The mechanic's companion, or, The Elements and practice of carpentry, joinery, bricklaying, masonry, slating, plastering, painting, smithing, and turning : comprehending the latest improvements and containing a full description of the tools belonging to each branch of business, with copious directions for their use and an explanation of the terms used in each art : also an introduction to practical geometry

Preface

MORE than a century has elapsed since an ingenious and useful work on the Arts connected with Building was published under the title of Mechanical Exercises, by the celebrated Joseph Moxon: that it was both useful and popular the various editions testify, and at this time it is become scarce and rarely to be met with. I* can be no disparagement to its ingenious author, to say that the progress of science, and the changes in matters of art have rendered the work obsolete and useless. It treated on Smithing, Joinery, Carpentry, Turning, Bricklaying, and Dialling.

I have followed the excellent plan of Moxon and treated each art distinctly : I have first described the several tools belonging to each branch of business, next the methods of performing the various manual vi PREFACE.

operations or exercises, to which they are applicable, these are further illustrated and explained by numerous plates ; the descriptions are made as plain and familiar as possible ; and there are few operations but will be found fully and clearly explained : finally to each is added an Index and extensive Glossary of terms used by workmen in each art, with references also to the plates : and it has been my endeavour that the description with its definition should be clear, and show the connection between the science and the art, thereby producing a pleasing and lasting eflfect upon the mind.

The arts treated of are as follow: Carpentry, Joinery, Bricklaying, Masonry, Slating, Plastering, Painting, Smithing, and Turning, the whole preceded by a slight introduction to Practical Geometry, and illustrated by forty copper-plates.

These exercises commence with those arts which work in wood, namely. Carpentry and Joinery which are much alike in their tools and modes of working : then comes Bricklaying, which with Carpentry are certainly the most essential of all in the construction of a building.

PREFACE. vii

Masonry and Bricklaying are in reality branches of the same art, and both founded upon principles truly Geometrical, yet I have given the precedence to Bricklaying, because it is of the most general use in this country ; yet it is generally admitted, that Masonry is the more dignified art of the two, or indeed of all the arts concerned in the formation of an edifice. On that difficult and intricate subject, the Theory of Arches, I have endeavoured to give a familiar, and I hope a satisfactory illustration.

Slating comes next to cover in the building: then Plastering, which is used in the finishing of buildings, and furnishes the interior with elegant decorations, and conduces both to the health and comfort of the inhabitants : Painting is not less useful than ornamental; it adds to the elegance of buildings, and tends to the preservation of the materials, whether wood or plaster.

Smithing or Smithry is extensively useful in almost every department of art as well as building; by it are made the tools which perform all the operations of the before mentioned arts, and therefore, though last, should not be least in our esteem. The use of viii PREFACE.

iron has also of late years been very much extended ; in wheels for machinery, Iron Bridges, Rail roads, Boats, Roofs, Floors, and various other articles not necessary to enumerate here.

Turning is a curious Mechanical Exercise, and though not absolutely necessary in building, may be employed with advantage in many of its decorations. In this article I have given a legitimate definition of elliptic turning, by which, its principles are deduced to be that of the ellipsegraph or common trammel, and this without entering into further demonstration. This art is illustrated by plates, showing the principles of the machines, as well as by views of the machines and tools

As the practice of the arts here treated of, is founded in Geometry, and as the descriptions of the materials and of the tools may be referred to the several figures of that science, I have prefixed to (he work such definitions as are necessary to the comprehension of any drawing or design, which is to be executed, accompanied by many useful problems, which will enable the mechanic to understand the configuration of its several parts in practice.

PREFACE. ix

and to perform many useful problems upon true scientific principles. The problems for setting out work upon the ground, and those for reducing drawings to any scale or proportion, even without knowing the scale of the original drawing, will be found interesting, and very useful in practice.

