ROOF. 



..md cutting the wall-plate in a reverfe form to fit it. This 

 method is far preferable to the other, as it is not liable 

 to be drawn, which the other is very Subject to, when the 

 timber Ihrinks. 



Ridge-tree is a piece of timber fixed in the vertex of a roof, 

 where the common rafters meet on each fide of it ; the upper 

 edge of it is higher than the rafters, for the purpofe of fixing 

 the lead which goes over it to cover the ends of the dates 

 in the upper courfe. 



Straps are thin pieces of iron running acrofs the junction 

 of two or more parts of a trufs or frame of carpentry, 

 branching out from the interfedtion in the direction of the 

 feveral pieces, for the purpofe of fecuring them to each 

 other. They ought always to be double, wiss. one (trap 

 on each fide ; and their ends Itrongly bolted to each of the 

 pieces. 



The ufes of the various parts are illullrated as follows ; and 

 here it may be proper to obferve, that though every one of 

 the parts above defined may be found in the fame roof, it 

 is not necefiary that a complete roof Should have all thefe 

 parts ; the introduction of many of them depends on the dif- 

 itance of the walls, the contour of the roof, the partitions 

 below, the quantity of head-room wanted in the garret- 

 rooms, &c. 



Of common roofs, the fimpleft conftru&ion is that which 

 confilts of two rafters, A B and 13 C, Plate XLII. fig. 8; 

 D and E are wall-plates, on which the feet A and C of the 

 rafters reft ; the bottom of the rafters is cut in the form of 

 a right angle (called by workmen a bird's mouth), reverfed 

 to the wall-plate, and is fixed to it with nails ; but this 

 form can only be applied to buildings that have their walls 

 at no great diltance from each other. 



The next form is that of having two rafters, A B, B C, 

 Plate XLII._/fj. 7, a collar-beam D E, with two wall-plates, 

 F and G, below. This form will admit of a greater diftance 

 between the walls than the other : the beam is placed in the 

 fituation D E, in order to give head-room within ; but 

 when the (pan, EG, of the walls is considerable, the parts 

 A D and CE being confidered as levers, and acted upon by 

 the re-action of the walls, the rafters are either liable to 

 be broken at the points D and E, or curved with a con- 

 cavity on the upper edges. 



The third form of common roofs confifts of two rafters, 

 A B, BC, PlateXLll. fig. 10, a tic-beam AC, for pre- 

 venting the rafters from pulhing out the walls, a collar or 

 ftraining-beam I) E, and two puncheons, or ftuds, FG and 

 H I, for keeping the rafters ftraight : this conftruttion is 

 ufed for cheapneSs, and may be executed with fafety in 

 houles not exceeding forty-five feet wide ; but it is necefiary 

 to have partitions immediately below, or at no great diftance 

 from the ftuds. Inftead ot Supporting every oppofite pair 

 of rafters, as in this example, 111 many roofs of this con- 

 Itruclion, the rafters take the place of principals, and are 

 fixed at 7, 8, 9, or 10 feet from each other, and purlins run 

 over the heads of the puncheons at K and L ; and at the 

 ends of the collar-beams at M and N, between every two 

 rafters, fmall rafters are fixed to the purlins, the wall-plates 

 at bottom, and the ridge-tree at the top. 



Tin molt Simple continuation of a trufs is that confifting 

 of the following pan;, Plate X L 1 1 .fig. 9. A B the tie-beam, 

 cocked upon the wall-plates C and 1) ; E K the king-pod ; 

 A G and B H principal rafters, fixed to the king-poll at the 

 joggles, G and H ; L M and N O ftrutts, mortifed into the 

 rafters at L and N, and joggled to the king-poll at M and O. 

 Other names of timbers will be Full v illullrated by the de- 

 scriptions ot other roots in due order of SucceSSion. What 

 has been faid may Suffice lor the prefent. 



Prop. III. 



The pofition of feveral rafters, A B, BC, C D, D E, &c. 

