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PREFACE AND INTRODUCTION.
A COMPLETE set of Earthwork Tables has been hitherto a desideratum. I have constructed the following in order to supply what I consider, and have felt to be, and what I believe is generally felt to be, a want. These, starting with a base of six feet in breadth, advance, by successive increments of one foot, up to 36 feet of base. Thence we advance to 38, 40, 45, terminating with 50 feet. In each of the Tables, the four slopes in most general use, viz. to 1, 1 to 1, 1ļ to 1, and 2 to 1, have respectively two columns, and I have arranged them in the manner which I believe will be found the most convenient in every-day practice. With the exception of the first four Tables, which are calculated to bases so narrow as to call for a depth of not more than 30 feet, all are calculated to a depth of 60 feet, with intervals of three inches for the thirteen bases which are in most general use, and of six inches for the remaining bases.
Supplementary Tables are added which may be used in a variety of ways, but which are chiefly intended to supply intermediate slopes which are not given in the Tables of Bases. The unit of length is taken at one English foot, which I think will be found better than any multiple of it; and if the longitudinal scale of the section to be calculated be in links instead of feet, the contents of each cutting or embankment, as obtained from the Tables, will be correctly reduced by multiplying it by 66 and dividing by 100, or, which is the same thing, multiplying simply by •66. The formulæ by which I have calculated the tabular numbers have permitted great compression of matter valuable for prompt reference, with a completeness of result beyond what I have yet found in Earthwork Tables. The first of these qualities is eminently obtained in Mr Bidder's Tables, and the second perfectly in Sir John MacNeill's; but the former from over-condensation, and the latter from their unwieldy expansion, are alike unsatisfactory.
I have appended a Table designed for the rough but speedy measurement of Earth work by means of transparent paper or horn, which will be found of great use by Resident Engineers and Contractors in the cursory measurements of works ; it has been of eminent service in my own practice. A Table for the speedy calculation of land to English and Irish acres is also added, as well as Tables of Gradients, and Resistances on Roads, which may prove useful in laying out lines.
I have checked the whole by such an accurate method, and in such a careful manner, as induces me to believe that no error lies undetected, but that the whole, even to the last decimal, will warrant the confidence which I hope will be placed in, and the favour which I trust will be given to, these Earthwork Tables.
INNERLEITHEN, May 1865.