This work, which treats of the first rudiments of practice, will be found particularly interesting and useful to gentlemen who practise, or are fond of the mechanical exercises, and to young men or apprentices in any of the professions, though, on some occasions, the older workmen may be benefitted by a perusal. The terms introduced are those in general use amongst workmen in London : and on this account it will be of essential service to young men coming to the metropolis. An art cannot be taught but by its proper terms. Other branches of art might have been introduced into this work, but those here treated of are intimately connected with each other, and have a natural afl[inity, and will, it is presumed, form upon the whole, a very interesting work to young mechanics j those who wish for further information in the building art, and particularly

B

X PREFACE.

on what relates to Geometrical Construction, may consult my other publications on Practical Carpentry.

Every art is improved by the emulation of its competitors : it is therefore the ardent hope of the author that the reader may not be disappointed of meeting with abundance of that information which his mind may be desirous to obtain.

PETER NICHOLSON.

PRACTICAL, GEOMETRY.

GEOMETRY is the science of extension and magnitude : by Geometry the various angles of a building and the position of its sides are determined, as a square, a cube, a triangle, &c. : Boards and all Tools used by the Carpenter and Joiner are geometrical constructions : by Geometry all kinds of roofs and various other things laying in oblique angles are determined : the proper construction of all sorts of arches and groins depend entirely upon the principles of Geometry. I have, therefore, prefaced this work with an explanation and definition of such geometrical figures as will frequently occur in carrying on of works, and which are therefore necessary to be well known by all artizans and workmen, as well as by those who may superintend them: this slight introduction to Geometry will also be useful to all persons who wish to understand the practice and descriptions of the handy, works herein explained.

Geometry is the science of extension, and magnitude, and consists of theory and practice.

The theoretical part is founded upon the reasoning of selfevident principles ; it demonstrates the construction, and shows the properties of regularly defined figures. The theory is the fisindation of the practical part ; and without a knowledge of it, no invention to any degree certain can be made. The use of Geometry is not confined only to speculative truths in Mathematics,

GEOMETRY.

but the operations of mechanical arts owe their perfection to it ; drawing and setting out every description of work, are entirely dependent upon it.

DEFINITIONS.

1. A point is that which has position, but not magnitude.

2. A line is the trace of a point, or that which would be described by the progressive motion of a point, and consequently has length only.

3. A superfices has length and breadth.

4. A solid is a figure of three dimensions, having length, breadth, and thickness. Hence surfaces are extremities of solids, and lines the extremities of surfaces, and points the extremities of lines.

If two lines will always coincide, however applied, when any two points in the one coincides with the two points in the other, the two lines are called straight lines, or otherwise right lines.

A curve continually changes its direction between its extreme points, or has no part straight.

Parallel lines are always at the same distance, and will never meet, though ever so far produced. Oblique right lines change their distance, and would meet if produced.

One line is perpendicular to another, when it inclines no more to one side than another.

A straight line is a tangent to a circle, when it touches the circle without cutting when both are produced.

An angle is the inclination of two lines towards one anotlier in the same plane, meeting in a point.

Angles are either right, acute, or oblique.

A right angle is that which is made by one line perpendicular to another, or when the angles on each side are equal.

An acute angle is less than a right angle.

An obtuse angle is greater than a right angle.

GEOMETRY.

A plane is a surface with which a straight Une will every where coincide : and is otherwise called a straight surface.

Plane figures, bounded by right lines, have names according to the number of their sides, or of their angles, for they have as many sides as angles : the least number is three.

An equilateral triangle is that whose three sides are equal.

An isosceles triangle has only two sides unequal.

A scalene triangle has all sides unequal.

A right-angle triangle has only one right angle.

Other triangles are oblique-angled, and are either obtuse or acute.

An acute-angled triangle has all its angles acute.

An obtuse-angled triangle has one obtuse angle.

A figure of four sides, or angles, is called a quadrilateral, or quadrangle.

