CARPENTER'S AND JOINER'S HAND-BOOK. THE CAEPEUTEE'S AND JOINER'S HAND-BOOK: CONTAININCr A COMPLETE TREATISE ON FRAMING HIP AND VALLEY ROOFS. TOGETHER WITS MUCH VALUABLE INSTRUCTION FOR ALL MECHANICS AND AMATEURS, USEFUL RULES, TABLES, ETC., . NEVER BEFORE PUBLISHED. REVISED EDITION WITH ADDITIOm. BY PRACTICAL ARCHITECT AND BUILDER, AUTHOR OF «'THE ART OF SAW-FILING." ILLUSTRATED BY FORTY-THREE ENGRAVINGS. NEW YORK : JOHN WILEY & SONS, 15 AsTOR Place. 1882, Entered according to Act of Congress, ih the year 1863, By H. W. holly, the Clerk's Office of the District Court of the United States for the District of Connecticut. PEEFACE. This work has been undertaken by tbe antlior to supply a want long felt by tlie trade : that is, a cheap and convenient "Pocket Guide/' containing the most use- ful and necessary rules for the carpenter. The writer, in his progress " through the mill," has often felt that such a work as this would have been of great value, and some one principle here demonstrated been worth many times the cost of the book. It is believed, therefore, that this book will commend itself to those interested, for the reason that it is cheap, that it is plain and easily understood, and that it is useful. CONTENTS. ART. 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 Difference between the hip and valley roof 6 Hip and vaUey combined 7 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 lY 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. ART. 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 2t 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 3t Piling wood on a side-hill 38 Another mysterious splice 39 To find the height of a tree 40 To cut bridging to fit 41 Building fence over a hill 42 To draw an oval with a string 43 To find the speed of shafting 44 To glue mitre and butt joints 45 To find the number of gallons in a tank 46 To find the area of a circle 47 Capacity of wells and cisterns 48 Weights of various materials 49 THE CARPENTER'S AND JOINER'S HAND-BOOK- HIP AND YALLEY EOOES. 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 tbat this important part of a carpenter's work should be familiar to every one who expects to bes.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- 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 andhevels of hijp and common rafters. 'hetppp (Fig. 1) represent the face of the plates of the building ; d^ the deck-frame : HAND-BOOK. 9 a is the seat of the hip-rafter; 5, of the jack ; and of the common rafter. Set the rise of the roof from the ends of the hip and common rafter towards e square from a and G / connect/* and then the line from ftoe will be tlie length of the hip and com- mon rafter, and the angles at ^ ^ will be the down bevels of the same. 2. Tojmd the length and hevel of thejaclc- raftei's, h (Fig. 1) is the seat of a jack-rafter. Set the length of the hip from the corner, 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 h / then from i to h 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 found in the same way, by extending them to meet the line A. The dovm 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 carpenter's 1), draw a line at right angles to extending to the face of the plates ^thh j upon the points where the lines cross, draw the half circle, just touching the Ymefej connect the point aty, where the half circle cuts the line a, with the points hh j 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 the jacks. Set the rise of the roof at e / set the length of the hip d from d to/* on one side of the deck, and from 6? to ^ on the other side ; ex- tend the jack J, and all the jacks on that side, to the line df^ for the length and top bevels ; extend the jack and all on that side, to the line d 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 carpenter'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. HAND-BOOK. 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 a to c / connect h and c : from 5 to ^ is the length of the valley- rafter, and the angle at g the bevel of the same ; set the length h c on the line from extend the jack^ to meet the line b d at e ; 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 the jack is on the hip ^ and the other on the valley. Fig. 5. a h (Fig. 5) is the hip, and c d the valley- rafters. Find the length of each according to the previous directions ; find the lines e and f 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. 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 7 i 16 THE carpenter's should be cut four feet four inches long, so | that the centre line on the hip, 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.) • P Fig. T. J 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 | i i HAiSTD-BOOK. 17 line c on the angle the hip-rafter is to lie, generally a mitre line ; draw the small lines 0^ parallel to the plate The more of these lines, the easier to trace the cnrve ; continue the lines o o where they strike the line c square from that line ; set the distances 1, 2, 3, 4, &c. (on (2, from the line h) on the line G Gj towards at right angles from c g ; through these points, 2, 4, 6, 8, e%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 (Fig. 7), the thickness required, wide enough to cut a common rafter; mark out the common rafter the full size. Then ni-et the len.g!:ths 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, * Do not attempt to £ret the form of a curved hip-rafter, or an- jrle bracket, by sweeping it from a centre. It cannot be done, for it is a part of an ellipse and not a part of circle. It can only be found by tracing it through the points as shown. 