6001. To Find the Cubical Contents of a Cylinder

6001.    To Find the Cubical Contents of a Cylinder. Find the area of the circular cud, as directed in No. 5987, and then multiply the area by the length of the cylinder; the product will be the cubical content. The same denomination of measurement must be adhered to throughout the calculation, as, if the diameter or area is in inches, the length must be in inches. Thus: to find the cubical content of a cylinder 8 inches in diameter and 3 feet long; we find in No. 5987 that the area of a circle 8 inches in diameter is 50.265 square inches; multiply this by 36 inches (3 feet reduced to inches, the same denomination as the given diameter), and the product is 1809.54 cubic inches, or 1 foot, 81.54 cubic inches.

6002. Table of Spherical Contents, etc.

6002.    Table of Spherical Contents, etc.. This table shows the relative proportions between the diameter, surface, and capacity (or cubical contents) of spheres.

Diameters.

Surfaces.

Capacities.

1

3.141

.523

2

12.567

4.188

3

28.274

14.137

4

50.265

33.51

5

78.540

65.45

10

314.159

523.6

15

706.9

1767.1

20

1256.6

4189.

25

1963.5

8181.

30

2827.

14137.

40

5026.

33510.

6003. To Find the Cubical Contents of Spars or Other Bound Timber

6003. To Find the Cubical Contents of Spars or Other Bound Timber. If the spar or timber were the same thickness through its entire length, the diameter of all parts would bo the same, and one measurement would suffice to obtain the correct diameter; its cubical contents could then be found in the same way as for a cylinder; but this is hardly ever the case, as the thickness or diameter is different in every part. If the spar tapers regularly from one end to the other, measure the diameter at each end, add the two measurements together, and divide their sum by 2; this will give the average diameter. A piece of timber of irregular thickness must be measured in portions, each portion extending as far as the tapering is regular, and the contents of the different portions added together to get the contents of the whole. Having obtained the correct diameter in inches, look for it in the next table, and opposite it, in the next column to the right, will be the contents in feet of 1 foot of timber in length ; multiply this by the length of the timber in feet, and the result will be the contents of the whole.

Thus, to find the contents of a 16-foot log whose average diameter is found to be 131/2 (that is, 13.5) inches, we find the figures on the next right hand column in the table are .99; this means that a log 1 foot long and 131/2 inches in diameter contains .99 or 99/100 of a cubic foot. Multiply this .99 by 16, the length of the log in feet, and we get 15.84, or about 157/8 cubic feet, which is the contents of the whole log.

About 10 per cent, should be deducted from the results given in the table when toll is charged on rafts of spars or logs, for the reason that many sticks of timber taper suddenly, and others are unequal in diameter when the average is taken.

Diameter Inches.

Contents. 1 foot long.

Diameter Inches.

Contents. 1 foot long.

4.

.0872

27.5

4.12

5.

.137

28.

4.28

6.

.196

28.5

4.43

7.

.267

29

4.59

7.5

.31

29.5

4.75

8.

.35

30.

4.91

8.5

.39

30.5

5.07

9.

.44

31.

5.24

9.5

.49

31.5

5.41

10.

.55

32.

5.58

10.5

.60

32.5

5.76

11.

.66

33.

5.94

11.5

.72

33.5

6.12

12.

.79

34.

6.31

12.5

.85

34.5

6.49

13.

.92

35.

6.68

13.5

.99

35.5

6.87

14.

1.07

36.

7.07

14.5

1.15

36.5

7.27

15.

1.23

37.

7.47

15.5

1.31

37.5

7.67

16.

1.40

38.

7.88

16.5

1.48

38.5

8.09

17.

1.58

39.

8.30

17.5

1.67

39.5

8.51

18.

1.77

40.

8.73

18.5

1.87

40.5

8.95

19.

1.97

41.

9.17

19.5

2.07

42.

9.61

20.

2.18

43.

10.08

20.5

2.29

44.

10.555

21.

2.40

45.

11.044

21.5

2.52

46.

11.541

22.

2.64

47.

12.049

22.5

2.76

48.

12.566

23.

2.89

49.

13.095

23.5 24. 24.5 25.

3.11 3.14 3.27 3.41

50. 51. 52. 53.

13.635 14.186 14.747 15.320

25.5

3.55

54.

15.904

26.

3.69

55.

16.499

26.5

3.83

56.

17.104

27.

3.98

57.

17.720