A parallelogram is a quadrilateral, which has both pairs of its opposite sides parallel, and takes the following particular names:

A rectangle is a parallelogram, having all its angles right ones.

A square is an equilateral rectangle, having all its sides equal, and all its angles right ones.

A rhombus is an equilateral parallelogram whose angles aro oblique.

A rhomboid is an oblique-angled parallelogram, and its opposite sides only are equal.

A trapezium is a quadrilateral, which has neither pair of its sides parallel.

A trapezoid hath only one pair of its opposite sides parallel.

Plane figures having more than four sides, are in general called polygons, and receive other particular names according to the number of their sides or angles.

A pentagon is a polygon of five sides, a hexagon of six sides, a heptagon seven, an octagon eight, an eneagon nine, a decagon ten, an undecagon eleven, and a dodecagon twelve sides.

A regular polygon has all its sides, and its angles equal ; and if they are not equal, the polygon is irregular.

An equilateral triangle is also a regular figure of three sides, and a square is one of the four ; the former being called a trigon, and the latter a tetragon.

A circle is a plane figure, bounded by a curve line, called the circumference, which is every where equi-distant, from a certain point within, called its centre.

The radius of a circle is a right line drawn from the centre to the circumference.

A diameter of a circle is a right line, drawn through the centre terminating on both sides of the circumference

An arc of a circle is any part of the circumference.

A chord is a right line joining the extremities of an arc.

A segment is any part of a circle bounded by an arc and its chord.

A semicircle is half a circle, or a segment cut ofTby the diameter.

A sector, is any part of a circle bounded by an arc, and two radii, drawn to its extremities.

A quadrant, or quarter of a circle, is a sector having a quarter part of the circumference for its arc, and the two radii perpendicular to each other.

The height or altitude of any figure is a perpendicular, let fall from an angle or its vertex, to the opposite side, called the base.

The measure of any right lined angle, is an arc of any circle contained between the two lines wh'ch form the angle, the angular point being the centre.

A solid is said to be cut by a plane, when it is divided into two parts, of which the common surface of separation is a plane, and this plane is called a section.

DEFINITIONS OF SOLIDS.

A prism is a solid, the ends of which are similar, and equal parallel planes, and the sides parallek grams.

If the ends of the prism are perpendicular to the sides, the prism is called a right prism.

GEOMETRY.

If the ends of the prism are oblique to the sides, the prism is

called an oblique prism.

If the ends and sides are equal squares, the prism is called a cube. If the base or ends are parallelograms, the solid is called a

parallelepiped.

If the bases and sides are rectangles, the prism is called a rectangular prism.

If the ends are circles, the prism is called a cylinder.

If the ends or bases are ellipsis, the piism is called a cylindroid.

A solid, standing upon any plane figure for its base, the sides of which are plane triangles, meeting in one point, is called a pyramid.

The solid is denominated from its base, as a triangular pyramid is one upon a triangular base, a square pyramid one upon a square base, &;c<,

If the base is a circle or an ellipsis, then the pyramid is called a cone.

If a solid be terminated by two dissimilar parallel planes as ends, and the remaining surfaces joining the ends be also planes, the solid is called a prismoid.

If a part of a pyramid next to the vertex be cut off by a plane parallel to the base, the portion of the pyramid contained between the cutting plane and the base is called the frustum of a pyramid.

A solid, the base of which is a rectangle, the four sides joining the base plane surfaces, and two opposite ones meet in a line parallel to the base, is called a cuneus or wedge.

A solid terminated by a surface which is every where equally distant, from a certain point within it, is called a sphere or globe.

If a sphere be cut by any two planes, the portion contained between the planes is called a zone, and each of the parts contained by a plane and the curved surface is called a segment.

If a semi-ellipsis, having an axis for its diameter, be revolved round this axis until it come to the place whence the motion began, the solid formed by the circumvolution is called a spheroid.

If the spheroid be generated round the greater axis, the solid is called an oblong spheroid.

