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Section.

Walls and foundations,

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Table-Kind of wood, spec. grav., both ends fixed and loaded in the

Falling bodies.

velocities,

middle. Breaking weight. Transverse strain,.
Formula for beams. Page 72в125,
Timber pillars, by RONDELET,

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HODGKINSON'S FORMULA for long square pillars,
BRERETON'S experiments on pine timber,
Safe load in structures,

Strength of cast-iron beams,

Strongest form, Fairbairn's form,

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Calculate the strength of a truss-beam,

To calculate a common roof,

Angles of roofs,

Beams, wrought-iron,--box.

GORDON'S RULES for cast-iron pillars,
Depth of foundations,

Walls of buildings,

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Parallelogram of forces. Polygon of do.,

Composition of motions. Page 72E.

Centre of gravity in a circle, square, triangle, trapezoid..
In a trapezium, cone or pyramid, frustrum of a, circular, sector,
semicircle, quadrant, circular ring,.

Of Solids.---Of triangular pyramid, a cone, conic frustrum, in any
polyhedron. Paraboloid, frustrum of a, prismoid, or ungula.
Spherical segment, .

310-12

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310x7

310x5

31018

310/20

310w4

.3.03

FORCE AND MOTION.

311

Theoretical and actual mean velocities of.

Virtual

312 and 319m

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Of a liquid, 316, body lighter than water, 318, of a powder soluble
in water,

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Table-Specific gravities of bodies. Weight one cubic foot in
pounds,

Table-Average bulk in cubic feet of one ton, 2240 pounds, of vari-
ous materials,
Table-Shrinkage or increase per cent. of materials,

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Mechanical powers, levers, pulleys, wheels, axles, inclined plans,
screws, with examples,

Virtual velocity,

FRICTION. COULOMB AND MORRINS' experiments coefficient of the
angle of repose,.

Table-Friction of plane surfaces sometime in contact,
Table-Friction of bodies in motion,

319a

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319a

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319

319% to 31927

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Friction of axles in motion,

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Work done by man and horse vertically, 319s
Actions on machines,

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319

ROADS AND STREETS.

Roman roads, Appian way, Roman military roads, Carthaginian,
Greek, and French roads,

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German, Belgium, Sweden, English, Irish, and Scotch roads,
Presentment for making and repairing roads,
Making or repairing MCADAMIZED ROADS,
Shrinkage allowance for.

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How the railroad was built over the Menomenee marsh near Mil-
waukee, Wisconsin,

.319v

RETAINING WALLS for roads. l'age 72111,

.3197

Parapet walls, drainage, drain holes, materials, sandstone, limestone.
Table-WALKER'S EXPERIMENTS on the durability of paving, . . . . . .319v
Stones in London, England, in A.D. 1830 and 1831. Seventeen
months,

..319v

Table of compression of materials in road making, etc. Page 72j13,.319~

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Section.

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Table and formulas of friction on roads. Page 72114,
McNeil's improved dynamometer. Page 72j14,
PONCELET'S VALUE of draught to overcome friction,
Table-Showing the lengths of horizontal lines, equal to ascending
and descending planes. Pressure of a load on an inclined plane.
Page 72j13.

Table-MORIN'S EXPERIMENTS. With examples. Page 72j16.
Table c-Laying out curves. Radius 700 feet to 10,560 feet radius,
by chords and their versed sines in feet, showing how to use them
in laying out curves of less radius than 700. Page 72j17.

CANALS AND EXCAVATIONS.

Page 72K. (See Sec. 421),

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To set out a section of a canal on a level surface,
To set out a section when the surface is inclined,
To find the embankment, and to set off the boundary of,
Area of section of excavation or embankment,
When the slope cuts the bottom of the canal,
Mean height of a given section whose area =
slopes r,

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When the slopes are the same on both sides,
When the slopes are unequal,

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320

321

321a

32 b

3211

332

A, base

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To find the content of an excavation or embankment. Page 72T,... 327
Prism, prismoid, cylinder, frustrum of a cone, pyramid frustrum of
a pyramid, prismoid, 334,...

327

BAKER'S method of laying out curves, and calculating, earth works,
do. modified. Page 72v,..

