Appendix Note H, [Tables showing heat expansion of granite and other materials]

Charles Babbage

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Credits

John van Wyhe, Ph.D., Cambridge University digitized and converted to html Charles Babbage's The Ninth Bridgewater Treatise 2nd ed. (London, 1838). In December 2008 George P. Landow proofed the text, reformatted it, rescaned the images, added missing paragraphing throughout, and made links to materials on this site.

Directions

Page breaks in the original are indicated as follows: [498/499]. Where pagebreaks divide words, the complete word appears after the page break

Contents

Preface

Chapter I. Nature of the Argument

Chapter II. Argument in favour of Design from the changing of Laws in Natural Events

Chapter III. Argument to show that the Doctrines in the preceding Chapter do not lead to Fatalism

Chapter IV. On the Account of the Creation, in the First Chapter of Genesis

Chapter V. Further View of the same Subject

Chapter VI. Of the Desire of Immortality

Chapter VII. On Time

Chapter VIII. Argument from Laws intermitting—on the Nature of Miracles

Chapter IX. On the permanent Impression of our Words and Actions on the Globe we inhabit

Chapter X. On Hume's Argument against Miracles

Chapter XI. Reflections on the Inquiry in the preceding

Chapter XII. On the Nature of a Superintending Providence

Chapter XIII. A priori Argument in favour of the Occurrence of Miracles

Chapter XIV. Thoughts on the Nature of Future Punishments

Chapter XV. Reflections on Free Will

Conclusion

Sections of the Appendix

Appendix Note A, On the great law Which Regulates Matter

Appendix Note B, On the Calculating Engine

Appendix Note C, Extract from the Theory of Probabilities of LaPlace

Appendix Note D, On Miracles

Appendix Note E, On Humes Argument against Miracles

Appendix Note F, On the Consequences of Central Heat

Appendix Note G, On the action of existing causes in producing elevations and subsidences in portions of the earth's surface

Appendix Note G, On the action of existing causes in producing elevations and subsidences in portions of the earth's surface

Appendix Note I [Extracts from two letters of Sir J. Herschel]

Appendix Note K. On the Elevation of Beaches by Tides

Appendix Note L.On Ripple-Mark

Appendix Note M.On the Age of Strata, as Inferred from the Rings of Trees Embedded in Them

Appendix Note N. On a Method of Multiplying Illustrations from Woodcuts

Table [1]

Showing the Expansion of Beds of Granite variously heated, from One Degree to One Hundred Degrees Fahrenheit, and from One to Five Hundred Miles thick.

Miles.

One Degree.

Twenty Degrees.

Fifty Degrees.

One Hundred Degrees.

 

 

Feet.

Feet.

Feet.

Feet. I

1

.02548

.5095

1.274

2.548

5

.13

2.55

6.37

12.74

10

.25

5.10

12.74

25.48

15

.38

7'64

19.11

38.21

20

.51

10.19

25.48

50.95 i

25

.64

12.74

31.85

63.C9

30

.76

15.29

38.2J

76.43

35

.89

17.83

44.58

89.17

40

1.02

20.38

50.95

101.90

45

1.15

22.93

57.32

114.64

50

1.27

25.48

63.69

127.38

55

1.40

28.02

70.06

140.12

60

1.53

30'57

76.43

152.86

65

1.66

33.12

82.80

165.59

70

1.78

35.67

89.17

178.33

75

1.91

38.21

95.5

191.07

80

2.04

40.76

101.90

203.81

85

2.17

43.31

108.27

216.55

90

2.29

45.86

114.64

229.28

95

2.42

48.40

121.01

242.02

100

2.55

50.95

127.38

254.76

150

3.82

76.43

191.07

382.14

200

5.10

101.90

254.76

509.52

500

12.74.

254.76

636.90

1273.80

[221/222]

Table [2]

Showing the Expansion of Beds of Granite variously heated, from Two Hundred Degrees to Three Thousand Degrees Fahrenheit, and from One to Five Hundred Miles thick.

Miles.

Two Hundred Degrees.

Five Hundred Degrees

One Thousand Degrees

Three Thousand Degrees.

 

 

Feet.

Feel.

Feet.

Feet.

1

5.095

12.738

25.476

76.428

5

25.5

63.7

127.4

382.1

10

51.0

127.4

254.8

764.3

15

76.4

191.1

382.1

1147.4

20

101.9

254.8

509.5

1528.6

25

127.4

318.5

636.9

1910.7

30

152.9

382.1

764.3

2292.8

35

178.3

445.8

891.7

2675.0

40

203.8

509.5

1019.0

3057.1

45

229.3

573.2

1146.4

3439.3

50

254.8

636.9

1273.8

3821.4

55

280.2

700.6

1401.2

4203.5

60

305.7

764.3

1528.6

4585.7

65

331.2

828.0

1655.9

4967.8

70

356.7

891.7

1783.3

5350.0

75

382.1

955.4

1910.7

5732.1

80

407.6

1019.0

2038.1

6114.2

85

433.1

1082.7

2165.5

6496.4

90

458.6

1146.4

2292.8

6878.5

95

484.0

1210.1

2420.2

7260.7

100

509.5

1273.8

2547.6

7642.8

150

764.3

1910.7

3821.4

11464.2

200

1019.0

2547.6

5095.2

15285.6

500

2547.5

6369.0

12738.0

38214.0

The table was calculated from experiments made under the direction of Colonel Totten, by Mr. H. C. Bartlett, of the United States Engineers; an account of which is given in the American Journal of Science, Vol. XXII. p. 136.

From the result of these experiments it was found that, for every degree of Fahrenheit,

Granite expands ..........000004825

Marble.........................000005668

Sandstone ....................000009532

The tables were computed by the Calculating Engine, from the first line, which was deduced from the experiment. It will be observed that the numbers given are always true to the last figure, a compensation which the Engine itself made. In order to find the expansion for marble, increase the numbers by one-sixth. To find the expansion for sandstone, double the numbers found in the table.

Other experiments have since been made by Mr. Adie, of which an account is given in the thirteenth volume of the Transactions of the Royal Society of Edinburgh: from these I have selected the following list of expansions: —

Roman Cement expands ......... .00000750

Sicilian White Marble ...............00000613

Carrara Marble ...................... .00000363 [223/224]

Sandstone, from Craigleith quarry.......00000652

Slate, from Penrhyn, Wales ....... .00000576

Peterhead Red Granite............... .00000498

Arbroath Pavement.....................00000499

Caithness Pavement.....................00000497

Greenstone, from Ratho ..............00000449

Aberdeen Grey Granite ...............00000438

Best Stock Brick ..........................00000306

Fire Brick.....................................00000274

Black Marble, Galway .................00000247 [224/225]



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14 December 2008