APPENDICES
APPENDIX A
SOME USEFUL MATHEMATICAL FORMULAS
| π = 3.14159 (π is a Greek letter pronounced Pi) |
| d = diameter of a circle |
| r = radius of a circle |
| p = periphery, or circumference of a circle |
| The area of a circle = πr² |
| The circumference of a circle = πd |
| The diameter of a circle | = | p | = | p |
| π | 3.14 |
| The radius of a circle | = | p | = | p |
| 2π | 6.28 |
| The surface of a sphere = 4πr² = πd² |
| The volume of a sphere | = | 4 | πr³ | = | 1 | πd³ |
| 3 | 6 |
APPENDIX B
THE METRIC OR DECIMAL SYSTEM
The metric system is a French system of weights and measures much used in the arts and sciences in every civilized country and as each unit is multiplied or divided by 10 to obtain ascending or descending values it is much more convenient to use than the older English system of arbitrary measures.
The metric system is based on the meter, which is one-ten millionth of the distance from the Earth’s equator to the North Pole. There are five units, the four latter being derived from the meter and these are:
1. The meter which is the unit of length and is about 3.280 feet in length.
2. The are which is the unit of surface and is 100 square meters in area.
3. The liter which is the unit of capacity and is 1 cubic decimeter, which is equal to 1.0567 United States quarts.
4. The stere which is the unit of solidity and is equal to 1 cubic meter.
5. The gram is the unit of weight and is the weight of 1 cubic centimeter of distilled water at its maxim density.
APPENDIX C
METRIC MEASURES OF LENGTH AND VALUES IN INCHES
| Divisions | Millimeter | (mm) | = | 0.001 m. | = | 0.03937 inch |
| Centimeter | (cm) | = | 0.01 m. | = | 0.3937 inch | |
| Decimeter | (dm) | = | 0.1 m. | = | 3.937 inches | |
| Unit Meter | (m) | = | 1. m. | = | 39.37 inches | |
| Multiples | Dekameter | (Dm) | = | 10. m. | = | 393.7 inches |
| Hektometer | (Hm) | = | 100. m. | = | 328. feet and 1 inch | |
| Kilometer | (Km) | = | 1,000. m. | = | 0.62326 mile | |
| Myriameter | (Mm) | = | 10,000. m. | = | 6.2326 miles | |
APPENDIX D
METRIC MEASURES OF WEIGHT AND VALUES IN ENGLISH WEIGHT
| Divisions | Milligram | (mg) | = | 0.001 g | = | 0.0154 grain | avoirdupois |
| Centigram | (cg) | = | 0.01 g | = | 0.1543 grain | “ | |
| Decigram | (dg) | = | 0.1 g | = | 1.5432 grain | “ | |
| Unit Gram | (g) | = | 1 g | = | 15.432 grains | “ | |
| Multiples | Dekagram | (Dg) | = | 10 g | = | 0.3527 ounce | “ |
| Hektogram | (Hg) | = | 100 g | = | 3.5274 ounces | “ | |
| Kilogram | (Kg) | = | 1,000 g | = | 2.2046 pounds | “ | |
| Myriagram | (Mg) | = | 10,000 g | = | 22.046 pounds | “ | |
APPENDIX E
TO CHANGE METRIC TO ENGLISH MEASURE AND VICE VERSA
| To Change | To | Multiply by |
|---|---|---|
| Inches | Centimeters | 2.54 |
| Feet | Meters | 0.3048 |
| Miles | Kilometers | 1.6093 |
| Square Inches | Square Centimeters | 6.4516 |
| Square Feet | Square Meters | 0.0929 |
| Square Yards | Square Meters | 0.8361 |
| Cubic Inches | Cubic Centimeters | 16.3872 |
| Cubic yards | Cubic Meters | 0.7646 |
| Fluid ounces | Cubic Centimeters | 29.574 |
| Quarts | Liters | 0.9464 |
| Ounces (avoirdupois) | Grams | 28.3495 |
| Grains | Milligrams | 64.789 |
| Pounds (avoirdupois) | Kilograms | 0.4536 |
| Meters | Inches | 39.37 |
| Meters | Feet | 3.2808 |
| Kilometers | Miles | 0.6213 |
| Square Centimeters | Square Inches | 0.155 |
| Square Meters | Square Yards | 1.196 |
| Cubic Centimeters | Cubic Inches | 0.0610 |
| Cubic Meters | Cubic Yards | 1.308 |
| Cubic Centimeters | Fluid Ounces | 0.0344 |
| Liters | Quarts | 1.0567 |
| Grams | Grains | 15.4324 |
| Kilograms | Pounds | 2.204 |
APPENDIX F
SIZES OF TWIST DRILLS FOR TAPS OR SCREWS
| No. of Drill | No. of Tap or Screw | No. of Threads to the Inch | |||
|---|---|---|---|---|---|
| Use | 38 | for | 4 | — | 36 |
| “ | 32 | “ | 6 | — | 32 |
| “ | 28 | “ | 8 | — | 32 |
| “ | 22 | “ | 10 | — | 24 |
| “ | 13 | “ | 12 | — | 24 |
APPENDIX G
SIZES OF TAPS AND DIES
| No. of Tap or Die | Threads to Inch |
|---|---|
| 4 | 36 |
| 6 | 32 |
| 8 | 32 |
| 10 | 24 |
| 12 | 24 |
APPENDIX H
SIZES OF MACHINE SCREWS AND NUTS
Machine screws and nuts are numbered the same as dies and taps.
