Class . 
 Book_ 
 
 T 
 
 H SgqZ 
 
 
 .Hi^ 
 
 
 /So>7 
 
f<. 
 
 THE 
 
 CARPENTER'S AND JOINER'S 
 
 HAND-BOOK: 
 
 CONTAINING 
 
 A COMPLETE TREATISE ON FRAMIXG 
 HIP AND VALLEY ROOFS. 
 
 TOGETHER WITH 
 
 MUCH VALUABLE INSTRUCTION FOR ALL MECHANICS AND 
 
 AMATEURS, USEFUL RULES, TABLES, ETC., 
 
 NEVER BEFORE PUBLISHED 
 
 / . BY 
 
 rr 
 PEACTICAL AKCniTECT AND BFILDEK, 
 
 ILLUSTRATED BY THIRTY-SEYEN ENGRAVlNaS. 
 
 NEW YORK : 
 
 JOHN WILEY & SOX, 535 BROADWAY, 
 
 1867. 
 

 Entered according to Act of Congress, in the year 1868, 
 
 By H. W. holly, 
 
 In the Clerk^s Office of the District Court of the United States for 
 the District of Connecticut 
 
 By Transfer from 
 U.S. Naval Academy 
 Aug. 26 1932 
 
 # 
 
 sit 
 
4 
 
 ^ PEEFACE, 
 
 This work has been undertaken by the 
 antbor to supply a want long felt by tbe 
 trade: tbat is, a cbeap and convenient 
 "Pocket Guide/' containing tbe most use- 
 ful and necessary rules for tbe carpenter. 
 
 Tbe writer, in bis progress " tbrougb tbe 
 mill," bas often felt tbat sucb a work as tbis 
 would bave been of great value, and some 
 one principle bere demonstrated been worth 
 many times tbe cost of tbe book. 
 
 It is believed, tberefore, tbat tbis book will 
 commend itself to tbose interested, for tbe 
 reason tbat it is cbeap, tbat it is plain and 
 easily understood, and tbat it is useftd. 
 
CONTENTS. 
 
 AET. 
 
 To find the lengths and bevels of hip and common 
 
 rafters 1 
 
 To find the lengths, &c., of the jacks 2 
 
 To find the backing of the hip , 3 
 
 Position of the hip-rafter 4 
 
 Where to take the length of rafters 5 
 
 Difierence between the hip and valley roof 6 
 
 Hip and vaUey combined *l 
 
 Hip-roof without a deck 8 
 
 To frame a concave hip-roof 9 
 
 An easy way to find the length, &c., of common 
 
 rafters 10 
 
 Scale to draw roof plans 11 
 
 To find the form of an angle bracket 12 
 
 To find the form of the base or covering to a cone. . . 13 
 
 To find the shape of horizontal covering for domes. . 14 
 
 To divide a line into any number of equal parts 15 
 
 To find the mitre joint of any angle 16 
 
 To square a board with compasses 17 
 
 To make a perfect square with compasses 18 
 
 To find the centre of a circle 19 
 
 To find the same by another method 20 
 
 Through any three points not in a line, to draw a 
 
 circle 21 
 
 Two circles being given, to find a third whose area 
 
 shall equal the first and second 22 
 
6 CONTENTS. 
 
 ▲ST. 
 
 To find the form of a raking crown moulding 23 
 
 To lay out an octagon from a square 24 
 
 To draw a hexagon from a circle 25 
 
 To describe a curve by a set triangle 26 
 
 To describe a curve by intersections 2*1 
 
 To describe an elliptical curve by intersection of 
 
 lines 28 
 
 To describe the parabolic curve 29 
 
 To find the joints for splayed work 30 
 
 Stairs 31 
 
 To make the pitch-board 32 
 
 To lay out the string 33 
 
 To file the fleam-tooth saw 34 
 
 To dovetail two pieces of wood on four sides 35 
 
 To splice a stick without shortening 36 
 
 The difference between large and small files 3*7 
 
 Piling wood on a side-hill 38 
 
 To find the number of gallons in a tank 39 
 
 To find the area of a circle 40 
 
 Capacity of wells and cisterns 41 
 
 "Weights of various materials 42 
 
THE CARPENTER'S AND JOINER'S 
 
 HAND-BOOK- 
 
 HIP AND VALLEY EOOFS. 
 
