Memoir of Frank Russell FirthLee and Shepard, 1880 - 143 pages |
Contents
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Common terms and phrases
A₁ arc AP assume axis bisecting calculated central angle centre line column common tangent compound curve correction cot A2 cot F curvature curve joining deflection degree of curve diagram draw Diff direction Draw the chord elevation embankment engineer equal equation ex sec external distance feet fifth column formula frog F given curve gives Hence inches intersect joining two tangents KO'a length locate log vers long chord main line main track maximum grade measured middle ordinate middle point obtained parallel tangent point of curve point of tangent prismoid produced R₁ R₂ radii radius ratio right angles S₁ S₂ side simple curve slope stakes station straight subchord subtended subtracting surface switch Table tangent point tion transit point valvoid vers A2 vertex vertical whence Δι
Popular passages
Page 204 - A + 75 it is -f^M; and the same for corresponding points on the other side of B. The corrections in the case shown are subtractive, since M is negative. They are additive when M is positive, and the curve concave upward.
Page 261 - To find the angle or arc corresponding to a given logarithmic sine, tangent, cosine, or cotangent. — If the given logarithm is found in the proper column take out the degrees and minutes directly; if not, find the two consecutive logarithms between which the given logarithm would fall, and adopt that one which corresponds to the least number of minutes; which minutes take out with the degrees, and divide the difference between this logarithm and the given one by the adjoining tabular difference...
Page 208 - ... feet below grade. The embankment is protected at the upper end of the drain by a bit of vertical wall, enclosing the end of the pipe. If necessary, a paved gutter may lead to it. Where stone abounds, the bed of a dry ravine may be partly filled with loose stone, extending beyond the slopes a few feet, which will prevent the accumulation of water. When the flow of water is estimated to be too great for two lines of the largest pipe, a culvert is required.
Page 258 - ... of the calculation. By this rule we have Number Logarithm 1.384 0.141136 .1384 9.141136 .01384 8.141136 .001384 7.141136 etc. etc. No confusion need arise from this method in finding a number from its logarithm; for although the logarithm 6.141136 represents either the number 1,384,000, or the decimal .0001384, yet these are so diverse in their values that we can never be uncertain in a given problem which to adopt.
Page 258 - ... number are given in the first column, the fourth at the top of the other columns. The first two figures of the mantissa are given only in the second column, but these are understood to apply to the remaining four figures in either column following, which are comprised between the same horizontal lines with the two. If a number (after cutting off the ciphers at either end) consists of not more than four figures, the mantissa may be taken direct from the table ; but by interpolation the logarithm...
Page 263 - Find in the. proper column two consecutive logarithms between which the given logarithm falls. If the title of the given function is found at the top of that column read the degrees from the top of the page; if at the. bottom read from the bottom. Find the value of (q...
Page 261 - The above rules do not apply to the first two pages of this table (except for the column headed cosine at top) because here the differences vary so rapidly that interpolation made by them in the usual way will not give exact results. On the first two pages, the first column contains the number of seconds for every minute from 1...
Page 262 - These two pages may be used in the same way when the given angle lies between 88° and 92°, or between 178° and 180°; but if the number of degrees be found at the bottom of the page, the title of each column will be found there also; and if the number of degrees be found on the...
Page 185 - ... reading, proportional to the distance of the rod from the instrument. But the errors being equal for equal distances, and the backsights and foresights having opposite signs in our calculations, the errors cancel when the distances are equal. Hence, to avoid errors in elevation, each new...
Page 261 - ... fourth are the last three figures of a logarithm which is the difference between the log sin and the logarithm of the number of seconds in the first column. The first three figures and the characteristic of this logarithm are placed, once for all, at the head of the column. To find the log sin of an arc less than 2° given to seconds. Reduce the given arc to seconds, and take...