18 THE carpenter's then nse 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 from 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. Fig. S. 11. The length of the rafter will be from a to 5, on the edge of the board. Always buy a square with the inches on one side divided * Of courpe a convex roof is framed on the same plan. The same thing precisely, reversed. hand-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 hracket for a cornice. Let a (Fig. 9) be the common bracket ; draw the parallel lines o o o^io meet the 20 THE carpenter's mitre line c ; square tip on eacli line at and set the distances 1, 2, 3, 4, (fee, on the common bracket, from the line 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 hase or covering for a cone. i^lg. 10. Ler 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 c till it meets the line & at <^ / on 6? for a centre, with 1 and 2 for a radius, describe HAND-BOOK. 21 which will be the shape of the base re- quired; /*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. 10, 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. Fig. 11. Draw the line a through the centre of the dome (Fig. 11); divide the height from h to 22 THE carpenter's G into as many parts as there are to be courses of boards, or tin. Through 1 and 2 draw a line meeting the centre line at d j 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 and so on for the other courses. 15. To divide a line into any nuinber of equal jparts. Fig. 12. Let a h (Fig. 12) be the given line. Draw the line a at any convenient angle, to ah ; set the dividers any distance, as from 1 to 2, and run off on a as many points as you wish to divide the line a l into ; say Y parts ; HAND-BOOK. 23 connect the point Y with 5, and draw the lines at 6, 5^ 4, (fee, parallel to the line 7 J, and the line a h 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 CARPENTEe's 17. To square a loard with compasses. 1 Fig. 14. Let a (Fig, 14) be the board, and h the point from which fo square. Set the com- passes from the point h any distance less than the middle of tlie board, in the direc- tion of G, Upon G for a centre sweep the circle, as shown. Then draw a straight line from where the circle tenches the lower edge of the board, through the centre c^ cutting the circle at d. Then a line from h through 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 j^erfect sq;uaTe with a pair of compasses. Fig. 15. Let a l (Fig. 15) be the lengtli of a side of the proposed square ; upon a and 5, with the whole length for radius, sweep the parts of circles a d and 5 c. Find half the distance from a to e 2it f ; then upon e for a centre sweep the circle cutting/l Draw the lines from a and through where the circles intersect at c and d ; connect them at the top and it will, form a perfect square. 3 26 THE carpenter's 19. To find the centre of a circle. Fig. 16. Upon two points nearly opposite each other, as J (Fig. 16), draw the two parts of circles, cutting each other at 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. 17. Lay a square upon the circle (Fig. 17), with the corner just touching the outer edge of the circle. Draw the line a i across the circle where the outside edges of the square touch it. Then half the length of the line a 1) 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. Fig. 18. Let a h c (Fig 18) be the given points. i Upon each of these points sweep the parts | of circles, cutting each otlier, 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 w^here but part ; of the circle is given, as from aio c. 22. Two circles leing given^ to find a third I whose surface or area shall equal the first j and second. ■ HAND-BOOK. 29 rig. 19. Let a and h (Fig. 19) be tlie given circles. Place tlie diameter of each at right angles to the other as at 3, connect the ends at c and then c d will be the diameter of the circle required. 23. To find the form of a raking crown moulding. Fig. 20. so THE carpenter's m (Fig. 20) is tlie form of the level crown moulding; r c \% the pitch of the roof. Draw the line Z, which shows the thickness of the moulding. Draw the lines o o par- allel to the rake. Where these lines strike the face of the level moulding, draw the hor- izontal lines 1, 2, 3, &c. Draw the line f 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, &c., and you have the form of the raking moulding. Hold the raking moulding in the mitre I)ox, on the same pitch that it is on the roof, the box being level, and cut the mitre in that position. 