 The framing of liip and valley roofs, being 
 of a different nature from common square 
 rule framing, seems to be^ understood by 
 very few. It need scarcely be said, that it is 
 very desirable that this important part of a 
 carpenter's work should be familiar to 
 every one who expects to be rated as a first- 
 class workman. The system here shown is 
 proved, by an experience of several years, 
 to be perfectly correct and practicable ; and, 
 as it is simple and easily understood, it is 
 believed to be the best in use. Care has 
 been taken to extend the plates so as to de- 
 
8 
 
 THE carpenter's 
 
 monstrate eacli position or principle by it- 
 self, so that the inconvenience and confusion 
 of many lines and letters mixed np with 
 each other may be avoided. 
 
 Article 1. — To find the lengths and levels 
 of hip and common rafters. 
 
 Fig. 1. 
 
 Let j9jf>jp (Fig. 1) represent the face of the 
 plates of the building ; d^ the deck-frame : 
 
hand-book:. 9 
 
 a is tlie seat of the hip-rafter; 5, of the 
 jack ; and c^ of the common rafter. Set the 
 rise of the roof from the ends of the hip and 
 common rafter towards e e^ square from a 
 and G / connect^ and e^ then the line from 
 fioe will be the length of the hip and com- 
 mon rafter, and the angles at ^ ^ will be the 
 down bevels of the same. 
 
 2. To find the length andhevel of the jack- 
 rafters, 
 
 l (Fig. 1) is the seat of a jack-rafter. Set 
 the length of the hip from the corner, g^ to 
 the line on the face of the deck-frame, and 
 join it to the point at g. Extend the jack h 
 to meet this line at A/ then from i to A will 
 be the length of the jack-rafter, and the 
 angle at h will be the top bevel of the same. 
 
 The length of all the jacks is lound in the 
 same way, by extending them to meet the 
 line A. The dov^n bevel of the jacks is the 
 same as that of the common rafter at e, 
 
 3. To find the hacking of the hip-rafter. 
 At any point on the seat of the hip, a (Fig. 
 
10 THE CAEPENTER's 
 
 1), draw a line at riglit angles to a^ extending 
 to the face of the plates at ^ ^ / upon the 
 points where the lines cross, draw the half 
 circle, just touching the line/*^; connect the 
 point aty, where the half circle cuts the line 
 a^ with the points ^ ^ / the angle formed at^ 
 will be the proper backing of the hip-rafter. 
 
 It is not worth while to back the hip-raf- 
 ter unless the roof is one-quarter pitch or 
 more. 
 
 4. It is always desirable to have the hip- 
 rafters on a mitre line, so that the roof will 
 all be the same pitch ; but when for some 
 reason this cannot be done, the same rule is 
 employed, but the jacks on each side of the 
 hip are different lengths and bevels. 
 
HAND-BOOK, 
 
 11 
 
 Fig. 2. 
 
 The heavy line from d (Fig. 2), shows the 
 seat of the hip-rafter ; a and 5, the jacks. Set 
 the rise of the roof at e / set the length of 
 the hip d e^ from d to/* on one side of the 
 deck, and from dio g on the other side ; ex- 
 tend the jack 5, and all the jacks on that 
 side, to the line df^ for the length and top 
 bevels ; extend the jack a^ and all on that 
 side, to the line d g^ for the length and bevels 
 on that side of the hip. The down bevels 
 of the jacks will be the same as that of the 
 common rafters on the same side of the 
 roof. 
 
12 
 
 THE CAEPENTER S 
 
 5. The lengths of hips, jacks, and valley- 
 rafters should be taken on the centre line, and 
 the thickness or half thickness allowed for. 
 (See Fig. 3.) 
 
 Fig. 3. 
 
 6. The valley-roof is the same as the hip- 
 roof inverted. The principle of construction 
 is the same, with a little different applica- 
 tion. 
 
HAKD-BOCK. 
 
 13 
 
 Fig. 4. 
 
