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Q. How, then, would you proceed, to find how many solid fech inches, &c. are contained in a solid body?
A. Multiply the length, breadth and depth to gether.
1. How many solid feet in a block 4 feet thick, 2 feet wide, and 5 feet long? Ans. 4X2X5=40 solid feet.
2. How many solid or cubic feet in a block 12 inches long, 12 inches wide, and 12 inches thick? A. 1 solid foot
Q. When a load of wood contains 128 solid feet, what is is called ?
A. I cord.
3. How many solid feet in a pile of wood 8 feet long, 4 feet wide, and 4 feet high? A. 128,=1 cord. How many cords of wood in a pile 8 feet long, 4 feet wide, and 8 feet high? A. 256 solid feet, = 2 cords.
Q. In common language, we say of a load of wood brought to market. if it is 8 feet long, 4 feet high, and 4 feet wide, that it is a cord, or it contains 8 feet of wood. But this would make 128 solid feet; what, then, is to be understood by saying of such a load of wood, thai it contains 8 feet of wood ? or, in common language, “ there is 8 feet of il” ?
A. As 16 solid feet, in any form, are of 128 feet, that is, } of a cord, it was found convenient, in reckoning, to call every 16 solid feet 1 cord foot; then 8 such cord feet will make 128 solid feet, or 1 cord, for 8 times 16 are 128.
Q. How, then, would you bring solid feet into cord feet? A. Divide by 16. 4. How many cord feet in a pile of wood 8 feet long, 2 feet high, and I foot wide ? How many in a load 8 feet long, 2 feet high, and 2 feet wide? 8 feet long, 4 feet wide, and 2 feet high?
5. If, in purchasing a load of wood, the seller should say that it contains 3 cord feet, how many solid feet must there be in the load ? How many solid feet to contain 4 cord feet? 5 cord feet? 6 cord feet? 7 cord feet? 8 cord feet? 9 cord feet?
6. How many cord feet in a pile of wood 8 feet long, ; foot wide, and 4 feet high ?
In performing this last example, we multiply 4 feet (the height) by 1 foot (the width), making 4; then, this 4 by 8 feet (the length), making 12 - 10
(cord feet),= 2 cord feet, Ans. But, instead of multiplying the 4 by the 8 feet in length, and dividing by 16, we may simply divide by 2, without multiplying; for the divisor, 16, is 3 timos as large as the multiplier, 8; consequently, it will produce the same result as before ; thus, 4 X 1=4-2=2 cord feet, Ans., as before.
Q. When, then, a load of wood is 8 feet long, or contains two lengths, each 4 feet (which is the usual length of wood prepared for market), what easy method is there of finding how many cord feet such a load contains ?
A. Multiply the height and breadth together, and divide the product by 2.
7. How much wood in a load 8 feet long, 3 feet high, and 2 feet wide ? 3 X 2=6: 2=3 cord feet, Ans.
8. How many cord feet in a load of wood 2 feet high, y feet wide, and of the usual length ? 3 feet high and 2 feet wide? 3 feet wide and 3 feet high? 4 feet wide and 4 feet high? 4 feet wide and 6 feet high? How many cords in a load 4 feet high, 4 feet wide ?
9. How wide must a load of wood be, which is 8 feet long and 1 foot high, to make 1 cord foot? How wide to make 2 cord feet? 3 cord feet? 6 cord feet? 10 cord feet?
10. What will a load of wood 8 feet long, 34 feet wide, and 4 feet high, cost, at $1 per foot ?
The foregoing remarks and illustrations may now be embraced
in the following
A. Multiply the length, breadth and depth together.
Q. When the length of wood is 8 feet, how can you find the number of cord feet it contains, without multiplying by 8 and dividing by 16?
A. Multiply the breadth and height together, and divide the product by 2 ; the quotient will be cord feet.
Q. How do you bring cord feet into cords?
A. Divide by 8. Note. If the wood is only 4 feet in length, proceed as last directed; then. u 8 feet in length is 2 times as much wood as only 4 feet in length, hence | the result, founil as above, will be the answer in cord feet; that is, divide by ? twice, or once by 4.
Exercises for the Slate.
1. How many solid feet in a load of wood 8 feet long, 4 feet wide, and 31 feet high? 4x3=14+2=7 cord feet, Ans.
2. How many feet in a load of wood 5 ft. 6 in. high, 3 ft. 9 in wide, and of the usual length ?
(Reduce the inches to the decimal of a foot.) A. 102 =10 ft.
