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XLVII. To locate a turnout.

137

XLVIII. Crossings on straight lines

139

XLIX. Crossings on curves

139

L. Elevation of the outer rail on curves.

141

Table for same

142

LI. Trackmen's table of curves and spring of rails. 143

Explanation of same

144

LIST OF TABLES.

I. Time of meridian passage of North Star above the

pole for the year 1870, and on

149

II. Time of extreme elongation of North Star for the

year 1870, lat. 40°, and on .

150

III. Azimuths of the North Star, and their natural tan-

gents

150

IV. Roods and perches in decimal parts of an acre 151

V. Decimals of an acre in one chain length of 100 feet,

and of various widths.

151

VI. Acres, roods, and perches in square feet

152

VII. Circular arcs to radius of 1

152

VIII. Feet in decimals of a mile

153

IX. Inches reduced to decimal parts of a foot

153

X. Radii and their logarithms, middle ordinates, and

deflection distances

155

XI. Squares, cubes, &c., of numbers from 1 to 1042 .

161

XII. Logarithms of numbers, 1 to 1000.

179

XIII. Logarithmic sines, cosines, tangents, and cotan-

gents

197

XIV. Natural sines and tangents

243

XV. Chords, versed sines, external secants, and tangents

of a one-degree curve .

269

XVI. Slopes for topography

315

XVII. Rise per mile of various grades

317