 Let a h (Fig. 4) represent the valley-rafter ; 
 j j are corresponding jack-rafters. Set the 
 rise of the roof from aio c ; connect h and 
 c : from J to ^ is the length of the valley- 
 rafter, and the angle at c the bevel of the 
 same ; set the length h c on the line from a; 
 extend the jack^ to meet the line o d at e f 
 then from etof is the length of the jack, 
 and the angle at e the top bevel of the same. 
 
 7. When the hip and valley are combined^ 
 
14 
 
 THE carpenter's 
 
 SO that one end of tliejack is on the hip^ and 
 the other 07i the valley. 
 
 Fig. 5. 
 
 a h (Fig. 5) is the liip, and c d the valley- 
 rafters. Find the length of each according 
 to the previous directions ; find the lines e 
 and/* as before. 
 
 Extend the jacks j j to the line e^ for the 
 top bevel on the hip : extend the same on 
 the other end to the line/*, for the top bevel 
 on the valley ; the whole lengths of the jacks 
 
 >*!> 
 
HAND-BOOK. 
 
 15 
 
 is from the line/* to the line e. If the hip 
 and valley rafters lie parallel, the bevel will 
 be the same on each end of the jack. 
 
 8. In framing a hip-roof without a deck- 
 ing or observatory, a ridge-pole is nsed, and 
 of such a length as to bring the hip on a 
 mitre line; but this ridge-pole must be cut 
 half its thickness longer at each end, or the 
 hip will be thrown out of place and the 
 whole job be disarranged. 
 
 Fisr. 6. 
 
 This is illustrated by the figure. Suppose 
 the building to be 16 by 20, the ridge would 
 require to be four feet long ; but if the stick 
 is four inches thick, for instance, then it 
 
16 
 
 THE CARPENTER S 
 
 should be cut four feet four inclies long, so 
 that the centre line on the hip, a, will point 
 to the centre of the end of the ridge-pole, 
 J, at four feet long. This simple fact is often 
 overlooked. 
 
 9. To frame a concave hip-roof. — (This 
 is much used for verandas, balconies, sum- 
 mer-houses, &c.) 
 
 To find the curve of the hip. 
 Let a (Fig. 7) be the common rafter in its 
 true position, the line h being level. Draw the 
 
HAND-BOOK. 17 
 
 line G Cj on the angle the hip-rafter is to lie, 
 generally a mitre line ; draw the small lines 
 0^ parallel to the plate j9. The more of these 
 lines, the easier to trace the curve ; continue 
 the lines o o o^ where they strike the line c c^ 
 square from that line ; set the distances 1, 2, 
 3, 4, &c. (on a^ from the line V) on the line 
 G G^ towards e^ at right angles from c g ; 
 through these points, 2, 4, 6, 8, &c., trace 
 the curve, which will give the form of the 
 hip-rafter. 
 
 To get the joints of the jack-rafters, take 
 a piece of plank d^ (Fig. 7), the thickness 
 required, wide enough to cut a common 
 rafter; mark out the common rafter the 
 full size. Then get the lengths and bevels, 
 the same as a straight raftered roof, which 
 this will be, looking down upon it from 
 above; then lay out your joints from the 
 top edge of the plank, as/y ; cut these joints 
 first, saw out the curves afterwards, and you 
 will have your jacks all ready to put up. 
 Cut one jack of each length by this method, 
 
18 THE carpenter's 
 
 then use this for a pattern for the others, so 
 as not to waste stuff. It will be seen that 
 the down bevel is different on each jack, 
 from the curve^ but the same Jfrom a straight 
 line, from point to point of a whole rafter. 
 
 10. A quick and easy way to find the 
 lengths and hevels of common rafters. 
 
 Suppose a building is 40 feet wide, and 
 the roof is to rise seven feet. Place your 
 steel square on a board (Fig. 8), twenty- 
 inches from the corner one way, and seven 
 inches the other. The angle at c will be 
 the bevel of the upper end, and the angle 
 at d^ the bevel of the lower end of the rafter. 
 
 Fiff. 8. 
 
 11. The length of the rafter will be from 
 a to J, on the edge of tlie board. Always buy 
 a square with the inches on one side divided 
 
HAKD-BOOK. 
 
