Part 42

It is evident, however, that round objects can also be shown in linear perspective, placing reference lines on the object and representing these as if they were real lines. A cylinder is thus shown in fig. 313 of which the end planes will appear very distinctly in sharp outlines.

Vertically, only the outlines of the cylinder, as contrasted against space, will appear as distinct outlines, while the reference lines will not appear and are therefore shown only as dotted lines.

Fig. 314 shows the approximate or scale perspective with all the axes drawn and the corresponding angles and scales marked. The outlines of the object running in these directions appear all parallel to the axes.

The approximate or scale perspective completely avoids all the difficulties of choosing a point of sight, of having several views, vanishing points and measurement points, and thus offers a representative view, with a great saving of time and labor. Particularly for mechanical purposes, where an artistic impression is not called for, it presents a distinct advantage over the true or real perspective.

AND

INDEX]

Useful Tables for Draughtsmen.

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.