PREFACE. THE following work is designed for the use of Students, Mechanics, and Engineers, and the purpose of the author has been to present a full set of rules whereby may be readily determined the Lines, Areas, Surfaces, Solidities or Volumes, and Centres of Gravity of various Regular and Irregular Figures. In the progress of the work, it was essayed to present a familiar rule for the surface, volume, and centre of gravity of every figure, but, in consequence of the impracticability of reducing the rules in some cases to a formula at all consistent with the design of the work, such cases as presented this difficulty were abandoned: as it occurs, however, the number of them has been very essentially reduced by the aid and advice of Professors A. E. Church, U. S. Military Academy, West Point, and G. B. Docharty, N. Y. Free Academy. In consequence of the great number of works on Mensuration that have been submitted to the public, the inference is a fair one that the author, in this case, has not presented any novelties whereby he may anticipate any particular notice or attention; he trusts, however, that a reference to the result of his labors will show that, in the essential points of the extent of the figures submitted, as well in their number as variety of |