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the design, after whicti, they are to be prepared or formedaccording to the rules of constructive carpentry.

We shall here state a few of the elementary propositions,with the principles of trussing, and offer some observationson the best forms of bodies constructed of timber work, to beused under various circumstances. And as it is impossible,in complex parts, to give all the minutiae with mathematicalprecision, this deficiency will, in a great measure, be compen-sated by general information.

The application of mechanical principles to carpentry wasfirst introduced in this country by Professor Robinson, ofEdinburgh, in the Encyclopedia Britannica , whose elaboratepapers on this subject prepared the way for that investiga-tion which has since been so ably followed out by others.In 1814, Mr. P. Nicholson drew up a complete article in everydepartment of carpentry, for Rees’s Encyclopedia , where thisbranch of the art, as depending upon the principles ofmechanics, was particularly inculcated ; and though severalof the plates have been engraved and published some yearsago, the manuscript relative to this particular branch hasbeen retained for the article Roof, in this work, to which,indeed, it chiefly pertains.

In this application of mechanical science, Alex. Nimmo,Esq., F.R.S.E., the celebrated engineer, also published a veryneat and well-connected theory of mechanical carpentry,under the article Carpentry, in the Edinburgh Encyclo-pedia ; but perhaps the best work extant on this subject isTredgold ’s Elementary Principles of carpentry, whichcontains a mass of the most valuable information, in the mostconvenient and available form.

Under the article Curb Roof, of the present Work, thereader will find an investigation of the best forms fora roof,restricted to certain data. The observations on the strengthof timber are reserved for that article; but the practicalrules derived therefrom will be here introduced preparatoryto the general design of mechanical carpentry; and as thesewill be chiefly applicable to practice, we shall show the rulesunder their most simple form ; discarding such as, thoughaccurate, would be too complex for common use.

To find the comparative strength of timber.Definition. — The depth of a piece of timber is its dimen-sion in the direction of the pressure.

Proposition I.— To find the comparative strength ofdifferent timbers.

Rule.— Multiply the square of the depth of each pieceinto its thickness ; and each product being divided by itsrespective lengths, will give the proportional strength ofeach.

Example. —Suppose three pieces of timber of the followingdimensions :

The first 6 inches deep, 3 inches thick, and 12 feet long.The second 5 inches deep, 4 inches thick, and 8 feet long.The third 9 inches deep, 8 inches thick, and 15 feet long.The comparative weight that will break each piece isrequired.

OPERATIONS.

First. Second.

6 deep 5 deep

6 5

36

3 thick

25

4 thick

Length 12 ) 1089

Length 8 ) 100

12 and a half.

Third.

9 deep9

81

8 thick

Length 15 ) 648 (43 and a fifth.60

Therefore, the weights that will break each are nearly'proportion to the numbers 9, 12, and 43, leaving out t ^fractions; in which it is to be observed, that the numbe r ,is almost five times the number 9 ; therefore the third P 1 ®of timber will bear almost five times as much weight as *first ; and the second piece nearly once and a third 1 .weight of the first piece ; because the number 12 is one 9a third greater than the number 9. e

The timber is supposed to be everywhere of the "texture, otherwise these calculations cannot hold true. , JProposition II.— Given the length, breadth, and ^Py-ea piece of timber ; to find the depth of another piece, tr"length and breadth are given, so that it shall bear the s aweight as the first piece, or any number of times more. , $Rule.—M ultiply the square of the depth of the first p 1 ® j,into its breadth, and divide that product by its length :tiply the quotient by the number of times you wouldthe other piece to carry more weight than the first; 9 jmultiply the product by the length of the last pie ce >'divide the product by its width; out of this last qu ot 'extract the square root, which is the depth required. 6Example 1 .—Suppose a piece of timber 12 feet lot’s’ 5inches deep, 4 inches thick ; another piece 20 feet l 0ll * c einches thick ; required its depth, so that it shall bear 1the weight of the first piece.

Proof.

6 deep 9.7

6 9.7

12 ) 144

12

2 times24

20 length

67.9

873

94.09 1

1.91 remainder

96.00

5

5 ) 480

20)480

24

96 ( 9.7, or 9.8 nearly, for the depth.81

187 ) 15001309

191 on* ’

Example 2. —Suppose a piece of timber 14 feet 1

inches deep, 3 inches thick ; required the depth 01