339

Tables for calculating earthwork deduced from BAKER, KELLY, and
SIR JOHN MCNEIL's tables. Page 72y to 72н*.

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To change circumferentor to quarter compass bearings,
Classification of land by Sir Richard Griffith,

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135

167

171e

218

309m

309

.30911

Scale for arable land,

Scale of prices for pasture, .

3090

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Table of produce,

One hundred statute acres under a live years' rotation. l'age 72B21.
Superior finishing land,.

Increase in valuation for its vicinity to towns,

Classification of buildings,

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Valuation of water-power, 310m, 310w,

Valuation of horse-power,

Page 72в40, 72в41, 72в42,

Form of field-book,.

Annual valuation of houses in the country, slated,.
Annual valuation of houses in the country, thatched,

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.310v

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Analysis of grains and straws, vegetables and legumes,
Analysis of ashes of miscellaneous articles,

.310F

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310G

Per centage value of manures for nitrogen and phosphoric acid,

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Value of the Vena contracta from various writers on hydraulics, . . . .310c*
Angles of convergance. Page 72в102.
Coefficients of discharge over weirs,
Coefficients of Blackwell's experiments,
Poncelet and Lebros' experiments.

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72B104,

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Value of discharge Q through various orifices,
Available power of water,

Retaining walls, by Poncelet,

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.310E*

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.310F*

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Specific gravities, breaking weight and traverse strains of beams.

supported at both ends, and loaded in the middle,

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Specific gravities of bodies,.

Average bulk in cubic feet per ton of 2240 pounds.

Shrinkage or increase per cent. of materials. Page 7211,.

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Walker's experiments on paving stones in a street in London,
Compression pounds avoirdupois required to crush a cube of one and

one-half inches. Page 72j13.

Table of uniform draught on given inclinations.

Page 72113.
Lengths of horizontal lines equal to ascending planes. Page 72115.
Morin's experiments with vehicles on roads. Page 72j16.
Table C-For laying out curves, chord A B = 200 feet, or links or any
multiple of either giving radius of the curve. Half the angle of

deflection the versed sine at one-half, the chord, or the versed sine
of the angle, also versed sine of one-half, one-fourth, and one-
eighth the angle. Page 72j17.
Table a-Calculating earthwork prismoids.
Table -Calculating earthwork prismoids.
Table c-Calculating earthwork prismoids.
Sundial. Table for latitudes 41°, 49°, 54°, 36′ 12°, 30′. Page 211*27, .390*
Levelling books, English and Irish Board of Works, method,

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Natural sines to every minute, five places of decimals from 1° to 90°.
Page 721* to 72R*.

Natural cosines as above. A guide line is at every five minutes.
Natural tangents and cotangents, same as for the sines. 72s* to 72B**.
The sines are separate from the cosine and tangents to avoid errors.
Both tables occupy twenty pages nicely arranged for use.
Traverse table, by McDermott, entirely original, calculated to the
nearest four places of decimals, and to every minute of degree in
the left hand column numbered from 1 at the top to 60 at the bot-
tom, at the top are 1 to 9 to answer for say 9 chains 90 chains,
90 links or 9 links. The latitudes on the left hand page, and de-
partures on the right hand page for 45 degrees, then 45 to 90 are
found at the bottom, contains 88 pages.

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Lengths of circular arcs obtained by having the chord and versed sine, 171
Areas of segments of circles whose diameter is unity,

173

To reduce square feet to acres and vice versâ,.
Table VIIIa. Properties of polygons whose sides are unity,.
Table IX. Properties of the five regular bodies,

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Table X. To reduce square links to acres,

Table XI.

ment,

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To reduce hypothenuse to base, or horizontal measure

Table XII. To reduce sidereal time to mean solar time,
Table XIII. To reduce mean solar time to sidereal time,
Table XIV. To reduce sidereal time to degrees of longitude,
Table XV. To reduce longitude to sidereal time,
Table XVI.

sea in miles

Table XVII.

Table XVIII.

Table XIX.

Table XX.

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Section

173

177

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178

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178

179

179

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Dip or depression of the horizon, and the distance at
corresponding to given heights, .

