T H 
 
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Book ,\\U1 — 
 
 Copyright N°. 
 
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 COPYRIGHT DEPOSIT: 
 
STAIR-BUILDING 
 
 INSTRUCTION PAPER 
 
 PREPARED BY 
 
 Fred T. Hodgson 
 
 Architect and Editor 
 Member of Ontario Association of Architects 
 Author of "Modern Carpentry," "Architectural Drawing, Self- 
 Taught. '" "The Steel Square," "Modern Estimator," Etc. 
 
 AMERICAN SCHOOL OF CORRESPONDENCE 
 
 CHICAGO ILLINOIS 
 
 U.S.A. 
 
LIBRARY of CONGRESS 
 
 9fteviu!> v v deceived 
 MIN 20 1908 
 
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 *v 2r /fay 
 0U884 XXs, 4 
 
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 Copyright 1907 by 
 American Schooe of Correspondence 
 
 Entered at Stationers' Hall, London 
 All Rights Reserved 
 
 
STAIR-BUILDING 
 
 Introductory. In the following instructions in the art of Stair- 
 building, it is the intention to adhere closely to the practical phases 
 of the subject, and to present only such matter as will directly aid 
 the student in acquiring a practical mastery of the art. 
 
 Stair-building, though one of the most important subjects con- 
 nected with the art of building, is probably the subject least under- 
 stood by designers and by workmen generally. In but few of the 
 plans that leave the offices of Architects, are the stairs properly laid 
 down ; and many of the books that have been sent out for the purpose 
 of giving instruction in the art of building, have this common defect — 
 that the body of the stairs is laid down imperfectly, and therefore 
 presents great difficulties in the construction of the rail. 
 
 The stairs are an important feature of a building. On entering 
 a house they are usually the first object to meet the eye and claim 
 the attention. If one sees an ugly staircase, it will, in a measure, 
 condemn the whole house, for the first impression produced will 
 hardly afterwards be totally eradicated by commendable features 
 that may be noted elsewhere in the building. It is extremely important, 
 therefore, that both designer and workman shall see that staircases 
 are properly laid out. 
 
 Stairways should be commodious to ascend — inviting people, 
 as it were, to go up. When winders are used, they should extend 
 past the spring line of the cylinder, so as to give proper width at 
 the narrow end (see Fig. 72) and bring the rail there as nearly as 
 possible to the same pitch or slant as the rail over the square steps. 
 When the hall is of sufficient width, the stairway should not be less 
 than four feet wide, so that two people can conveniently pass each 
 other thereon. The height of riser and width of tread are governed 
 hy the staircase, which is the space allowed for the stairway; but, 
 as a general rule, the tread should not be less tl^an nine inches wide, 
 and the riser should nol be over eight inches high. Seven-inch riser 
 
STAIR-BUILDING 
 
 Fig. 1. 
 
 Illustrating Rise, Run, and 
 Pitch. 
 
 and eleven-inch tread will make an easy stepping stairway. If you 
 increase the width of the tread, you must reduce the height of the riser. 
 The tread and riser together should not be over eighteen inches, 
 and not less than seventeen inches. These dimensions, however, 
 cannot always be adhered to, as conditions will often compel a devia- 
 tion from the rule: for instance, in large buildings, such as hotels, 
 railway depots ; or other public buildings, treads are often made IS 
 
 inches wide, having risers of from 
 2h inches to 5 inches depth. 
 
 Definitions. Before pro- 
 ceeding further with the subject, 
 it is essential that the student 
 make himself familiar with a few 
 of the terms used in stair-building. 
 The term rise and run is 
 often used, and indicates certain 
 dimensions of the stairway. Fig. 
 1 will illustrate exactly what is 
 meant; the line A B shows the run, or the length over the floor the 
 stairs will occupy. From B to C is the rise, or the total height from 
 top of lower floor to top of upper floor.* The line D is the pitch or 
 line of nosings, showing the angle of inclination of the stairs. On 
 the three lines shown — the run, the rise, and the pitch — depends 
 the whole system of stair-building. 
 
 The body or staircase is the room or space in which the stairway 
 is contained. This may be a space including the width and length 
 of the stairway only, in which case it is called a close stairway, no rail 
 or baluster being necessary. Or the stairway may be in a large 
 apartment, such as a passage or hall, or even in a large room, openings 
 being left in the upper floors so as to allow road room for persons on 
 the stairway, and to furnish communication between the stairways 
 and the different stories of the- building. In such cases we have what 
 are known as open stairways, from the fact that they are not closed 
 on both sides, the steps showing their ends at one side, while on the 
 other side they are generally placed against the wall. 
 
