CONTENTS. A SELECTION OF GEOMETRICAL PROBLEMS.

PLATE I. To draw a straight line parallel to a given line, and at a given distance from it-To bisect a given straight line-To divide a given line into any number of equal parts-To draw a straight line equal to the circumference of a given circle-To construct a plain scale for drawing a small plan proportionate to a larger one-To find the centre of a circle or the radius of a curve-To draw a circle through any three given points-To erect a perpendicular.

II. To strike a segment by a triangular guide, the chord and height being givenThe chord and height of a segment of a circle of large radius being given, to find the curve without recourse to the centre-Having an are of a circle given, to raise perpendiculars from any point or points without finding the centre-To draw a tangent to a circle or portion of a circle without having recourse to the centre-Upon a given straight line to describe any regular polygon-Upon a given side to draw a regular pentagon. III.-Upon a given side to draw a hexagon-To draw a heptagon-How to describe an octagon in a given square-To draw a straight line equal to any given part of a circle -To find the stretch out of a semicircle-Definition of polygon-Definition of parallelogram.

IV. To strike an ellipse or oval with the compasses, the length or major axis being given-To describe an ellipse within a given square, or when the major and minor axes are given-Method of drawing an egg-shaped oval-Graphic illustration of what an ellipse really is-Another method of drawing an ellipse-To draw a parabola-To draw an ellipse with a trammel.

V. To strike a pattern for a round, tapering, or flue article, or a frustum of a cone -The plan of a round flue body to be cut in three pieces-Two or three methods of describing ovals.

VI. The pattern of an article where the sides are straight and the ends semicircular -The pattern of an oblong tapering pan in two parts or sections.

VII. The pattern for a tapering oblong article in one piece, such as a flue oblong candlestick The pattern for a tapering oval article in four pieces or sections.

VIII. To describe a tapering oval body in one piece-A method of drawing an ellipse or oval with a string and pencil.

IX. The pattern of an egg-shaped oval tapering body-Another method of describing an oval tapering body.

X-To describe a tapering oval body where the tapering is not equal on all sides. XI. The pattern for a square tapering article or pyramid-The pattern for a tapering octagon body in one piece-The pattern for a diamond-shaped tapering body in one piece -The pattern of a square funnel where one side is straight or upright.

XII. The pattern for a square or rectangular tapering top or tray, with sides and bottom in one piece-The pattern for a hexagon mould or tray, having the bottom and sides in one piece-The pattern of an irregular octagon pan or tray, with the siles or bottom in one piece-The pattern of an oblong pan, with round corners, but struck from different centres, and tapering more at the ends than sides.

XIII-A pattern for a tapering top, the base being straight at the sides, and with circular ends, the hole in the top to be circular and parallel with the base (similar to a tea-bottle top).

XIV. The pattern for a tapering article, oval at the base and round at the top (such as an oval canister top, having a round hole for the neck and cover).

XV. A pattern for the tapering sides of a tray, having various curves.

XVI. The pattern for an oblong tapering bath.

XVII. The pattern of an elbow at right angles, in a round pipe-A pattern of an elbow in a round pipe at any angle required (in this case an obtuse angle)-The pattern of a tapering piece of pipe to join two upright cylinders to form a double elbow.

XVIII. The pattern for a T-piece, or to join two cylinders at right angles-The pattern of two cylinders for joining at an oblique angle for slanting direction.

XIX. The pattern for a lobster-back cowl-The pattern for a round pipe, to form a semicircle for connection to other pipes.

XX. The pattern for a cone and cylinder to intersect or meet at right angles with their axes.

XXI. A cylindric section through any given angle-To draw an ogee arch-Another method-To find the covering of an ogee dome, the plan of which is hexagonal.

XXII. The pattern for a rectangular base and bottom in one piece, where the flue or curve is equal on all sides (such as may be used as a base for either an aquarium or a fern-case)—The pattern for a hexagon base.

XXIII. The pattern for a vase, octagon shape.

XXIV. The pattern for a vase having twelve sides (duodecagon).

XXV. The pattern for a cone with an elliptic base-The pattern of an oblique cone, or the frustum of a cone cut parallel with the base.

XXVI. The pattern for a round-end bath tapering more at the ends than at the sides.
XXVII. The pattern for a hip bath.

XXVIII. The pattern for a travelling sitz bath.

XXIX. The pattern for a globe formed of twelve pieces joined together-The pattern for a triangular pedestal, or pyramid, with all three sides alike (an equilateral triangle) -To obtain the radius required for striking the pattern of a slightly tapering article, without the necessity of producing lines to meet.

XXX. The patterns for the sides of an irregular octagon pan.

XXXI. The pattern for a cover and neck of an irregular octagon article, such as a

tureen.

XXXII. The pattern for the top of a jack screen.

APPENDIX.-RULES FOR BOILER-MAKING, ETC.: Template making-To build a tubalar boiler of 36 inches, inside diameter of two plates in the circle-To find the breadth of the template for a given dome at any particular place, by calculation-To find the template for a given short egg-end spherical-To find the template for a given long eggend parabola; the breadth and length of the template at any particular place-To find the templates for a given barrel spheroid; the breadths and lengths at any particular place by calculation. MENSURATION OF SURFACES: Four-sided figures-TrianglesTrapezoids and trapeziums-The circle-Ellipse or oval-Mensuration of solids-For superficies-For the solidity-Cylinders and prisms-Cones and pyramids-Spheres and segments of spheres. APPROXIMATE RULES FOR FINDING THE WEIGHT OF DIFFERENT FIGURES OF WROUGHT IRON AND STEEL: For round iron-For square iron-For square, angled T, convex, or any figure of beam iron-For square cast-steel-For round eaststeel-Table I. Weight of wrought iron and steel-II. Weight of boiler plates-III. Weight of malleable round iron-IV. Weight of malleable square iron-V. Weight of malleable flat iron-VI. Weight of a superficial square foot of plate or sheet iron-VII. For ascertaining the weight of malleable iron pipes-Rule-VIII. Weight of ordinary angled iron. INDEX.

Warner.- New Theorems, Tables, and
Diagrams for the Computation of
Earth-Work:

Designed for the use of Engineers in Preliminary and Final Estimates, of
Students in Engineering, and of Contractors and other non-professional
Computers. In Two Parts, with an Appendix. Part I.-A Practical
Treatise; Part II.-A Theoretical Treatise; and the Appendix. Con-
taining Notes to the Rules and Examples of Part I.; Explanations of the
Construction of Scales, Tables, and Diagrams, and a Treatise upon
Equivalent Square Bases and Equivalent Level Heights. The whole
Illustrated by numerous original Engravings, comprising Explanatory
Cuts for Definitions and Problems, Stereometric Scales and Diagrams,
and a Series of Lithographic Drawings from Models, showing all the
Combinations of Solid Forms which occur in Railroad Excavations and
Embankments. By JOHN WARNER, A. M., Mining and Mechanical Engi-
neer. 8vo.

$5.00

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