GEOMETRY.

If the solid be generated round the lesser axis, the solid is called an oblate spheroid.

A solid of any of the above structures, hollow within, so as to contain a solid of the same structure, is called a hollow solid.

PLATE I.

A an acute angle.

B two lines inclined, and would meet and form an angle if produced.

C a perpendicular c d is said to be perpendicular to a h, and the angles c d a, cb d axe both right angles.

D several angles meeting at a point ; when this is the case, each is denoted by three letters, the right angle is the criterion of judging of every other angle ; db c is a right angle, a & c an obtuse angle, e & c an acute angle.

E a right angle.

F an acute angle, being less than a right angle

G an obtuse angle, being greater than a right angle.

H an equilateral triangle all the three sides a b, b c, c a being equal.

I an isosceles triangle, a b and b c being only equal. K a scalene triangle, all the sides being unequal. L a right angled triangle.

M, N, O, P, Q, R quadrilaterals or quadrangles, M N 0 P are parallelograms; M N rectangles ; M an oblong; N a square; O a rhomboid ; P a rhombus ; Q a trapezium ; and R a trapezoid.

T, U,V polygons, T a pentagon, U a hexagon, and V an octagon.

W a circle, a the centre, b a point in the circumference, aba. radius.

X a circle, c the centre, d and e points in the circumference, <i e a a diameter, or a chord passing through the centre.

GEOMETRY.

Y a circle, d and e points in the circumference, <Z c a chord ; d / c the less segment, and (Z g- e the greater.

A 1, B 1 segments, ac b, a cb arcs, ab, ab chords; B 1 a semicircle.

C 1, D 1 sectors, D 1 a quadrant, c a, cb radii at right angles, a b arc.

E 1 a triangle, ab, b d, da the sides, a b the base, d c a perpendicular to the base called the altitude.

PLATE II.

Fig. 1, 2, 3, 4 are all parallelepipeds and consist of six sides ; when two opposite sides are perpenc(icular to the other four, the parallelopiped is denominated a rectangular prism, and if the four sides be equal rectangles, the prism is called a square prism as fig. 1,2; and if all the four sides are equal squares, the prism is called a cube, as fig. 1. The reason why called a parallelopiped is because each pair of opposite sides are parallel planes. The structure of a rectangular prism occurs more frequently in the practice of carpentry and joinery than any other form whatever, all timbers and boards for the use of building are cut into this form. Doors, shutters, &;c. are thin rectangular prisms, as fig. 4.

Fig. 5 is a cylinder.

Fig. 6 a hollow cylinder.

Fig. 7 the section of a cylinder cut off by a plane parallel to the axis.

Fig. 8 the sector of a cylinder contained by two planes forming an angle, and the curved surface of the cylinder ; the line of concourse of the planes being parallel to the axis of th'6 cylinder.

Fig. 9 a prisraoid ; the ends of chisels which contain the cutting part is of this form.

Fig. 10 a wedge ; the end of a chisel contained by the face and the basil are of this form.

GEOMETRY.

Fig. 11a square pyramid.

Fig. 12 an octagonal pyramid inverted

Fig. 13 a cone.

Fig. 14 inverted hollow cone.

Fig. 15 a sphere.

Fig. 16 a spheroid.

Prob. I. From a given point in a given straigU line, to erect a "perpendicular. Pl. 3. Fig. i.

Let F F be the given straight line, and C the given point. Take any two equal distances C a and C 6 on each side of the point C : from the points a and h with any equal radii greater than C a or C 5, describe arcs cutting each other in D. Draw D C and it will be the perpendicular required.

Pbob. II. To hi fall a perpendicular from a given point to a given straight line. Pl. 3. Fig. 2.

Let C be the given point and E F the given straight line. From the point C describe an arc cutttng E F at a and b. With any equal radii greater than the half of a & describe arcs cutting each other at D. Draw C D and it will be the perpendicular required.

