Using Percentage

(1) To find the percentage of any number when the rate per cent is given: Multiply the number by the rate per cent and set the decimal point two places to the left.

Example: Find 7.5 per cent of 35. 35X7.5 = 262.5; decimal point moved two places to the left gives Ans. 2.625

(2) To find what rate per cent one number is of another: Add two ciphers to the percentage and divide by the number on which the percentage is reckoned.

Example: What per cent of 75 tons is 9 tons? 900/75 = 12.

Ans. 12 per cent.

(3) To find a number when the rate per cent and the percentage are known: Add two ciphers to the percentage and divide by the rate per cent.

Example: If 68 pounds is 15 per cent of the entire charge, how many pounds in the total charge? Ans. 6800/15 = 453.33 pounds.

(4) To find what number is a certain per cent more or less than a given number: (a) When the given number is more than the required number, add two ciphers to the number and divide by 100 plus the rate per cent.

Example: 465 is 35 per cent more than what number?

Ans. 46500/(100+35)135 = 344.4.

(b) When the given number is less than the required number add two ciphers to the number and divide by 100 minus the rate per cent.

* In no case, shall the defection bo under 0.10 of an inch.

Storage Data. Square Box Measure

SIEE

(inches)

Capacity

24 X16 X28

1 barrel

16 Xl6 3/4X 8

1 bushel

8iX 8iX 4

1 gallon

4 X 4iX 4

1 quart

Molding Material Weights

Material

Amount (cu. ft).

Weight (ton)

River sand

21

1

Pit sand

22

1

Stiff clay

28

1

Example

526 is 23 per cent less than what number?

Ans. 52600/(100-23) = 52600/77=683.116

Mensuration

Circumference of a circle

= diameterX3.1416

Area of a square or rectangle

-base side X height

Area of a triangle

=base X 1/2 X perpendicular height

Area of a circle

= diameter squared X .7854

Convex surface of a cylinder

- circumference X height

Convex surface of a sphere

= circumference X diameter

Contents of a rectangular solid

= area of base X height

Contents of a cylinder

=area of base circle X height

Contents of a sphere

= cube of diameter X .5236

One side of square having same area as given circle

diameter X .8862 or circumference X .2821

Conversion Factors

Inches

X 0.08333

=feet

Square inches

X 0.00695

=sq. feet

Cubic inches

X 0.00058

=cu. feet

Cubic inches

X 0.004329

=U. S. gallons

Cubic feet

X 1728

=cu. inches

Cubic yards

X 27

=cu. feet

U. S. gallons of water X 8.33

= pounds

U. S. gallons of water X 231.00

= cu. inches

Pounds of water

X 27.72

= cu. inches

Ounces of water

X 1.735

= cu. inches

Circular Areas And Circumferences

DlAMETER

Area

CIRCUMFERENCE

DIAMETER

Abba

CIRCUMFERENCE

DlAMETER

Abba

Circumference

DlAMETER

Abba

Circumference

1/2

0.0123

.3926

10

78.54

31.41

80

706.86

94.24

65

3318.3

204.2

1/2

0.0491

.7854

i

86.59

32.98

31

754.76

97.38

66

3421.2

207.3

0.1104

1.178

11

95 Q3

84.55

32

804.24

100.5

67

3525.6

210.4

0.1963

1.570

1/2

103.86

36.12

33

855.30

103.6

68

3631.6

213.6

0.3067

1.963

12

113.09

37.69

84

907.92

106.8

69

3739.2

216 7

0.4417

2.356

1/3

122.71

39.27

35

962.11

109.9

70

3848.4

219 9

1

0.6013

2.748

13

132.73

40.85

36

1017.8

113.0

71

3959.2

223 0

1

0.7854

3.141

1/2

143.13

42.41

37

1075.2

116.2

72

4071.5

226.1

;

