.

2. The Are (°), or square dekametre (qdkm), for surfaces.

3. The Stere (st), or cubic metre (cbm), for volumes.

4. The Litre (1), or cubic decimetre* (cbdm), for small volumes. 5. The Gramme ("), for weights; equal to the weight of one cubic centimetre* of water at 4° C.

39.2° F.

The units are all divided and multiplied decimally. Subdivisions are indicated by Latin prefixes; multiples, by Greek prefixes.

Metric numbers are written decimally, with the point placed immediately after the unit, as 10.15m, which may be read “10 and 1 metres," or, "10 metres, 1 decimetre, 5 centimetres."

The metre is very little more than 39.37 in. The kilometre is a little less than of a mile.

Reduction from one denomination of the table to another is made by simply moving the decimal point to the right or left: to the right for lower denominations; to the left for higher denominations. Thus it will be seen that operations with metric numbers are similar to those with decimals.

The are equals about 10 sq. ft. The hectare equals about 21

acres.