Entered, according to Act of Congress, in the year 1874, by

D. VAN NOSTRAND

In the Office of the Librarian of Congress, Washington, D. C.

Page 36, lines 8, 7, 5, 4, and 3 from bottom: table 10 should be table 15.

Page 37, line 2 from top: table 10 should be table 15.

Page 37, line 3 from top: table 15 should be table 17.

Add to note on page 69: "and multiplied by two, the minus 8+8' corrections for 2

11."

tions are readily found by Mr. Trautwine's well-known and very ingenious diagrams, than which for the purpose intended probably no better means can be devised. When these heights have been ascertained, the use of the special Correction Tables in connection with those of level cuttings will reduce to a minimum the labor of computing the prismoidal contents. If further tables of level cuttings are considered necessary, the reader is referred to Mr. Trautwine's "Excavation and Embankment," or to the example given at the end of this work, by careful attention to which any required table may be written out with entire accuracy in a few hours. Special corrections for any side slopes may be obtained by Rule 12.

Not an inconsiderable advantage of the present method is that, by

MAY 7 1907

SN.D •H83

PREFACE.

THIS work claims to present a new and systematized method of finding the prismoidal contents of Earthwork by means of Tables accompanied by Rules so plain and simple of application as to fit it for the common uses of Engineers.

When the ratios of the side slopes are constant between end sections of which the transverse surface lines are sensibly similar, all ordinary cases of thorough cut and fill, terminal pyramids, side-hill work, and borrow pits are covered by Formulæ (17), (18), and (19), and the prismoidal contents for all side slopes and bases are taken from Tables 4 and 5 by Rules (1), (2), and (3).

In the method used, the heights of equivalent level sections are not involved, nor is any calculation needed for 100-feet lengths beyond ascertaining the half-sum and the difference of two quantities. For the most part Tables do the work of the calculator, and any one who can approximate cubic contents by the rough method of "Average Areas" is competent to obtain the prismoidal contents by the Rules given.

The tables of level cuttings are not needed when areas are given, and are included chiefly for use in preliminary estimates when the only data are the centre heights and the angles of the transverse surface slopes. With these, the heights of equivalent level sections are readily found by Mr. Trautwine's well-known and very ingenious diagrams, than which for the purpose intended probably no better means can be devised. When these heights have been ascertained, the use of the special Correction Tables in connection with those of level cuttings will reduce to a minimum the labor of computing the prismoidal contents. If further tables of level cuttings are considered necessary, the reader is referred to Mr. Trautwine's "Excavation and Embankment," or to the example given at the end of this work, by careful attention to which any required table may be written out with entire accuracy in a few hours. Special corrections for any side slopes may be obtained by Rule 12.

Not an inconsiderable advantage of the present method is that, by

giving accurate corrections for the familiar approximations in general use, the calculator has the element of error constantly before him, and must speedily learn by practice, if not by theory, the cases in which such corrections become important. But while enough is given, both by rule and example, in Part II. to guide the least theoretical in the use of the tables, in Part I. a strictly mathematical investigation of principles and derivation of formulæ is submitted to the careful reader.

The article on Correction of Contents for Curvature was suggested by that on the same subject in "Henck's Field-Book," but, by the formulæ and table of factors given, in ordinary cases the corrections are much more readily obtained in practice.

All of the tables in this work have been calculated by the writer, and, as the system used was that of continued additions with special tests at intervals, it is believed that they will be found absolutely correct within the purposed limits, whether the last figure of any amount given be intended to express the nearest whole number or the nearest decimal.