 Plate XLIII. fig. 1, being given in a vertical plane, joined 

 together and moveable about the angular points B, C, D, E, 

 &c. while the points A and G remain ftationary ; it is re- 

 quired to find the proportion of the forces at the angles, fo 

 that the rafters may be kept in equihbrio. 



Through the points B, C, D, E, &c. draw the vertical lines 

 Bi'.Cra, Dp, Ej-, &c. being the direction of the forces. Make 

 Bi of any indefinite length, and complete the parallelogram 

 B h i I. Make C/ equal to l&i, and complete the parallelo- 

 gram Clmn. Proceed in this manner with all the remaining 

 parallelograms, making the two oppofite forces 111 the 

 direction of each rafter equal to each other, and the diagonals, 

 B/', Cm, Dp, E s, Sec. will repreSent the forces required, as 

 is evident from the construction. Then, to find the propor- 

 tion of the weights upon any two angles, the fine of any 

 angle is the fame with the fine of its Supplement, therefore 

 the fine of the angle A BC is the fame as the fine of Kb I; or 

 B i i ; and the fine of B C D the fame as the fine ofCnm) 

 likewife the line of the angle C m I is equal to the fine of the 

 alternate angle mCn, and the fine of the angle D po is equal 

 to the fine ef the angle p D q ; moreover, the line of the 

 angle iY>k is equal to the line of the angle m C /, and the fine 

 of the angle m C » is equal to the fine of the angle ^>D 0, and 

 fo on : then, becaufe the fides of triangles are as the fines 

 their oppofite angles, it will be by trigonometry, 



B i : B i, or C / :: S • B I « r or A B C : S . B i I, or i B b 

 CI: I m, or D :: S . C m I, or m C n : S . m C /, or ;' B i 

 Do: f, or Er :: S . D/>o,or p 1) q : S . p Do, or mCn 



E r : s r, or F a :: S . E s r, or v F u : S . s E r, or p D q 

 F u : F «:: S • Fvu, or v F no : S . vu F,orE FG 



Therefore B i : F v :: S . A B C x S . v F u x S . v F w 

 :S.iBiixS.«Bix S . E F G 



,.,, f _. r S.ABC S.EFG 



I herefore B / : F v :: . n Q -^r7> i o r 5 P~ 



£> . ID b x S.iBl S.vYuxb.v Fid 



That is, the weights on any two angles are as the fines 

 of thefe angles directly, and reciprocally as the product of 

 the fines of the two parts of thefe angles, divided by the ver- 

 tical lines. 



Cor. 1. — Hence the weights on any two angles are as 

 the lines of the angles directly, and as the product of the 

 colines of the two parts of thefe angles reciprocally. For 

 draw B H perpendicular to B ;', and produce / B and A B 

 to I and K ; then will the angle K B I, equal to the angh- 

 h B i, be the cofine of the angle H B K ; wss. thecofineof 

 the angle of elevation of lh<- rafter A B above the horizon ; 

 and becaufe C B I is the Supplement of i B C, the angles C B 1 

 and C B ;' have the lame line, and the angle C B I is the co- 

 lli, e ill the angle 11 li C; via. the angle of elevation of 

 the rafter B C. 



Cur. 2. — Hence alio, the weights on any two angles are 

 .is the 1 1 : i l s of the angles directly, and as the produces of 

 the Secants of elevation jointly, becaufe the Secants of any 

 twoangl 1 are 1 ipi ally as the colines of thefe angles. 



Cor. 3. — The force which any raSter makes in its own di- 

 11 1 tion is as the Secant of its elevation. For make A P equal 

 to B h ; draw the lines P N, I II, n L, &C. parallel to the 

 vertical lines P. /', C m, Sec. and draw A N, B H, C L, 

 &c. paralli Ito the horizon ; then becaufe the angles N A P, 



I I li /•, 1.1'h, &c. 1 elevation, and AN, 

 B 1 1, C L, &c. arc all • qual, S A N, B H, C L, See. bo 



confidered as radii, A P, B /, C ••;, .^e. are the Secants 

 of elevation, which alio repreient the torces on the ratters. 

 Cor. 4. — Hence the horizontal prelfures at A and G are 



equal ; 