APPENDIX I
REDUCING FRICTION
When two bodies are rubbed together the motion is opposed by a force called friction. When two surfaces slide against each other the friction between them is proportional to the force pressing them together. The amount of friction depends upon the pressure of the bodies, the roughness of their surfaces and also slightly on their adhesion. The friction is the same regardless of the speed with which the surfaces slide over each other.
The co-efficient of friction is the measure of friction and this is found by dividing the force of friction by the force pressing the surfaces together. Here are a few co-efficients of sliding friction:
| Per cent. | |
|---|---|
| Oak on Oak with Fibers parallel without lubricant | 0.42 |
| Oak on Oak with Fibers parallel rubbed with soap | 0.16 |
| Cast Iron on Oak | 0.42 |
| Cast Iron on Cast Iron, not lubricated | 0.15 |
| Cast Iron on Cast Iron, lubricated | 0.10 |
| Iron on Brass | 0.16 |
| Brass on Brass | 0.20 |
| Iron on Bronze, without lubricant | 0.25 |
| Iron on Bronze, thoroughly lubricated | 0.06 |
| Cast Iron Wheels on Rails (Rolling Friction) | 0.004 |
| Ball Bearings (Rolling Friction) | 0.001 |
APPENDIX J
WEIGHT OF CASTINGS COMPARED WITH WOOD PATTERNS
The following table shows what the weight of a casting will be compared with the weight of the wood pattern from which it was made, less the weight of the core point, or piece projecting from the pattern to support it.
| A Wood Pattern Weighing One Pound | Will Make a Casting Weighing | ||||
|---|---|---|---|---|---|
| Pattern of | Cast Iron Pounds | Brass Pounds | Copper Pounds | Bronze Pounds | Zinc Pounds |
| Pine | 14 | 15.8 | 16.7 | 16.3 | 13.5 |
| Beech | 9.7 | 10.9 | 11.4 | 11.3 | 9.1 |
| Oak | 9 | 10.1 | 10.4 | 10.3 | 12.9 |
| Birch | 10.6 | 11.9 | 12.3 | 12.2 | 10.2 |
| Mahogany | 11.7 | 13.2 | 13.7 | 13.5 | 11.2 |
| Brass | 0.84 | 0.95 | 0.99 | 0.98 | 0.81 |
APPENDIX K
GEARS AND GEARINGS
A spur-gear is a gear with teeth cut on its periphery, that is an ordinary cog-wheel. Miter gears are two bevel gears of the same diameter which run together. A large miter gear will not mesh with a small miter gear nor with another bevel gear in the proper manner. Miter and bevel gears cannot be interchanged with other sets like spur gears.
Fig. 129. CROSS SECTION OF GEAR
All miter gears that you buy ready cut are made so that their shafts run at right angles to each other as shown in Fig. 129, but you can have them cut to order to run at any angle you want.
To find the pitch, pitch diameter, circular pitch, etc., of both spur and bevel gears use these rules:
- π = 3.14159
- p = pitch
- n = number of teeth
- pd = pitch diameter
- od = outside diameter
- cp = circular pitch
To Find the Pitch:
| p | = | n |
| pd |
To Find the Number of Teeth:
| n = p × pd |
To Find the Pitch Diameter:
| pd | = | n |
| p |
To Find the Outside Diameter of Spur Wheels:
| od | = | (2 + n) |
| p |
To Find the Circular Pitch:
| cp | = | π |
| pd |
To Find the Distance Between the Centers of Two Spur Gears:
| (n¹ + n²) |
| 2 |
| p |
Where n¹ + n² = the sum of the teeth of both gears.
APPENDIX L
SOME USEFUL ALLOYS
| Name of Alloy | Parts of Copper | Parts of Tin | Parts of Zinc | Parts of Lead | Parts of Other Metals |
|---|---|---|---|---|---|
| Gun Metal | 91 | 9 | |||
| Bell Metal | 75 | 25 | |||
| Phosphor Bronze | 92½ | 7 | ½ phosphorus | ||
| Aluminum Bronze | 90 | 10 aluminum | |||
| Common Brass | 66⅔ | 33⅓ | |||
| Brazing Metal (soft) | 50 | 12½ | 37½ | ||
| German Silver | 60 | 20 | 20 nickel | ||
| Common Solder | 50 | 50 | |||
| Fine Solder | 66⅔ | 33⅓ | |||
| Babbitt Metal | 3 | 89 | 8 antimony | ||
| Pewter | 80 | 20 | |||
| Type Metal | 80 | 20 antimony | |||
| Aluminum Solder | 95 | 5 bismuth |
Magnetic Alloy.—An alloy that has strong magnetic properties is made of 25 parts of manganese, 14 parts of aluminum and 61 parts of copper, yet none of these metals are even slightly magnetic.
APPENDIX M
SOME HARD SOLDERS
Hard solders melt only at red heat and are used for soldering gold, silver, brass and other metals where a good strong joint is needed.
| Metal to be Soldered | Parts of Gold | Parts of Brass | Parts of Silver | Parts of Zinc | Parts of Other Metals |
|---|---|---|---|---|---|
| Gold | 66.67 | 22.22 | 11.11 copper | ||
| Silver | 43.75 | 50 | 6.25 | ||
| Brass | 87.5 | 12.5 |
APPENDIX N
HIGH SPEED STEEL
A special steel alloy which is largely used for turning tools in engine lathes and which will cut ordinary steel when the latter is revolved at a high surface velocity is called high speed steel. A tool made of high speed steel will not lose its temper and will keep its cutting edge hour after hour if they are kept cool by a stream of water running on them. A good high speed steel for machine tools is known by the trade name of blue-chip and is manufactured by the Firth-Sterling Steel Company of Pittsburg, Pa.