 19 
 
 into twelfths, then you have a convenient 
 scale always at hand for such work as this. 
 The twenty inches shows the twenty feet, 
 half the width of the building ; the seven 
 inches, the seven foot rise. Now the distance 
 from a to 5, on the edge of the board, is 
 twenty-one inches, two-twelfths, and one- 
 quarter of a twelfth, therefore this rafter will 
 be 21 feet 2^ inches long. 
 
 12. To find the form of an angle IracTcet 
 for a cmmice. 
 
 Fig. 9. 
 
 Let a (Fig. 9) be the common bracket ; 
 draw the parallel lines o o o, to meet the 
 
20 
 
 THE CARPENTER S 
 
 mitre line c ; square up on each line at c, 
 and set the distances 1, 2, 3, 4, (fee, on the 
 common bracket, jfrom the line d^ on the 
 small lines from c ; through these points, 2, 
 4, 6, &c., trace the form of the bracket. 
 This is the same principle illustrated at Fig. 
 7 and Fig. 20. 
 
 13. To find the form of a lase or covering 
 for a cone. 
 
 Fiff. 10. 
 
 Let a (Fig. 10) be the width of the base 
 to the cone. Draw the line h through the 
 centre of the cone ; extend the line of the 
 side G till it meets the line h ^i d ; on d for 
 a centre, with 1 and 2 for a radius, describe 
 
HAND-BOOK. 
 
 21 
 
 e^ wluch will be the shape of the base re- 
 quired; y*will be the joint required for the 
 same. 
 
 14. To find the shape of horizontal cover- 
 ing for circular domes. 
 
 The principle is the same as that employed 
 at Fig. IO5 supposing the surface of the dome 
 to be composed of many plane surfaces. 
 Therefore, the narrower the pieces are, the 
 more accurately they will fit the dome. 
 
 d 
 
 fl 
 
 yT 
 
 9 ^ry 
 
 / 
 
 -- fc ^ ^ 
 
 / 
 
 s\ 
 
 1 
 
 4\ 
 
 I ^ 
 
 \ 
 
 1 c 
 
 i 
 
 Fig. 11. 
 
 Draw the line a through the centre of the 
 dome (Fig. 11) ; divide the height from h to 
 
THE CAEPENTEr's 
 
 c into as many parts as there are to be ' 
 courses of boards, or tin. Throngli 1 and 2 
 draw a line meeting tbe centre line at d ; 
 that point will be the centre for sweeping 
 the edges of the board g. Through 2 and 
 3, draw the line meeting the centre line at 
 e / that will be the centre for sweeping the 
 edges of the board Tc^ and so on for the other 
 courses. 
 
 15. To divide a line into any number of 
 equal parts. 
 
 Let a h (Fig. 12) be the given line. Draw 
 the line a c^ at any convenient angle, to ah ; 
 set the dividers any distance, as from 1 to 2, 
 and run off on a c^ as many points as you 
 wish to divide the line a l into ; say 7 parts ; 
 
HAND-BOOK. 23 
 
 connect tlie point -7 with l^ and draw the 
 
 lines at 6, 5, 4, (fee, parallel to the line 7 
 
 5, and the line a l will be divided as desired. 
 
 16. To find the mitre joint of any angle. 
 
 Fig. 13. 
 
 Let a and h (Fig. 13) be the given angles ; 
 set off from the points of the angles equals 
 distances each way, and from those points 
 sweep the parts of circles, as shown in the 
 figure. Then a line from the point of the 
 angle through where the circles cross each 
 other, will be the mitre line. 
 
24 THE carpenter's 
 
 17. To square a hoard with compasses. 
 
 Fig. 14. 
 
 Let a (Fig. 14) be the board, and h the 
 point from which to square. Set the com- 
 passes from the point h any distance less 
 than the middle of the board, in the direc- 
 tionof e. Upon c for a centre sweep the 
 circle, as shown. Then draw a straight line 
 from where the circle touches the lower edge 
 of the board, through the centre c^ cutting 
 the circle at d. Then a line from h through 
 6?, will be perfectly square from the lower 
 edge of the board. This is a very useful 
 problem, and will be found valuable for lay- 
 ing out walks and foundations, by using a 
 line or long rod in place of compasses. 
 
hand-book:. 
 
