Useful Tables for Draughtsmen.
Reading edition
TABLE OF DECIMAL EQUIVALENTS. 8ths, 16ths, 32ds and 64ths of an Inch.
8ths.
1⁄8 = .125
1⁄4 = .250
3⁄8 = .375
1⁄2 = .500
5⁄8 = .625
3⁄4 = .750
7⁄8 = .875
16ths.
1⁄16 = .0625
3⁄16 = .1875
5⁄16 = .3125
7⁄16 = .4375
9⁄16 = .5625
11⁄16 = .6875
13⁄16 = .8125
15⁄16 = .9375
32nds.
1⁄32 = .03125
3⁄32 = .09375
5⁄32 = .15625
7⁄32 = .21875
9⁄32 = .28125
11⁄32 = .34375
13⁄32 = .40625
15⁄32 = .46875
17⁄32 = .53125
19⁄32 = .59375
21⁄32 = .65625
23⁄32 = .71875
25⁄32 = .78125
27⁄32 = .84375
29⁄32 = .90625
31⁄32 = .96875
64ths.
1⁄64 = .015625
3⁄64 = .046875
5⁄64 = .078125
7⁄64 = .109375
9⁄64 = .140625
11⁄64 = .171875
13⁄64 = .203125
15⁄64 = .234375
17⁄64 = .265625
19⁄64 = .296875
21⁄64 = .328125
23⁄64 = .359375
25⁄64 = .390625
27⁄64 = .421875
29⁄64 = .453125
31⁄64 = .484375
33⁄64 = .515625
35⁄64 = .546875
37⁄64 = .578125
39⁄64 = .609375
41⁄64 = .640625
43⁄64 = .671875
45⁄64 = .703125
47⁄64 = .734375
49⁄64 = .765625
51⁄64 = .796875
53⁄64 = .828125
55⁄64 = .859375
57⁄64 = .890625
59⁄64 = .921875
61⁄64 = .953125
63⁄64 = .984375
TABLE OF DECIMAL EQUIVALENTS Of Millimeters and Fractions of Millimeters.
mm. Inches.
1⁄50 = .00079
2⁄50 = .00157
3⁄50 = .00236
4⁄50 = .00315
5⁄50 = .00394
6⁄50 = .00472
7⁄50 = .00551
8⁄50 = .00630
9⁄50 = .00709
10⁄50 = .00787
11⁄50 = .00866
12⁄50 = .00945
13⁄50 = .01024
14⁄50 = .01102
15⁄50 = .01181
16⁄50 = .01260
17⁄50 = .01339
18⁄50 = .01417
19⁄50 = .01496
20⁄50 = .01575
21⁄50 = .01654
22⁄50 = .01732
23⁄50 = .01811
24⁄50 = .01890
25⁄50 = .01969
26⁄50 = .02047
27⁄50 = .02126
28⁄50 = .02205
29⁄50 = .02283
30⁄50 = .02362
31⁄50 = .02441
32⁄50 = .02520
33⁄50 = .02598
34⁄50 = .02677
35⁄50 = .02756
36⁄50 = .02835
37⁄50 = .02913
38⁄50 = .02992
39⁄50 = .03071
40⁄50 = .03150
41⁄50 = .03228
42⁄50 = .03307
43⁄50 = .03386
44⁄50 = .03465
45⁄50 = .03543
46⁄50 = .03622
47⁄50 = .03701
48⁄50 = .03780
49⁄50 = .03858
1 = .03937
2 = .07874
3 = .11811
4 = .15748
5 = .19685
6 = .23622
7 = .27559
8 = .31496
9 = .35433
10 = .39370
11 = .43307
12 = .47244
13 = .51181
14 = .55118
15 = .59055
16 = .62992
17 = .66929
18 = .70866
19 = .74803
20 = .78740
21 = .82677
22 = .86614
23 = .90551
24 = .94488
25 = .98425
26 = 1.02362
10 mm. = 1 Centimeter = 0.3937 inches.
10 cm. = 1 Decimeter = 3.937 „
10 dm. = 1 Meter = 39.37 „
25.4 mm. = 1 English Inch.
RULES RELATIVE TO THE CIRCLE.
