No.

Log.

1.05

•049

11

•095

1.15

•14

1.2

•182

1.25

•223

1.3

•262

1.33

488

1.35

•8

1.4

.336

1.45

.372

1.5

•405

1.55

•438

1.6

•47

1.65

•5

1.66

•506

1.7

.531

1.75

•56

1.8

.588

1.85

•612

1.9

•642

1.95

•668

2.

•693

2.05

•718

2.1

•742

2.15

.765

2.2

•788

2.25

•811

2.8

•838

2.33

•846

2.35

•854

24

•875

2.45

•896

2.5

•916

2.55

•936

2.6

•956

No.

Log.

.265

•975

2.66

•978

2.7

•993

2.75

1.012

2.8

1.03

2.85

1.047

2.9

1.065

2.95

1.082

3.

1.099

3.05

1.115

3.1

1.131

3.15

1.147

3.2

1.163

3.25

1.179

3.3

1.194

3.33

1.202

3.35

1.209

3.4

1.224

3.45

1 238

3.5

1.253

3.55

1.267

3.6

1.281

3.65

1.295

3.66

1.297

3.7

1.308

3.75

1.322

3.8

1.335

3.85

1.348

3.9

1.361

3.95

1.374

4.

1.386

4.05

1.399

4.1

1.411

4.15

1.423

4.2

1.435

No.

Log.

4.25

1.447

4.3.

1.459

4.33

1.465

4.35

1.47

4.4

1.482

4.45

1.493

4.5

1.504

4.55

1.515

4.6

1 426

4.65

1.537

4.66

1.54

4.7

1.548

4.75

1.558

4.8

1.569

4.85

1.579

4.9

1.589

4.95

1.599

5.

1.609

5.05

1.619

5.1

1.629

5.15

1.639

5.2

1.649

5.25

1.658

5.3

1.668

5.33

1.673

5.35

1.677

5.4

1.686

5.45

1.696

5.5

1.705

5.55

1.714

5.6

1.728

5.65

1.732

5.66

1.733

5.7

1.74

5.75

1.749

No.

Log.

5.8

1.768

686

1.766

5.9

1.775

5.95

1.783

6.

1.792

6.05

1.8

6.1

1.808

6.15

1.816

6.2

1.824

6.25

1.833

68

1.841

6.33

1446

6.35

1.848

6.4

1.856

6.45

1.864

6.5

1.872

6.55

1.879

6.6

1.887

6.65

1.895

6.66

1.896

6.7

1.902

6.75

1.91

6.8

1917

6.85

1.924

6.9

1.931

6.95

1.939

7.

1.946

7 05

1.953

71

1.96

7.15

1.967

7.2

1.974

] 46

1.981

7.3

1.988

7.33

1.991

7.35

1.995

No.

Log.

7.4

2-001

7.45

2408

7.5

2.015

7.55

2.022

74

2.028

7.65

2.035

746

2 036

7.7

2.041

7.75

2.048

7.8

2.054

7.85

2.061

7.9

2.067

7.95

2.073

8.

2.079

8.05

2.088

81

2.498

815

2.098

8.2

2.104

8.25

2.11

8.8

2.116

8.33

2.119

8.35

2.122

8.4

2.128

8.45

2.134

8.5

2.14

8.55

2.146

86

2.152

8.65

2.158

848

2.159

8.7

2.168

875

2.169

8.8

2.175

8.85

2.18

8.9

2.186

8.95

2.192

Note

The Hyp. Log of any number not in the table may be found by multiplying a common log. by 2.302585053, usually by 2.3

Example

Assume steam to enter a cylinder at a pressure of 34. lbs. per square inch, and to be cut off at ¼ the length of the stroke of the piston, the stroke being 10 feet; what will be the mean pressure?

10 feet + .5 for clearance=120.5 ins., stroke 10 / 4 + .5 for clearance = 30.5 int.

Then 120.5 / 30.5 =3.95, the relative expantion.

Log. of number 3.95 = 1.374, which + 1 = 2.374.

2.374 X 34.7 / 3.95 = 82.3778 / 3.95 = 20.855 lbs.

When the Relative Expansion or Number falls between two numbers in the Table, proceed as follows: Take the difference between the logs, of the two numbers. Then, as the difference between the numbers is to the difference between these logs., so is the excess of the expansion over the least number, which, added to the least log., will give the log. required.

Illustration

The expansion is 4.84, the logs, for 4.8 and 4.85 are 1 569 and 1.579, and their difference .01. Hence, as 4*85 ∞ 4.8 = .05: 1.579 ∞ 1.569 = 01 :: 4.84 - 4.8 = 04 : 008, and 1.669 + .008 = 1.677 = the log. required.