 25 
 
 18. To make a perfect square with a. jpair 
 of compasses. 
 
 Tiff. 15. 
 
 Let a I (Fig. 15) be tlie length of a 
 Bide of the proposed square ; upon a and h^ 
 with the whole length for the radius, sweep 
 the parts of circles a d and h c. Find half 
 the distance from a to e at f ; then upon e 
 for a centre sweep the circle cutting/*. Draw 
 the lines from ^ and 5, through where the 
 circles intersect at c and d / connect them 
 at the top and it will form a perfect square. 
 
26 THE carpenter's 
 
 19. To find the centre of a circle. 
 
 Upon two points nearly opposite each 
 other, as (3^ & (Fig. 16), draw the two parts 
 of circles, cutting each other ^X c d ; repeat 
 the same at the points e f ; draw the two 
 straight lines intersecting at ^, which will 
 be the centre required. 
 
HAND-BOOK. 
 
 20. Another method. 
 
 27 
 
 Fig. IT. 
 
 Lay a square upon the circle (Fig. 17), 
 with the corner jnst touching the outer edge 
 of the circle. Draw the line a^l) across the 
 circle where the outside edges of the square 
 touch it. Then half the length of the line a 
 h will be the centre required. No matter 
 what is the position of the square, if the cor- 
 ner touches the outside of the circle, the re- 
 sult is the same, as shown by the dotted 
 lines. 
 
28 THE carpenter's 
 
 21. Through any three points not in a line^ 
 to draw a circle. 
 
 Fiff. 18. 
 
 Let a h c (Fig 18) be the given points. 
 Upon each of these points sweep the parts 
 of circles, cutting each other, as shown in the 
 figure ; draw the straight lines d d^ and where 
 they intersect each other will be the centre 
 required. This method may be employed 
 to find the centre of a circle where but part 
 of the circle is given, as from a to c, 
 
 22. Two circles 'being given^ to find a third 
 whose surface or area shall equal the first 
 and second. 
 
HAND-BOOK, 
 
 29 
 
 Fig. 19. 
 
 Let a and h (Fig. 19) be tlie given circles. 
 Place the diameter of each at right angles to 
 the other as at 3, connect the ends at c and 
 dy then c d will be the diameter of the 
 circle required. 
 
 23. To find the form of a raking crown 
 moulding. 
 
 Fij?. 20. 
 
30 THE carpenter's 
 
 m (Fig. 20) is the form of the level crown 
 moulding; r c h the pitch of the roof. 
 Draw the line l^ which shows the thickness 
 of the moulding. Draw the lines o o o, par- ' 
 allel to the rake. Where these lines strike 
 the face of the level moulding, draw the hor- 
 izontal lines I5 2, 3, &c. Draw the line y 
 square from the rake : set the same distances 
 from this line that you find on the level 
 moulding 1, 2, 3, &c. Trace the curve 
 through these points 1, 2, 3, cfec, and you 
 have the form of the raking moulding. 
 
 Hold the raking moulding in the mitre 
 box, on the same pitch that it is on the roof, 
 the box being level, and cut the mitre in 
 that position. 
 
 24. To make an octagon^ or eight-sided 
 figure^ from a square. 
 
HAND-BOOK. 
 
 31 
 
 Fiff. 21. 
 
 Let Fig. 21 be the square ; find tlie centre 
 a J set tlie compasses from the corner J, to 
 a ; describe the circle cutting the outside line 
 at c and d ; repeat the same at each corner, 
 and draw lines c e^ f g\lid^ and ij. These 
 lines will form the octagon desired 
 
 25. To draw a hexagon or six-sided fig- 
 ure on a circle. 
 
 Each side of a hexagon drawn within ar 
 circle is just half the diameter of that circle. 
 Therefore in describing the hexagon (Fig. 22), 
 first sweep the circle ; then without altering 
 the compasses, set off from a to &, from h to <?, 
 and so on. Join all these points, a^ J, <?, 
 
32 
 
 THE CARPENTER S 
 
 &c., and you have an exact hexagon. Join 
 V J, d^ and/*, and you have an equilateral tri- 
 angle ; join d^ e^ and the centre, and you 
 have another triangle, just one-sixth of the 
 hexagon described. 
 