Prob. m. When the point is at or near the end of the line. MetJiod first, Pl. 3. Fig. 3.

Let C be the given point, E F the given line. In E F take any point a and with the radius a C describe an arc C D. Take any other point & in E F, and with the distance h C describe an arc, cutting the arc C D, at C and D, draw C D and it is the perpendicular required

GEOMETRY.

Prob. IV. To draw a perpendicular from a point at the end of a line. Pi. 3. Fig. 4.

Let E F be the given straight line, and F the given point. Take any point a above the line and with the radius a C describe an arc C F & cutting E F at 5. Draw b aC; then draw C F and it will be the perpendicular required.

Pbob. v. To bisect a straiglit line. Pr. 3. Fig. 5.

Lot E F be the given straight line. From E and F as centres, and with any distance greater than the half of E F as radii, describe two arcs cutting each other at A and B. Draw A B cutting E F at C, then E F is bisected in C.

Prob. vi. To bisect a given angle. Pl. 3. Fig. 6.

Let E F G be the given angle. From the point F describe an arc a b cutting F E and F G at the points a and b, also from the points a and b, with the same radius, or any other equal radii, describe arcs cutting each other in C. Draw F C and it will besect the angle as required. That is, the angle E F G is divided into two equal angles E F C and CFG.

Prob. vn. To make an angle equal to a given angle. Pi. 3. Fig. 7 and 8.

Let E F G be the given angle. Draw the straight line H L From the point F describe an arc a b cutting E F and F G at the points a and b. From H as a centre, with the same radius, describe an arc c d cutting H I at c. Make c d equal to a b. Draw RdG and the angle I H G is equal to E F G. as required.

GEOMETRY.

Prob. VIII. Through a given point to draw a line parallel to a given right line. Pl. 3. Fig. 9.

Let A B be the given right line, and D the given point. Draw any right Hne DA; in A B take any point c and make the angle B c E equal to the angle BAD, make c E equal to A D ; draw D E, then D E is parallel to A B.

Prob. ix. To draw a line parallel to another line at a given distance. Pt. 3. Fig. 10.

Let A B be the given right line, C the given distance from any two points in A B, as A and B as centres describe two arcs dYLe and fig. Draw II I to touch the arcs at the points H and I ; and H I is parallel to A B and at a given distance C.

Prob. x. Three straight lines, of which any two are greater than the third, being given to describe a triangle, the sides of which will he respectively equal to the three given lines. Pl. 3. Fig. 11.

Let the three straight lines be A B C : Make D E equal to C, from D as a centre with the distance of B describe an arc at F, From E as a centre with the distance A describe another arc, cutting the former at F. Join F D and F E ; and D E F is the triangle required.

Prob. xi. The side of an equilateral triangle being given to describe the triangle. Pl. 4. Fig. 1.

Let A be the given side. Place A upon any straight line B C and with the same extent from the points B and C as centres

GEOMETRY.

describe arcs, cutting each other in D. Join D B and D C, and B C D is the equilateral triangle required.

Prob. XII. To describe a square, ike sides of which shall he equal to a given right line. Pl. 4. Fig. 2.

Let A be the given right line, which place upon any straight line B C. Make the angle C B E a right angle, and B E equal to B C through the points E and C. Draw E D and D C parallei to B C, and B E, and B C D E is the square required.

Prob. xiii. To describe a hexagon, the sides of which shall he equal to a given line. Pl. 4. Fig. 3.

Let A. be the given line, which place upon any straight line B C. From the points B and C, with the distance B C describe arcs cutting each other at L With the distance I B or I C describe the circle B C D E F G, then apply the side B C successively to the circumference as chords, the circumference will be divided into equal parts, and the hexagon formed as required.

Prob. xiv. To describe any regular polygon, the sides of which shall he equal to a given line. Pl. 4. Fig. 4.