The circle contains a greater area than any other plane figure bounded by an equal perimeter or outline.
TO FIND CIRCUMFERENCE—
Multiply diameter by 3.1416.
Or divide diameter by 0.3183.
TO FIND DIAMETER—
Multiply circumference by 0.3183.
Or divide circumference by 3.1416.
TO FIND RADIUS—
Multiply circumference by 0.15915.
Or divide circumference by 6.28318.
TO FIND SIDE OF AN INSCRIBED SQUARE—
Multiply diameter by 0.7071.
Or multiply circumference by 0.2251.
Or divide circumference by 4.4428.
TO FIND SIDE OF AN EQUAL SQUARE—
Multiply diameter by 0.8862.
Or divide diameter by 1.1284.
Or multiply circumference by 0.2821.
Or divide circumference by 3.545.
SQUARE—
A side multiplied by 1.4142 equals diameter of its circumscribing circle.
A side multiplied by 4.443 equals circumference of its circumscribing circle.
A side multiplied by 1.128 equals diameter } of an equal circle.
A side multiplied by 3.545 equals circumference
A side multiplied by 1.273 equals circle inches
TO FIND THE AREA OF A CIRCLE—
Multiply circumference by one-quarter of the diameter.
Or multiply the square of diameter by 0.7854.
Or multiply the square of circumference by .07958.
Or multiply the square of 1⁄2 diameter by 3.1416.
Contents of cylinder = area of end × length. Contents of wedge = area of base × 1⁄2 altitude. Surface of cylinder = area of both ends × length × circumference. Surface of sphere = diameter squared × 3.1416, or = diameter × circumference. Contents of sphere = diameter cubed × .5236. Contents of pyramid or cone, right or oblique, regular or irregular = area of base × 1⁄3 altitude. Area of triangle = base × 1⁄2 altitude. Area of parallelogram = base × altitude. Area of trapezoid = altitude × 1⁄2 the sum of parallel sides.
ROMAN TABLE.
I. denotes One.
II. „ Two.
III. „ Three.
IV. „ Four.
V. „ Five.
VI. „ Six.
VII. „ Seven.
VIII. „ Eight.
IX. „ Nine.
X. „ Ten.
XI. „ Eleven.
XII. „ Twelve.
XIII. „ Thirteen.
XIV. „ Fourteen.
XV. „ Fifteen.
XVI. „ Sixteen.
XVII. „ Seventeen.
XVIII. „ Eighteen.
XIX. „ Nineteen.
XX. „ Twenty.
XXX. „ Thirty.
XL. „ Forty.
L. „ Fifty.
LX. „ Sixty.
LXX. „ Seventy.
LXXX. „ Eighty.
XC. „ Ninety.
C. „ One hundred.
D. „ Five hundred.
M. „ One thousand.
X̅. „ Ten thousand.
M̅. „ One million.
SOLID MEASURE, OR CUBIC MEASURE.
This is used in measuring bodies, or things having length, breadth and height or depth.
TABLE.
1728 cubic inches (cu. in.) make 1 cubic foot (cu. ft.).
27 cubic feet, „ 1 cubic yard (cu. yd.).
128 cubic feet, „ 1 cord (C.).
CIRCULAR MEASURE.
60 seconds (″) make 1 minute (′).
60 minutes „ 1 degree (°).
360 degrees „ 1 circum. (C.).
The circumference of every circle whatever, is supposed to be divided into 360 equal parts, called degrees.
A degree is 1⁄360 of the circumference of any circle, small or large.
A quadrant is a fourth of a circumference, or an arc of 90 degrees.
A degree is divided into 60 parts called minutes, expressed by the sign (′), and each minute is divided into 60 seconds, expressed by (″); so that the circumference of any circle contains 21,600 minutes, or 1,296,000 seconds.
LONG MEASURE—MEASURES OF LENGTH.
12 inches = 1 foot.
3 feet = 1 yard.
5 1⁄2 yards = 1 rod.
40 rods = 1 furlong.
8 furlongs = 1 common mile.
3 miles = 1 league.
The mile (5,280 feet) of the above table is the legal mile of the United States and England, and is called the statute mile.