0.9940

3.534

14

153.93

43.98

38

1134.1

119.3

73

4185.3

229.3

1

1.227

3.927

1/2

165.13

45.55

39

1194.5

122.5

74

4300.8

232 4

1.484

4.319

15

176.71

47.12

40

1256.6

125.6

75

4417.8

235 6

1.767

4.713

J

188.69

48 69

41

1320.2

128.8

76

4536.4

238.7

2.078

5.105

16

201 06

50.26

42

1385.4

131.9

77

4656.0

241.9

2.405

5.497

1/2

213.82

51.83

43

1452.2

135.0

78

4778.3

245.0

2.761

5.890

17

226.98

53.40

44

1520.5

138.2

79

4901.6

248.1

2

3.141

6.283

*

240.52

54.97

45

1590.4

141.3

80

5026.5

251.3

1/4

3.976

7.068

18

254 46

56.54

46

1661.9

144.5

81

5153.0

254.4

4.908

7.854

i

268.80

58.11

47

1734.9

147.6

82

5281.0

257.6

5.939

8.639

19

283.52

59.69

48

1809.5

150.7

83

5410.6

260.7

3

7.068

9.424

1/2

298.64

61.26

49

1885.7

153.9

84

5541.7

263 8

1/2

8.295

10.21

20

314.16

62.83

50

1963.5

157.0

85

5674.5

267.0

9.621

10.99

i

330.06

64.40

51

2042.8

160 2

86

5808.8

270.1

11.044

11.78

21

346 36

65.97

52

2123.7

163.3

87

5944.6

273.3

4

12.566

12.56

1

363.05

67.54

53

2206.1

166.5

88

6082.1

276.4

1/2

15.904

14.13

22

380.13

69.11

54

2290.2

169.6

89

6221.1

270 6

5

19.635

15.70

*

397.60

70.68

55

2375.8

172.7

90

6361.7

282.7

1/2

23.758

17.27

23

415.47

72.25

56

2463.0

175.9

91

6503.8

285.8

6

28.274

18.84

i

433.73

73.82

57

2551.7

179.0

92

6647.6

289.0

1/3

33.183

20.42

24

452.39

75.39

58

2642.0

182.2

93

6792.9

292.1

7

38.484

21.99

1/2

471.43

76.96

59

2733.9

185.3

94

6939.7

295.3

1/2

44.178

23.56

25

490.87

78.54

60

2827.4

188.4

95

7088.2

298.4

8

50.265

25 13

26

530 93

81.68

61

2922.4

191.6

96

7238.2

301.5

1/2

56.745

26 70

27

572.55

84.82

62

3019.0

194.7

97

7389.8

304.7

9

63.617

28 27

28

615.75

87.96

63

3117.2

197.9

98

7542.9

307 8

1/2

70.882

29.84

29

660.52

91.10

64

3216.9

201.0

99

7697.7

311.0

Weight Calculation

Weight of round iron per foot = Diameter (quarter inches) squared X 0.1666 Weight of flat iron per foot = Width X thickness X 3.333 Weight of plates per sq. ft. =5 pounds for each J inch in thickness Weight of chain = Diameter squared X 10.7 (approximate).

Safe load (pounds) for chain = Bar diameter (quarter inches) squared X 2000.

To compute weight of metal from weight of pattern, with no allowance lor cores or runners, multiply as follows:

Multiplication Factors

White Pine

Mahogany

Result

16.7

10 7

Cast iron

18

12 2

Brass

23

15.

Lead

15

9.

Tin

16

10.4

Zinc

Weight of brass pattern X .9 = weight of iron casting, approximately,

Specific Gravities And Weights Of Metals

Material

Specific Gravity

Weight per

Cubic Inch

(pounds)

Water, at 39.1° F.

1.

.036

Aluminum

2.6

.094

Antimony, cast 6.64 to 6.74

6.7

.237

Bismuth

9.74

.352

Brass, cast 7.8 to 8.4

8.1

.30

Bronze 8.4 to 8.6

8.5

.305

Copper, cast 8.6 to 8.8

8.7

.32

Gold, pure, 24 carat

19.25

.70

Iron, cast 6.9 to 7.4

7.21

.263

Iron,wrought 7.6 to 7.9

7.77

.281

Lead................

11.4

.41

Mercury, at 60° F.

13.58

.49

Platinum 21. to 22.

21.5

.775

Silver

10.5

.386

Steel, average

7.8

.283

Spelter or zinc 6.8 to 7.2

7.

.26

Tin, cast 7.2 to 7.5

7.35

.262

Pressure In Molds

Depth

Pounds

(ft.

(in).

(per sq. in).

1

.26

2

.52

3

.78

4

1.04

5

1.30

6

1.56

7

1.82

8

2.08

9

2.34

10

2.60

11

2.86

1

00

3.12

13

3.38

14

3.64

15

3.90

16

4.16

17

4.42

1

6

4.68

Depth

Pounds

(ft).

(in).

(per sq. in).

19

4 94

20

5.20

21

5.46

22

5.72

23

5.98

2

00

6.24

25

6.50

26

6.76

27

7.02

28

7.28

29

7.54

2

6

7.80

31

8.06

32

8.32

33

8.58

34

8.84

35

9.10

3

00

9.36

Depth

Pounds

(ft).

(in).

(per sq. in).

3

6

10.92

4

12.48

4

6

14.04

5

15.60

5

6

17.16

6

18.72

6

6

20.28

7

21.84

7

6

23.40

8

24.96

8

6

26.52

9

28.08

9

6

29.64

10

31.20

10

6

32.76

11

34.32

11

6

35.88

12

37.44

To find the total lifting pressure on the cope, multiply the pressure per square inch at a given depth below the pouring basin by the area (square inches) of the surface acted against. The result is in pounds.

Temperatures

Connection

Heat

(Degrees

Fahrenheit)

Core ovens

250 to 450

Bright iron becomes

yellow

435

purple

500

indigo

550

gray

750

Tin melts

445

Mercury boils

660

Lead melts

612

Zinc melts

775

Silver melts

1775

Copper melts

1885

Gold melts

1900

Iron bar red in

a dark room, just visible

950

ordinary office

1075

daylight, open air

1450

Cast iron melts

white

2075

gray

2230

Steel melts

2750

Annealing malleable iron

1600 to 1750

*From late scientific investigations.