Perform this last example by reducing the inches of a foot to a coinmon fraction. This method, in most cases, will be found preferable : thus, taking the law, example:óft. 6 in.=51 ft. = 4; then, 3 ft 9 in.=3f ft.=4 X
= 185 -2=-1196 =1076, Ans., as before. . 3. In a block 8 ft. 6 in. in length, 3 ft. 3 in. wide, and 2 ft. 9 in. thick, how many solid feet? A. Decimally, 75,96875 feet=7531 feet. By common fractions, 2
x x 2431=7532 feet, Ans., as before.
4. If a load of wood is 8 feet long and 3 feet wide, how higb must it be to make 1 cord ?
In this example, we know that the height multiplied by the width, and this product divided by 2, must make 8 cord feet, that is, 1 cord or load; lience, 8 X 2 = 16—3=51 feet, height, .Ins.
5. Ifa load of wood is 54 feet high, and 8 feet long, how wide must it be to make 2 cords?
2 cords = 16 cord fect; then, 16 X 2=32 = 53 = 6 feet wide, Ans.
6. If a load of wood is 5 feet high, and 8 feet long, how wide must it be to make 3 cords ?-9. 4 cords ?-12. 8 cords ?-24. A. 45 feet.
7. How many solid feet of timber in a stick 8 feet long, 10 inches thick, and 6 inches wide ?-3}. 10 feet long, 12 inches thick, and í ft. 3 in. wide ?-123. 20 ft. 6 in. long, 24 inches wide, and 1 ft. 9 in. thick ?-715. A. 87 ft.
8. In a pile of wood 10 feet wide, 3 ft. 3 in. high, and 1 mile long, how many cord feet, and how many cords?
A. 10725 cord feet = 1340% cords. 9. How many tons of timber in 2 sticks, each 30 feet long, 20 inches wide, and 12 inches thick ? A. 100 feet :-50=2 tons
10. How many bricks 8 inches long, 4 inches wide, and 27 inches thick, will build a wall in front of a garden, which is to be 240 feet long, 6 feet high, and 1 foot 6 inches wide ?
A. 51840 bricks,
TLXXXI. Q. From what is the word duodecimals derived !
A. From the Latin word duodecim, signifying twelve.
Q. In common decimals, we are accustomed to suppose any whole thing, as a foot, for instance, to be divided into ten equal parts; but bow is a font divided in duodecimals? and what are the parts called ?
A. Into twelve equal parts, called inches or primes ; and each of these parts into twelve other equal parts, called seconds; also each second into twelve equal parts, called thirds, and each third into twelve equal parts, called fourths, and so on to any extent whatever.
Q. What, then, are dnodecimas ?
Q. Now, since 12ths multiplied by 12this make 144ths, and 11 make T's ; also, 144ths multiplied by 12ths make 1728ths, and nig make Tłt; it is plain that we may write the fractions without their de nominators, hy making some mark to distinguish them. What marks are generally used for this purpose ?
A. 12ths, inches, or primes, are distinguished by an accent, thus; & signifies , 8 inches, or 8 primes; 7" = Tła, or 7 seconds ; 6'" =15, or 6 thirds, &c.
(e. We have seen tha: 12ths multiplied by 12ths produce 1941hs ; whal, then, is the product of 5! (inctics or primes) multiplied by 7 (nches)?
A. 35'', that is, 35 seconds, or .
Q. What is the product of 5" (seconds) multiplied by 7" (seconds)?
A. By placing as many marks or accents at the right of the product as there are marks at the right of both multiplier and multiplicand counted together.
Q. What, then, would 71|| (fifths) multiplied by 8!!! (sixths) produce ?
A. 56'"|||II, that is, 56 elevenths.
Q. From the preceding, what appears lo be the value of feet mul tiplied by primes or inches ? or what do feet multiplied by primes give ?
Note.—This might be extended in the same manner to any indefinite length The following table contains a few of these denominations.
TABLE. 12" (fourths). ..... make 1" (third.) 12" (thirds) ...... make 1" (second.) 12" (seconds) ...., make 1' (inch or prime.) 12 (inches or primes) make 1 foot. Q. How may duodecimals be added and subtracted ?
A. In the same manner as compound numbers ; 12 of a less denomination always making 1 of a greater, as in the foregoing table.