## 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 perCubic 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(DegreesFahrenheit) 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.