 26. To describe a curve hy a set triangle. 
 
 Fig. 23. 
 
 Let a h (Fig. 23) be the length, and c d 
 the height of the curve desired ; drive two 
 
HAND-BOOK. 33 
 
 pins or awls at e and e / take two strips s Sy 
 tack them together at d, bring the edges out 
 to the pins at e/ tack on the brace /*, to 
 keep them in place; hold a pencil at the 
 point d; then move the point d^ towards e, 
 both ways, keeping the strips hard against 
 the pins at e^ e^ and the pencil will describe 
 the curve, which is a portion of an exact cir- 
 cle. If the strips are placed at right angles, 
 the curve will be a half circle. 
 
 This is a quick and convenient way to get 
 the form of flat centres, for brick arches, 
 window and door heads, &c. 
 
 Fig. 24. 
 
 27. Fig. 24 shows the method of forming 
 
 a curve by intersection of lines. If the 
 
 points 1, 2, 3, &c., are equal on both sides. 
 
 the curve will be part of a circle. 
 3* 
 
34 
 
 THE CARPENTER S 
 
 28. Fig. 25 sliows how to form an ellipti- 
 cal curve by intersections. Divide the dis- 
 tance a J, into as many points as from 5 to <?, 
 
 
 
 -/ 
 
 2. 
 
 5 
 
 4- 
 
 
 
 
 J ^ 
 
 ^^-^ 
 
 .-^^^ 
 
 c 
 
 ^°~*^^^ 
 
 \ 
 
 -* 
 
 J. 
 
 ^ 
 
 .--^^ 
 
 
 
 ^^ 
 
 ^ 
 
 e« 
 
 5^ 
 
 
 
 
 
 
 \ 
 
 to 
 
 / 
 
 
 
 
 
 
 \ 
 
 
 Clf 
 
 
 
 
 I 
 
 
 
 Fig. 25. 
 
 and proceed as in Fig. 24. The closer the 
 points 1, 2, 3, &C.5 are together, the more 
 accurate and clearly defined will be the 
 curve, as at d, 
 
 29. Fig. 26 shows the parabolio curve. 
 
 Fig. 26. 
 
HAND-BOOK. 
 
 35 
 
 This is the form of the curve of the Gothic 
 arch or groin. 
 
 30. To find the joints for splayed work^ 
 such as hojppers^ trays^ c&c. 
 
 Fiff. 27. 
 
 Take a separate piece of stuff to find the 
 joints for the hopper, Fig. 27. Strike the 
 bevel /^, the bevel of the hopper, on the 
 
 Fig. 28. 
 
36 THE caiipent:e:k's 
 
 end of the piece (Fig. 28) ; nm the gauge- 
 mark G ivoTnf; then square on the edge from 
 a^ or where you want the outside joint, to h; 
 then square down from 5 to the gauge-mark 
 G / strike the bevel of the work f g^ from i 
 to d^ through the point at e. From a to d 
 will be the joint, the inside corner the 
 longest. If a mitre joint is wanted, set the 
 thickness of the stuff, measuring onfg^ from 
 d to h ; the line ^ A will be the mitre joint. 
 
 31. Stairs,"^ — It is not practicable in a 
 work of this size to go into all the details of 
 stair-building, hand-railing, &c., but a few 
 leading ideas on plain stairs may be intro- 
 duced. 
 
 First, measure the height of the story from 
 the top of one floor to the top of the next ; 
 also the run or distance horizontally from 
 the landing to where the first riser is placed. 
 
 * For a thorough treatise on stair-building in all its de- 
 tails, and many other subjects of interest to the builder, 
 I would recommend " The American House Carpenter," 
 by IX. a. Hatfield, New York. 
 
