~. Punmps.

Bolen, Crane & Co... ............ Newark,.N. J..................See Page 62 C. Henry Hall & Co.................. e e o e o os e e o is s to go to e o 'o to to 9 New York................... to to e $6 4 Charles B. Hardick Brooklyn, N.Y.............. to {{ 84 Hart, Ball & Hart Buffalo, N. Y.................. “ 136 J. B. Waring................................................ New York ...................... {{ 24 J. D. West & Co...... to e o e o e {{ “ ..... ............... {& 56 J. J. Walworth................................. to o e o e o 'o e g g g s Chicago, Ill................... {{ T24 J. S. Mundy w Newark, N. J.................. {{ 266 Miller. & Smith w .......New York........... * * * * * * * * to o e {{ 112 Posts & Kalkman......................... • . . . . . . . . . . . . . . . . { % “ ..................... • & 266 Speedwell Iron Works {{ “ ..................... {{ 122

Punches and Shears. Isaac H. Shearman....................................... Philadelphia, Pa............. See Page 80 L. W. Pond........................... ....................... Worcester, Mass............ e $6 158

Punching and Shearing Machines. Wm. Sellers & Co * * e o e o so o e o 'o e o 'o to e o se e g o e a g Philadelphia, Pa.............See Page 64 Wm. B. Bement & Son “. ..... • * * * * * * & & 4 168 Putty.

D. R. Hobart & Co * * * * * New York...................... See Page 126 Leffingwell & Co........................................... Cleveland, Ohio............ * & so “ 190

MEASURES.–CONTINUED.

ALE AND BEER MEASURE. (British). pints

The Standard Bushel contains 2150.42 cubic inches, or 77.627013 pounds avoirdupois of pure water at maximum density. Its legal dimensions are 18% inches Diameter inside, 19% inches cutside, and 8 inches deep ; and when leaped, the cone must be 6 inches high, making a heaped bushel equal to 1% struck ones.

Pints. Quarts. Gallons. Pecks. Bushels. Cubic Inches.
2 1 • ? - ? &

LIQUID Measure.

The standard gallon measures 231 cubic inches, or 8.33888 lbs. avoirdt pois of pure water, at about 39.85 degrees Fahr., the barometer at 30 inches.

Cylinders of the following sizes are closely approximating In 68SlıI'êS.

Height, Diameter, Height, Diameter,

inches. inches. - inches. inches. Gill............. • - - - - - - - - 3 ...... 1% | Quart..................... 6 ...... 3% % pint.................. 3% ...... 2% Gallon.............. ... .. 6 ...... 7 Pint...................... 3 ...... 3% 10 gallons............... 15 ...... 14

A cubic foot contains 7% gallons,

OOP Y/NG PAP E S S E S A S P E O / A / 7. Y.

. The Arch is of Steez. the Bed Plate is braced by out Patented Method, É. very got strength ; and all the parts are of proportions to bear the eaviest work in copying large Way BILLs, MANIFESTs, &c.

Address

T. SHRIVER & CO.,
333 East 56th Street, New York.

Quarry Tools.

Nelson Tool Works....................................... New York....................... See Page 30
. Railroad Baggage Checks.
W. W. Wilcox ... • . . . . . . . . . . . . . . . . . . . . . Chicago, Ill............... .....See Page 190
Railroad Bonds or Securities.
Geo. H. Crain & Co............. to e e o e o e o os e e o e o 'o e o so to .......Chicago, Ill....... * @ e o & s to t e o 'o o o See Page 124
O. W. Child.................................................. New York...................... { % 266
Railroad Car Forgings.
De Laney & Co.......................... to e e o e o & 9 o' to e o t e g o e o g Buffalo, N.Y..................See Page 98
Pittsburgh Forge & Iron Co...... e & e < e < e < e < e < e < * * * * * * * Pittsburgh, Pa............... { % 1.
Railroad Castings.
Bowlers, Maher & Brayton............................. Cleveland, Ohio............... See Page 42
Davenport, Fairbairn & Co............................. Erie, Pa......................... & 4 188
Jonas S. Heartt & Co..................................... Troy, N. Y..................... { { 134
Ramapo Wheel & Foundry Co....................... Ramapo, N. Y................. • & 6 256
Wason Manufucturing Co.............................. Springfield, Mass............ § { 146
- Railroad Chairs.
Pittsburgh Bolt Co............... ....................... Pittsburgh, Pa............... See Page 118
MENSURATION.—2 PAGES.
(From Hamilton.)
MENSURATION OF SURFACES.
Area of any parallelogram................. = base X perpendicular height.
Area of any triangle............ * * * * * * c e o s e e o g = base X % perpendicular height.
Area of any circle.............................. = diameter 2 × .7854. -
Area of sector of circle..................... = arc X % radius.
Area of segment of circle.................. = area of sector of equal radius, less area of
~. triangle.
Area of parabola............... * * * * * * * * * g e g g g ge = base X 2–3 height.
Area of ellipse.................................. = longest diameter X shortest diameter X
. * .7854.
Area of Cycloid......... ...................... = area of generating circle X 3. -
Area of any regular polygon............. = sum of its sides × perpendicular from its
centre to one of its sides -- 2.
Surface of cylinder............................ = area of both ends –- length X circum-
ference.
Surface of cone........ * * * * * * * * * * * * * g e e s e s e o e o a s = area of base + circum erence of base X %
- - slant height.
Surface of sphere...... * * * s is e s = e o e e is a e s = e e o e g o e = diameter2 × 3.1415.
Surface of frustrum........................... = sum of girt at both ends X % slant height
-- - area of both ends.
Surface of cylindrical ring...... to & G s e o e o e o e = thickness of ring added to the inner dia-
- meter X by the thickness X 9.86 8.
Surface of segment........................... = height of segment X whole circumference