Correction of the apparent altitude for refraction,
Sun's parallax in altitude,

Parallax in altitude of the planets,

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Reduction of the time of the moon's passage over the

meridian of Greenwich to that over any other meridian,
Best time for obtaining apparent time,
Best altitude for obtaining true time,

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Table XXI.
Table XXII.
Table XXIII. Polar tables, azimuths or bearings of stars in the
Northern and Southern hemispheres when at their greatest elonga-
tions from the meridian for every one-half a degree of latitude, and
from one degree to latitude 70°, and for polar distances 0', 40′, 0 45,
0′50′, 0°55′, 10, 15, 1°10′, 115′, 1°20′, 1°25′, 1°30′, 3°20′, 3′23′,
7°45, 750′, 7°55′, 8°0′, 11°30′, 11°35′, 11‍40′, 11°45′, 11°50′, 11°55′,
12°0′, 12.5, 12°40′, 12.45, 12°50′, 12.55, 13-0-13-5
15°25′, 15°30′, 15°33′, 15°40′, 15°45′, 15.0′,
[These will enable the Surveyor, at nearly any hour of the night, to
run a meridian line in any place until A.D. 2000.]
Azimuth of Kochab (Beta Ursaminoris), when at its greatest elonga-
tions or azimuths for 1875 and every ten years to 1995,
Table XXIV. Azimuths of Polaris when on the same vertical plane
with gamma in Cassiopeæ at its under transit in latitudes 2° to 70°
from 1870 until 1940,

-15°20′,

183

184

193

194

195

Table XXV. Azimuths of Polaris when vertical with Alioth in Ursa majoris at its under transit, same as for table XXIV, Table XXVI. Mean places of gamma (cassiopa), and epsilon (alioth), in ursa majoris at Greenwich from A. D. 1870 until 1950, 196 Table XXVII. Azimuth, or bearings of alpha, in the foot of the Southern cross (Crucis), when on the same vertical plane with beta in Hydri, or in the tail of the serpent from A. D. 1850 until 2150, and for latitude 12° to 6 ›

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Table XXVIII. Altitudes and greatest azimuths for January 1, 1867. For Chicago latitude 41°, 50′, 30′′ N., longitude 87°, 34′, 7′′ W., and Buenos Ayres 34°, 36′, 40′′ S., longitude 58°, 24′, 3′′ W., for thirteen circumpolar stars in the Northern hemisphere, and ten circumpolar stars in the Southern hemisphere, giving the magnitude, polar distance, right ascension, upper meridian passage, time to greatest azimuth, time of greatest E azimuth, time of greatest W azimuth, greatest azimuth, altitude at its greatest azimuth of each, 198 Table XXVIII. A. Table of equal altitudes, Table XXVIII. B. To change metres into statute miles, Table XXVIII. C. Length of a degree of latitude and longitude in miles and metres, Table XXIX.

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Table XXXI. Discharge of water through new pipes compiled from D'Arcy's official French tables for 0.01 to 1.00 metres in diameter, and ten centimetres high in 100 metres to 200 centimetres in 100 metres high,

201

D'Arcy's formula and example,

264

Table XXX. Weights and measures.

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a X Ò,707168.

a X 1,4142136
2

6. Perimeter of the square = A B+ B D + D C + C A = 4 a.

a V 2

7. Side of the inscribed octagon F G a=aX1,4142136—a =a X 0,414214, i. e., the side of the inscribed octagon is equal to the difference between the diagonal A D and the side A B of a square.

8.

2

Area of the inscribed circle a2 X 0,7854.

9. Area of the circumscribed circle 0,7854 × 2 a2.

10. Area of a square circumscribing a circle is double the square inscribed in that circle.

RHOMBUS.

11. (Fig. 3.) In a rhombus the four sides are equal to one another, but the angles not right-angled.

12. The area

ABXCE.

13. Or, area

the product of the side X perpendicular breadth

a2 X natural sine of the acute angle C A B; i.

ABX ACX nat. sine of the angle C A B

the area.

OF THE RECTANGLE OR PARALLELOGRAM.

14. (Fig. 2.) Let A. B a, BDb, and A D = d.

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16.

2

A 17. Area:

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radius of the circumscribing circle.

— a b or the length × by the breadth.

18. When a 2 b, the rectangle is the greatest in a semi-circle.

19. When a

greatest area.

a

2 b, the perimeter, A C+ CD + D B contains

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