24. To mahe an octagon^ or eight-sided figure^ from a square. HAND-BOOK. 31 F?g. 21. Let Fig. 2 i be the square ; find the centre a J set the compasses from the corner J, to a ; describe the circle cutting the outside line at c and 6?; repeat the same at each corner, and draw lines c f h and ij. These lines will form the octagon desired 25, To draw a hexagon or six-sided Jtg- nre on a circle. Each side of a hexao^on drawn within a 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 cc to 5, from h to c^ and so on. Join all these points, J, c^ 32 THE carpenter's Fig. 22. &C.5 and you tiave an exact hexagon. Join J, andy, and yon have an equilateral tri- angle ; join and the centre, ^nd you have another triangle, just one-sixth of the hexagon described. 26. To describe a curve hy a set triangle. Fig. 23. Let a I (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 tack them together at 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 J then move the point 6?, towards both ways, keeping the strips hard against the pins at 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- 34c THE carpenter's 28. Fig. 25 sliows how to form an ellipti- cal curve by intersections. Divide the dis- tance a by into as many points as from i to Fig. 25. and proceed as in Fig. 24. The closer the points 1, 2, 3, &c., are together, the more accurate and clearly defined will be the curve, as at d. 29. Fig. 26 shows the jparaholiG 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 hoppers^ trays^ &g. Fig. 2T. 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 1 c 1 / 36 THE carpenter's end of the piece (Fig. 28) ; ran tlie gange- mark c fromy ; then square on the edge from or where you want the outside joint, to 5/ then square down from 5 to the gauge-mark c / strike the bevel of the work f from i to 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 h will be the mitre joint. 31. Stair s,"^ — 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 E. G. Hatfield, New York. HAND-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, which is one less than the number of risers, because the upper floor forms a step for the last riser. Divide 125 by 15, which gives 8^ or 8^^^ inches, the neat width of the step, which with the nosing, will mseke about a 9J step. 32. To make a pitch-hoard. 4 38 THE carpenter's Fig. 29. Take a piece of tliin clear stuff (Fig. 29), and lay the square on tlie face edge, as shown in the figure, and mark out the pitch- board j9 with a sharp knife. 33. To lay out the string, JSTail a piece across the longest edge of the pitch-board, as at 5, 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. p Fig. SO. IIAND-BOOK. 39 The bottom riser must scribe down to the . thickness of the step narrower than the "Others. 34. To file the fleam-tooth saw. Fig. 31. Fig. 31 shows the manner of filing the fleam, or lancet toothed saw. a shows the form of the teeth, full size ; and 5, the position of holding the saw. The saw is held flat on the bench, and one side is finished before it 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 astonisliing rate, cut- ting equally botli 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. 82. a (Fig. 32) shows two blocks joined to- gether with a dovetail on four sides. This HAND-BOOK. looks at first like an impossibility, but h shows it to be a very simple matter. This is not of miicli practical nse except as a pnzzle. I liave seen one of these at a fair J. 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 Ijrolien stick loitJi- ont mahing it any shorter or using 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. 1 —I. - z \ } Fig. 33. 4* 42 THE carpenter's e ail (Fig. 33) sliows where the mast was broken. Out the piece a say three feet long, and the piece c six feet long, half way through the stick. Take ont 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 joint, the stick would be about as strong as ever. 37. Is there any difference in the angle of a large or small three-cornered fZe ? Certainly not : for the file is an equilateral triangle, equal on all sides. Fig. 34. Fig. 34 proves this. is a file measuring HAND-BOOK. 43 one incli on all sides ; cut off J, making a file i 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 2>iled perpendicularly^ eight feet long ^ four wide^ and four high^ contain a cord f It does not. 8 4 F4g. 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. 4:4 THE carpenter's Fig. 86. Place tliis frame on a side hill, so as to give it the position in Fig. 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 HAND-BOOK. 45 come together, and the frame contain noth- ing at all. It therefore becomes careful buyers of wood to consider where it is piled. 39. Another mysterious splice or puzzle joint, on the same principle as Fig. 32, is shown at Fig. 38. Fig. 38. The pieces slide together diagonally, as will be seen by Fig. 39. This shows one Fig. 39. piece and the way it is cut ont. The other 46 THE carpenter's piece is cut just like it, only it must^a^V with this one. 40. To find the height of a tree. 