CON

193

CON

th

Keom^ 10 ' 06 tW® is not at times in the power of the'The e,ter ’ ^ ul; w ' len it is, he ought to avail himself of it.ti 0tl s ' tUa tion of a point must be ascertained by the intersec-it w :,, * Wo lines, and since a line cannot be without breadth,a p ,: )e a n oblong, and the intersection of two lines will bep ara ,? e l°gram; when the lines cross at right angles, theangj„ e °o ram will form a square; and when at obliquere Vur be a rhombus. In all these cases, the point

le] 0 „ le< * ' s ' n the intersection of the diagonals of the paral-l he iti? 11 ' -^° w the least of all the parallelograms formed by

hat tl eisect ' on °f two lines of equal breadth, is a square;lo n ' e Sweater the obliquity of the lines of intersection, thefigure ^* e t l‘ e rhombus; and as the drawing of theof t] le ( < rP <in ds upon vision, the more indistinct will the angles

ti 0n o p ‘‘Sure so formed become, and consequently the situa-tl !e point must be almost guessed at. In some cases,

in of the intersection is of little consequence ; as,

the j nt ln " a curve by points, where the lines, which form•Uahe erseetion , fall very nearly in with the curve itself, or|, eoni„. V , ei ^ acute angles with the tangent, unless it be

eqai. j wmu

fiat if to fi n< l the points in the curve in a given ratio;frotp ’ )tl Hading a point, through which a line is to passpart s ^? 0t l ler given point, to meet a line, of which somethe a, 6 ether given or found, or to be found, it will be of■Ui 0tl of 08 . 1 consequence to determine with accuracy the situ-the ot | t le intermediate point; for the point ascertained inficcordi^ 5 *" J' ne w ill vary from its true place, more or less,

intersection.

g to the distance of the intermediate point found byrser' - 1 J

notberl«e 1"luitv

°hliq |)e er source of error, arising from the intersection ofnblin„ ; .."? ,!s . which will also be more or less accurate, as the1:i leas or greater, is, when one or both the linesdrawn through their extremities; even the

ejntg 11 , a dne being drawn its own breadth, will makethe rho, i ection f ’ a11 its own length (which is the diagonal ofu bo i, e to the end of the true intersection. Let it

Nbe 0 ° f n8idered . that the longer diagonal of the rhombusf atin-i,. ! l n y length whatever, depending upon the obliquity• Scr ipt| S 01lned by the two intersecting lines. In the! n a lii le 0l ; ' of adia g ram, when different points are ascertained. 01 iter t 0 ’ * n r )0 ' n ting out the line to the reader, it would be'!' s teu ( | 0 j. nai ne all the letters in the order as they stand,

*ula rlv . Pointing out the line by two of the letters, par-

•- ...

an) 68 i® still more necessary when several

111 ust

ci-d

My in . -

Cone a complicated diagram, where many other lines-s a'ee/ 16 ^' fbis is still more necessary when severaly givg 8 at same point, as the use of all the letters notio. a mn re i mme( j; a t e c i ue to identify the line from- shortens the description, as the same letters

tli e f 8ea a = a in> in pointing out the other lines which

of t

p Ut5 . n l : re petition, after a line has been drawn in the* ne ‘ n t)* 811 ' 011 . to cut a former, of saying, “ cutting such

. tfie f r arnier l’ ne ) and will thus supersede the necessity. ^laire,! " ent repetition, after a line has been drawn in the

Si >Ul e

8e ^ P° ,nt ” A or b, or whatever it may be; as the

j tlo n. cannot be in two lines, except at their inter-

at , r , l<ic 6s^ n .? *^‘ e boundaries of angular figures, it will only. 1 the 1 y to i— - • - • • -

extr/j,- 0 . name tb e letters progressively, as they stand*ap ~ ° ut tl, B m ! es . °P the sides, that is, at the angles; but to

r ac e

W' natug enclosure or perimeter, it would be neces-p t . b e first letter again, at the end of the series ofbe 8 , true, that a triangle, a quadrilateral, &c.of ! a > by g. understood, without naming the first letter® side* ln S the figure at the same time, or the number

^bo

«g. * as j n polygons the last side will always be

clu >r,l!. Se f numer ations and repetitions of letters mayJ> they lead sooner to an understanding of the

3 D

construction, shorten the language, and give accuracy to the | ■description. 1 !

CONSTRUCTIVE CARPENTRY shows the method of j !reducing wood into forms, and joining the parts, as directed j (by the rules of Descriptive Carphntrv, or by the laws ofstrength, and thereby forming a complete design.

It is much to be regretted that the first principles of thisdepartment of the art are frequently so little understood by !

those who are called upon to put them into practice. The !

young carpenter too often follows blindly in the track ofthose who have gone before him, without inquiry, and with-out even attempting to understand the mechanical construc-tion of the work he has just put together. We do not mean :that the practical builder must necessarily make himself ;master of the higher branches of science, but that it would 1obviously be of advantage to him that he should acquire that 1general knowledge of the elementary principles of the art, jwhich would enable him to select the best materials, andemploy them in the best manner. i

Every species of construction should be characterized bystability, and a careful regard to economy of materials. I

These objects can only be obtained by judicious combinations j jof the substances used, so that the greatest amount of ! jstrength be secured with the smallest expenditure of mate- j irial. Uidess the builder possess a considerable knowledge of | jthe principles of mechanics, unless he be acquainted with ; jthe effect of pressure, and the resisting powers of different , ;materials, he cannot comprehend, much less design, such ’ jcombinations ; but becomes a mere labourer putting together j ;the several parts of a work, without knowing their relative ! jdependence on each other, or the strength, or want of j !strength, of the whole. He is, indeed, from the want of such ; jknowledge as we have described, incapable of judging whatare the best forms of construction, or which of several !

modes of uniting timbers it is most advisable to make use of. j

It is the province of constructive carpentry to show this, and 1

the carpenter who is desirous to make himself thoroughly 'acquainted with his business, should study to acquire not ; :only a practical knowledge of its details, but also some insight iinto the principles on winch it is founded. 1 1

Constructive carpentry, it has been observed, is the method ! 'of reducing wood into forms, and the combining of several j jparts into a complete, firm whole. In most works, especially i !those of magnitude, it will frequently be necessary to join i ione or more pieces of timber, in order to obtain beams, &c. ;of sufficient size, and in order to economize material. The !

processes by which these objects are effected is a subject of j

the greatest importance, as on their being properly and sub- j

stantially performed depends the stability of the structure in j

which they are used. Under this article then we propose todescribe some of the most approved methods of uniting tim- \

ber, and to treat of the following operations, viz., the length- j

ening of beams, either by scarfing or joining them in pieces ; j

the strengthening of beams by trussing; the methods of join- i

ing two timbers at angles, in any given direction ; and, lastly, j

the mode of connecting several timbers, in order to perform j jcertain functions required by the design. 1

To lengthen a piece of timber, is to join or fasten two !separate pieces, so that a portion of the end of the onepiece shall lap upon a portion of the end of the other, thesides of both making but one continued surface, and forminga close joint, called a scarf.

It is evident, that in the formation of a continued straighttimber, if the joint consist of a plane, or planes, at rightangles to two opposite sides of the compound piece, but notat right angles to the plane of the other two opposite sides,the plane, or several planes, forming the scarf, will make the