• HAJS^D-BOOK. 37 
 
 Suppose the height to be 10 ft. 4 in., or 124 
 inches. As the rise to be easy should not 
 be over 8 inches, divide 124 by 8 to get the 
 number of risers : result, 15|^. As it does 
 not come out even, we must make the num- 
 ber of risers 16, and divide it into 124 inches 
 for the width of the risers : result, 7f , the 
 width of the risers. If there is plenty of 
 room for the run, the steps should be made 
 10 inches wide besides the nosing or projec- 
 tion ; but suppose the run to be limited, on 
 account of a door or something else, to 10 
 ft. 5 in., or 125 inches : divide the distance 
 in inches by the number of steps, w^hich is 
 one less than the number of risers, because 
 the upper floor forms a step for the last riser. 
 Di^dde 125 by 15, which gives 8^ or 8/^ 
 inches, the neat width x of the step, which 
 with the nosing, will make about a 9J step. 
 32. To make a pitch-hoard. { 
 
 4 
 
38 
 
 THE CARPENTERS 
 
 ^ 
 
 Fiff. 29. 
 
 Take a piece of tliin clear stuff (Fig. 29), 
 and lay the square on the face edge, as 
 shown in the figure, and mark out the pitch- 
 board^ with a sharp knife. 
 
 33. To lay out the string. 
 
 Nail a piece across the longest edge of the 
 pitch-board, as at Z>, so as to hold it up to 
 the string more conveniently. Then begin 
 at the bottom, sliding the pitch-board along 
 the upper edge of the string, and marking it 
 out, as shown at Fig. 30. 
 
 Fig. 30. 
 
HAND-BOOK. 39 
 
 The bottom riser mnst scribe down to the 
 thickness of the step narrower than the 
 others. 
 
 34. To file the fleam-tooth saw. 
 
 a 
 
 Fig. 8t 
 
 Fig. 31 shows the manner of filing the 
 fleam, or lancet toothed saw. a shows the 
 form of the teeth, full size ; and &, the position 
 of holding the saw. The saw is held flat on 
 the bench, and one side is finished before it 
 y is turned over. No setting is needed, and 
 the plate should be thin and of the very 
 best quality and temper. 
 
40 
 
 THE CARPENTER S 
 
 These saws cut at an astonishing rate, cut- 
 ting equally both ways, and cut as smooth 
 as if the work were finished with the keenest 
 plane. 
 
 35. To dovetail two pieces of wood show- 
 ing the dovetail on four sides. 
 
 Fig. 32. 
 
 a (Fig. 32) shows two blocks joined to- 
 gether with a dovetail on fonr sides. This 
 
HAND-BOOK, 
 
 41 
 
 looks at first like an impossibility^ but h 
 shows it to be a very simple matter. TMs 
 is not of mncb practical nse except as a 
 puzzle. I bave seen one of tbese at a fair 
 attract great attention; nobody could tell 
 how it was done. The two pieces should be 
 of different colored wood and glued to- 
 gether. 
 
 36. To mend or splice a hroTcen stick with- 
 out TRCtking it any shorter or itsing any new 
 stuff. 
 
 A vessel at sea had the misfortune to 
 break a mast, and there was no timber of 
 any kind to mend it. The carpenter ingeni- 
 ously overcame the difficulty, without short- 
 ening the mast. 
 
 (V I c 
 
 d 
 
 1 
 
 1 
 
 / 
 
 
 
 
 A 
 
 
 
 
 <l 
 
 
 cl 
 
 a 
 
 t 
 
 1 
 
 
 \ 
 
 _J 
 
 
 ; 
 
 
 
 Jis:. 33. 
 
42 THE cakpenter's 
 
 ^ at 1 (Fig. 33) shows where the mast was 
 broken. Cut the piece a 5, say three feet 
 long, and the piece c d^ six feet long, half 
 way through the stick. Take out these two 
 pieces, keeping the two broken ends to- 
 gether, turn them end for end, and put them 
 back in place, as shown at 2. 
 
 This arrangement not only brought the 
 vessel safe home, but was considered by the 
 owners good for another voyage. 
 
 By putting hoops around each j.oint, the 
 stick would be about as strong as ever. 
 
 37. Is there any difference in the angle 
 of a large or small three-cornered file ? 
 
 Certainly not : for the file is an equilateral 
 triangle, equal on all sides. 
 