of sphere of which it is a part.

POLYGONS.

1. To find the area of any regular said square by the number in 1st colur

polygon. Square one of its sides, and multiply mn of the following table.

2. Having a side of a regular polygon, to find the radius of a circumscribing

circle. Multiply the side by the corre 3. Having the radius (f a circums regular polygon. Multiply the radius

Number
Of Name of Polygon.
Sides.
3 ... Equilateral triangle
4 ... Square....................
5 ... Pentagon.................
6 ... Hexagon.................
7 ... Heptagon..............
8 ... Octagon ..................
9 ... Nonagon. ...............
10 ... Decagon..................
11 ... Undecagon.............. to
12 ... Dodecagon............. e

In the heads of the columns in above table

sponding number in the 2d column.
cribing circle, to find the side of the inscribed
by the corresponding number in 3d column.
2

3 Angle con

, S = side, and R = Radius,

OF ALL SIZES AND STYLES, suit ABLE For
Railroads, Heavy Manufacturers and Others.

ALSO,
TRUCKS OF ALL VARIETIES,
BACCACE AND EXPRESS BARROWS,

FIRE AND BURCLER PROOF SAFES and VAULT WORK.

W. A. DoEIN solo & Co. sé MAIN STREET, BUFFALo, N.Y.,

- - - - MANUFACTURERS’ AGENTS FOR Western New York, North Western Pennsylvania, Ohio and Ontarios Railroad Colors and Varnishese

Edward Smith & Co....................................... New York......, See Page 218 Railroad Engine Forgings.

De Laney & Co.............. Buffalo, N. Y.................. See Page 98

Pittsburgh Forge & Iron Co Pittsburgh, Pa............ to e e “ 174

MENSURATION.—CONTINUED.
PROPERTIES OF THE CIRCLE.

Diameter × 3.14159 = circumference.
Diameter × .8862 = side of an equal square.
Diameter × .7071 = side of an inscribed square.
Diameter2 × .7854 = area of circle.

Radius X 6.28318 = circumference.
Circumference + 3.14159 = diameter.

The circle contains a greater area than any plane figure, bounded by an equal perimeter or outline. The areas of circles are to each other as the squares of their diameters. Any circle whose diameter is double that of another contains four times the area of the other. Area of a circle is equal to the area of a triangle whose base equals the circumference, and perpendicular equals the radius.

MENSURATION OF SOLIDS.

Cylinder........................................... = area of one end X length.
Sphere s • a se e a es e e s e o se see ee e s = cube of diameter × .5236.
Segment of sphere............................. = square root of the height added to three

times the square of radius of base X by height and by .5236.

Cone or pyramid = area of base X 1–3 perpendicular height. Frustrum of a cone . = product of diameter of both ends + sum - of their squares, X perpendicular height × .2618. Frustrum of a pyramid...................... = sum of the areas of the two ends –- square root of their product, X by 1-3 of the perpendicular height. Solidity of a wedge = area of base X % perpendicular height. Frustrum of a wedge = % perpendicular height X sum of the - areas of the two ends. Solidity of a ring............................... = thickness + inner diameter, X square of the thickness, X 2.4674. POLYHEDRONS. 1. 2 3 4. Radius of Radius of * * e e Area of Cubic No. of Circumscribed Inscribed sides. Name. Circle. Circle. Surface. Contents. R = SX . R = SX A = S2X C = S3× 4 ... Tetrahedron...... .6124 ...... .2041 ...... 1.7320 ...... .1178 6 ... Hexahedron...... .866 * * * * * * .5 ...... 6. ...... 1. 8 ... Octahedron........ .7071 ...... .4082 ..... . 3.4641 ...... .4714 12 ... Dodecahedron.... 1.4012 ...... 1.1135 ...... 20.6458 ...... 7.6631 20 ... Icosahedron...... .951 ...... .7558 ...... 8.6602 ...... 2.1817

Side is length of linear edge of any side of the figure. 1.—Radius of Circumscribed Circle = Side multiplied by the number in 1st column corresponding to figure. 3.—Radius of Inscribed Circle = Side multiplied by the number in 26 column corresponding to figure. 3.—Area of Surface = Square of side multiplied by the number in 3d column corresponding to figure. - 4.—Cubic Contents = Cube of side multiplied by number in 4th column corresponding to figure.