'I. \ Fig. 40. Suppose you want a stick of timber 30 feet long, and want to know if a certain tree will make it. Measure o£E from tlie tree (Fig. 40), HAND-BOOK. 47 thirty feet on a level from where you will cut it down, ten feet back at set up your ten-foot pole; let some one hold it plumb while you put your eye at e. Then looking over the top of the pole where the eye strikes the tree at will be 30 feet from if the pole is held right. 41. To cut bridging to fit exactly the first time. Let etc. (Fig. 41), show the floor beams, being different distances apart. Snap a line at G to nail the bridging by, then snap an- other line at &, the distance from the 48 THE CAKPENTER'& deptli of the timber. Lay a piece of bridg- ing stuff (d) on the timber, and mark it on the under side by the timber as shown by the short dotted lines ; saw it correctly, and it will fit exactly when in place, no matter what distance apart the timber is. 42. Does it take more pickets to htdld a fence over a hill than on a level f This question has often been asked, and even published in some newspapers, and an- swered in the aflirmative by some very wise persons. At first thought it would appear that it would take more, but a look at Fig. 42 settles the question at once. In building a fence level from A to i?, we have a certain number of pickets as shown. Now suppose the curved lines ^ ^ to represent the rise and fall of a hill, we see, if the pickets from A to ' B are carried up by the dotted lines, they make the same fence over the hill and are no farther apart than on the level. HAKB-BOOK, 49 Fig. 4:2. > > A. w w 3 :^__r£:±i::> 50 THE CAKPEKTEE'S 43. To draw a regular oval with a string. Fig. 43. b Drive two pins at a a (Fig. 43), as far apart as half the length you want the oval ; put the string around the pins, and tie at 5, the same distance from a as from a to a. Place your pencil at J, and move it along, keeping it taut ; in the direction of a^ both ways letting the string slide on the pins, and not on the pencil. A regular oval is a cylinder cut at an angle of forty-five degrees. Savv^ a piece of lead pipe in a mitre box, and the end is a regular oval. 44. To find the sjpeed of shafting and pulleys. HAKD-BOOK. 51 Rule, Multiply tlie revolutions of the main or driving shaft by the diameter of the driving pulley, and divide by the diam- eter of the driven pulley. Example. Suppose the main line of shaft- ing through the shop is running at the rate of one hundred turns a minute. Tou wish to get a speed on another shaft of 400 revolutions. Put a 24 inch pulley on the main line, and belt on to a 6 inch pulley, thus 100 X 24 = 2,400 6 = 400. l^ow from this shaft running 400, you want a farther speed of 1,500. Put a 15 in. pulley and belt on to a 4 in. Thus 400 x 15 = 6,000 -T- 4 1,500. On this shaft running 1,500, put a 9 in. pulley and belt on to a 3 in., and you have 1,500 x 9 = 13,500 -f- 3= 4,500. Forty-five hundred revolutions a min- ute. To save pulleys and belts, you could put a 48 in. pulley on your main shaft, and belt- ing on to a 3 in. pulley, you would get 100 x 48 = 4,800 3 = 1,600. Sixteen hundred revolutions with only one belt. 52 THE carpenter's This rule, like all good rules, will work both ways. For instance, take the first ex- ample : our last shaft was running at forty- five hundred ; now call this the driving- shaft. 4,500 X 3 = 13,500 - 9 = 1,500 1,500 X 4t= 6,000 -5- 15 = 400 400 X 6 = 2,400 ~ 24 = 100 bringing us back to our original one hun- dred revolutions. 45. To glue mitre and hutt joints. It is considered a valuable secret by some that if mitre and butt joints are chalked be- fore gluing they will hold as well as any other joint. It is worth trying. 46. To find the number of gallons in a tank or hoXj multiply the number of cubic . feet in the tank by 7f . HAND-BOOK. 53 How many gallons in a tank 8 feet long, 4 feet wide, and 3 feet liigh ? 8 4^ 32 3 96 cubic feet. 672 72 Ans. 744 gallons. 54 THE carpenter's 47. To find the area or number of square feet in a cirele. Three-quarters of the square of the diam' eter will give the area. What is the area of a circle &fL in diam' eter ? 6 6 36 3 4 Ans, 27 feet. For large circles, or where greater accu- racy is required, multiply the square of the diameter by the decimal .785. \ HAKD-BOOK. 55 48. Capacity of wells and cisterns. One foot in depth of a cistern : 3 feet in diameter contains 55^ gallons. 3i u u a /jrg a 4 " " " 98 " ^ u u u 1241 " 5 " " 153i " 51 feet in diameter contains 185^ " 6 " 220| " 7 " " 300i " 8 " " " 392i " 9 " " 497 " 10 " " " 6131 a A gallon is required by law to contain eight pounds of pure water. 56 THE CARPEl^TEK'S 49. Weights of vdvious materials : Lbs. in a cubic foot. Cast-iron - - - - - 460 Cast-lead - - - - Y09 Gold - - 1,210 Platina - - - - 1,345 Steel - - 488 Pewter - - 453 Brass - 506 Copper - - 549 Granite - . - - - 166 Marble - - 170 Blue stone - 160 Pnmice-stone - 56 Glass - 160 Chalk - - - 150 Brick - - 103 Brickwork laid - - - 95 Clean sand - 100 Beech-wood - - 40 Ash . 45 Birch - - - - - 45 Cedar - - 28 HAITD-BOOK. 57 Lbs. in a cubic foot. Hickory 52 Ebony 83 Lignuin-vitae - - - - 83 Pine, yellow - - - . . 38 Cork ...... 15 Pine, white - - - - 25 Bircli charcoal - - - - 34 Pine "... - 18 Beeswax 60 "Water - - - - 62^ i i i