Set the given line upon any other convenient line, and with a radius equal to the given line, describe a semicircle upon this line. Divide the semicircle into as many equal parts as are to be sides in the polygon ; then the half of the diameter is one side of the polygon, through the centre of the semicircle, and through the second division from the other end of the diameter draw another right line, which will form an adjoining side to the former ; bisect

GEOMETRY.

Bach of these adjoining sides by perpendiculars, and the meeting of these perpendiculars will give the centre of a circle, which will contain the straight line given.

Fig. 4 is an example of a pentagon.

Fig. 5 is an example of a hexagon.

Fig. 6 is an example of an eneagon.

Pkob. XV. To inscribe a polygon in a given circle. Pl. 4. Fig. 7, 8.

Draw the diameter of the circle, and another diameter at right angles, produce this last diameter so that the part produced shall be three quarters of the radius ; divide the first diameter into as many equal parts as the polygon is to consist of sides : through the second division, and the extremity of the part produced of the other diameter, draw a line to cut the circumference without the points, the chord of the arc intercepted between the point in the circumference thus found and the diameter, applied successively to the arc, as other chords will form the polygon required.

Fig. 7 example in a pentagon, Fig. 8 example in an octagon.

Prob. XVI. A square being given to form an octagon, of which four of the sides at right angles to each other, shall be common to the middle parts of the sides of tJie square. Pl. 4. Fig. 9.

Let I G K L be the square given. Draw the diagonals I K and G L cutting each other at m ; from the centres I, G, K, L and with the radius I m, or G m, &c. describe arcs G B, A m

D, C m F, E ?ra H cutting the sides of the square, at A, B, C, D,

GEOMETRY.

Prob. XVII. In a given circle to inscribe a hexagon or an equaliteral. Pi-. 4. Fig. 10.

Apply the radius successively as chords A B, B C, C D D E, E F, F A, and A B C D E F A will be the hexagon.

From A with the radius A B or A F describe the arc B F. Join the chord B F. Make B D equal to B F; and join D F and B F D is the equilateral triangle required.

Prob. xviii. In a given circle to inscribe a square or an octagon. Pl. 4. Fig. 11.

Let A B C D E F G H A be the circle. Draw the diameters A E and C G at right angles. Join A C, C E, E G, G A and A C E G A will be the square required.

Bisect any two adjacent angles by diameters, and the whole circumference will be divided into eight equal parts, A B B C C D, D E, E F, F G, G H, H A ; the chords of which being joined will form the octagon A E C D E F G H A as ret quired.

Prob. xix. In a given circle to inscribe a pentagon. Pl. 4.

Let A B C D E A be the given circle. Draw the diameters A/ and ^ ^ at right angles, cutting each other in the centre at I: bisect g I at i: from i as a centre, with the distance i A, describe an arc A k cutting g h at Jc : from A as a centre, with A A; as a radius, describe an arc k E, cutting the circumference at E : join A E, then apply A E successively to the circumference as chords, and A B C D E will be the pentagon required.

PRACTICAL PROBLEMS PERFORMED ON THE GROUND.

Pkob. I. To erect a perpendicular from a given point C to a right line A B, by means of a Tape or String. Pl. 5. Fig. i.

Take two equal distances C A and C B, extend the tape to any length greater than A B, double it, put a pin in the meeting, open out the tape ; place one end of the double distance, or the ring at A, and let another person hold the other end at B, and a third person take hold of the string at the pin, and stretch it out to D, then the stake at D and the point C will be in a perpendicular to A B. To illustrate this, suppose C A, C B each ten feet, then A B is twenty feet ; you may extend the line to forty feet, which being doubled, the division will fall upon twenty feet, let the ring be put upon A, the divison of forty upon B; let the division of twenty feet in the middle of the line be extended out to D, while the ends A and B are held fast : then drive in the stake D, and it will give the point whence the perpendicular may be drawn to C, upon the right line A B.