 Fig. 34 proves this, a is a file measuring 
 
HAND-BOOK. 
 
 43 
 
 one inch on all sides ; cut off hj making a 
 file \ inch on the sides, it will readily be seen 
 that the angle is exactly the same. 
 
 Simple as this fact is, it is unknown to 
 many. 
 
 38. Does a pile of wood on a side hill 
 piled perpendicularly^ eight feet long ^ four 
 wide^ and four high^ contain a cord ? 
 
 It does not. 
 
 Fiff. 35. 
 
 To illustrate, let us make a frame (Fig. 
 35) just 4 by 8 in the clear. When this 
 frame stands level it will hold just a cord. 
 
44 
 
 THE CARPENTEKS 
 
 Place tliis frame on a side hill, so as to give 
 it the position in Fig. 36, it will be seen that 
 the 8 ft. sides are brought nearer together, 
 thus lessening its capacity. Continue to in- 
 crease the steepness of the ground, as at Fig. 
 37, or more, the 8 ft. sides would finally 
 
 Fig. ST. 
 
HAND-BOOK. 45 
 
 come together, and tlie frame contain noth- 
 ing at all. It therefore becomes careful 
 buyers of wood to consider where it is piled. 
 39. To find the numher of gallons in a 
 tanh or hox^ multiply the number of cubic 
 feet in the tank by 7f . 
 
 How many gallons in a tank 8 feet long, 
 4 feet wide, and 3 feet high? 
 
 8 
 
 4 
 
 32 
 3 
 
 96 cubic feet. 
 
 672 
 
 72 
 
 Ans. 744 gallons. 
 
46 THE 
 
 caepenter's 
 
 
 40. To find the 
 
 5 area or number of 
 
 square 
 
 feet in a circle. 
 
 
 
 Three-quarters 
 
 of tlie square of tlie diam- 
 
 eter will give tlie 
 
 area. 
 
 
 What is the area of a circle Qft. in 
 
 . diam- 
 
 eter ? 
 
 6 
 6 
 
 36 
 
 f 
 
 
 Ans, 
 
 2T feet. 
 
 
 For large circles, or where greater accu- 
 racy is required, multiply the square of the 
 diameter by the decimal .785. 
 
HAND-BOOK. 47 
 
 41. Capacity of wells and cisterns. 
 One foot in depth of a cistern : 
 
 3 feet in diameter contains 65^ gallons, 
 34 " " " 76 " 
 
 4 " " " 98 " 
 4i " " " 1241 " 
 
 5 " " « 153i " 
 5|- feet in diameter contains 186|^ " 
 
 6 " " " 220i " 
 
 7 " " " 300i " 
 
 8 " " " 392i " 
 
 9 " " " 497 " 
 10 " " " 613i " 
 
 A gallon is required by law to contain 
 eight pounds of pure water. 
 
48 THE carpenter's 
 
 42. Weights of various materials : 
 
 Lbs. in a 
 cubic foot. 
 
 Cast-iron - - - - - 460 
 
 Cast-lead - . - - - - 709 
 
 Gold 1,210 
 
 Platina 1,345 
 
 Steel 488 
 
 Pewter ----.. 453 
 
 Brass - . ... 506 
 
 Copper 549 
 
 Granite 166 
 
 Marble 170 
 
 Blue stone - ... 160 
 
 Pumice-stone - - - - 56 
 
 Glass 160 
 
 Chalk - - - - ' - - 150 
 
 Brick 103 
 
 Brickwork laid - - - - 95 
 
 Clean sand - - - - 100 
 
 Beech-wood - - * - - - 40 
 
 Ash - - - - - - 45 
 
 Birch - - - - - - 45 
 
 Cedar - - - - - 28 
 
HAFD-BOOK. 49 
 
 Lbs. in a 
 cubic foot. 
 
 Hickory 52 
 
 Ebony .83 
 
 Lignum-vitae - - - - 83 
 
 Pine, yellow - - - - 38 
 
 Cork 15 
 
 Pine, white - - - - 25 
 
 Birch charcoal - - - - 34 
 
 Pine " - - . - 18 
 
 Beeswax 60 
 
 Water 62^ 
 
 5