Section. Walls and foundations, Table-Kind of wood, spec. grav., both ends fixed and loaded in the Falling bodies. velocities, middle. Breaking weight. Transverse strain,. HODGKINSON'S FORMULA for long square pillars, Strength of cast-iron beams, Strongest form, Fairbairn's form, 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, Walls of buildings, Parallelogram of forces. Polygon of do., Composition of motions. Page 72E. Centre of gravity in a circle, square, triangle, trapezoid.. Of Solids.---Of triangular pyramid, a cone, conic frustrum, in any 310-12 310x7 310x5 31018 310/20 310w4 .3.03 FORCE AND MOTION. 311 Theoretical and actual mean velocities of. Virtual 312 and 319m Of a liquid, 316, body lighter than water, 318, of a powder soluble Table-Specific gravities of bodies. Weight one cubic foot in Table-Average bulk in cubic feet of one ton, 2240 pounds, of vari- Mechanical powers, levers, pulleys, wheels, axles, inclined plans, Virtual velocity, FRICTION. COULOMB AND MORRINS' experiments coefficient of the Table-Friction of plane surfaces sometime in contact, 319a 319a 319 319% to 31927 Friction of axles in motion, 3197 Work done by man and horse vertically, 319s 319 ROADS AND STREETS. Roman roads, Appian way, Roman military roads, Carthaginian, German, Belgium, Sweden, English, Irish, and Scotch roads, How the railroad was built over the Menomenee marsh near Mil- .319v RETAINING WALLS for roads. l'age 72111, .3197 Parapet walls, drainage, drain holes, materials, sandstone, limestone. ..319v Table of compression of materials in road making, etc. Page 72j13,.319~ Section. 3197 3197 3197 .3192 Table and formulas of friction on roads. Page 72114, Table-MORIN'S EXPERIMENTS. With examples. Page 72j16. CANALS AND EXCAVATIONS. Page 72K. (See Sec. 421), To set out a section of a canal on a level surface, When the slopes are the same on both sides, 320 321 321a 32 b 3211 332 A, base To find the content of an excavation or embankment. Page 72T,... 327 327 BAKER'S method of laying out curves, and calculating, earth works, 339 Tables for calculating earthwork deduced from BAKER, KELLY, and To change circumferentor to quarter compass bearings, 135 167 171e 218 309m 309 .30911 Scale for arable land, Scale of prices for pasture, . 3090 Table of produce, One hundred statute acres under a live years' rotation. l'age 72B21. Increase in valuation for its vicinity to towns, Classification of buildings, 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,. .310v Analysis of grains and straws, vegetables and legumes, .310F 310G Per centage value of manures for nitrogen and phosphoric acid, Value of the Vena contracta from various writers on hydraulics, . . . .310c* 72B104, Value of discharge Q through various orifices, Retaining walls, by Poncelet, .310E* .310E* .310F* Specific gravities, breaking weight and traverse strains of beams. supported at both ends, and loaded in the middle, .3.0v12 Specific gravities of bodies,. Average bulk in cubic feet per ton of 2240 pounds. Shrinkage or increase per cent. of materials. Page 7211,. Walker's experiments on paving stones in a street in London, one-half inches. Page 72j13. Table of uniform draught on given inclinations. Page 72113. deflection the versed sine at one-half, the chord, or the versed sine Natural sines to every minute, five places of decimals from 1° to 90°. Natural cosines as above. A guide line is at every five minutes. Lengths of circular arcs obtained by having the chord and versed sine, 171 173 To reduce square feet to acres and vice versâ,. Table X. To reduce square links to acres, Table XI. ment, To reduce hypothenuse to base, or horizontal measure Table XII. To reduce sidereal time to mean solar time, sea in miles Table XVII. Table XVIII. Table XIX. Table XX. Section 173 177 178 178 179 179 179 Dip or depression of the horizon, and the distance at Correction of the apparent altitude for refraction, Parallax in altitude of the planets, Reduction of the time of the moon's passage over the meridian of Greenwich to that over any other meridian, Table XXI. -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 › 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. 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. a X Ò,707168. a X 1,4142136 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. d 16. 2 A 17. Area: 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 |