 Sometimes stairways are left open on both sid-s, a practice not 
 
 *Note. — The measure for the rise of a stairway must always be taken from the top 
 of one floor to the top of the next. 
 
STAIR-BUILDING 
 
 uncommon in hotels, public halls, and steamships. When such stairs 
 are employed , the openings in the upper floor should be well trimmed 
 with joists or beams somewhat stronger than the ordinary joists used 
 in the same floor, as will be explained further on. 
 
 Tread. This is the horizontal, upper surface of the step, upon 
 which the foot is placed. In other words, it is the piece of material 
 that forms the step, and is generally from 1\ to 3 inches thick, and 
 made of a width and length to suit the position for which it is intended. 
 In small houses, the treads are usually made of f -inch stuff. 
 
 Riser. This is the vertical height of the step. The riser is gen- 
 erally made of thinner stuff than the tread, and, as a rule, is not so 
 heavy. Its duty is to connect the treads together, and to give the 
 stairs strength and solidity. 
 
 Rise and Run. This term, as already explained, is used to indi- 
 cate the horizontal and vertical dimensions of the stairway, the rise 
 meaning the height from the top of the lower floor to the top of the 
 second floor; and the run meaning the horizontal distance from the 
 face of the first riser to the face of the last or top riser, or, in other 
 words, the distance between the face of the first riser and the point 
 where a plumb line from the face of the top riser would strike the floor. 
 It is, in fact, simply the distance that the treads would make if put 
 side by side and measured together — without, of course, taking in 
 the nosings. 
 
 Suppose there are fifteen treads, each being 11 inches wide; 
 this would make a run of 15 X 11 = 165 inches =13 feet 9 inches. 
 Sometimes this distance is called the going of the stair; this, however, 
 is an English term, seldom used in America, and when used, refers 
 as frequently to the length of the single tread as it does to the run of 
 the stairway. 
 
 String-Board. This is the board forming the side of the stairway, 
 connecting with, and supporting the ends of the steps. Where the 
 steps are housed, or grooved into the board, it is known by the term 
 housed string; and when it is cut through for the tread to rest upon, 
 and is mitered to the riser, it is known by the term cut and mitered 
 string. The dimensions of the lumber generally used for the purpose 
 in practical work, are 94 inches width and J inch thickness. In the 
 first-class stairways the thickness is usually 1J- inches, for both front 
 and wall strings. 
 
STAIR-BUILDING 
 
 Fig. 2 shows the manner in which most stair-builders put their 
 risers and treads together. T and T show the treads; R and R, the 
 
 risers; S and S, the string; and 0, the 
 cove mouldings under the nosings X and 
 X. B and B show the blocks that hold 
 the treads and risers together; these 
 blocks should be from 4 to 6 inches 
 long, and made of very dry wood ; their 
 section may be from 1 to 2 inches square. 
 On a tread 3 feet long, three of these 
 blocks should be used at about equal 
 distances apart, putting the two outside 
 ones about 6 inches from the strings. 
 They are glued up tight into the angle. 
 First warm the blocks; next coat two adjoining sides with good, strong 
 glue; then put them in position, and nail them firmly to both tread 
 and riser. It will be noticed that the riser has a lip on the upper 
 edge, which enters into a groove in the tread. This lip is generally 
 
 Fig. 2, Common Method of Join- 
 ing Risers and Treads. 
 
 Fig. 3. Vertical Section 
 of Stair Steps. 
 
 Fig. 4. End Section 
 of Riser. 
 
 Fig. 5. End Section 
 of Tread. 
 
 about | inch long, and may be f inch or J inch in thickness. Care 
 must be taken in getting out the risers, that they shall not be made 
 too narrow, as allowance must be made for the lip. 
 
 If the riser is a little too wide, this will do no harm, as the over- 
 width may hang down below the tread; but it must be cut the exact 
 width where it rests on the string. The treads must be made the 
 exact width required, before they are grooved or have the nosing 
 
STAIR-BUILDING 
 
 Fig. 6. Side Elevation of Finish 
 
 ed Steps with Return 
 
 Nosings and Cove 
 
 Moulding. 
 
 worked on the outer edge. The lip or tongue on the riser should fit 
 snugly in the groove, and should bottom. By following these last 
 
 instructions and seeing that the blocks are 
 well glued in, a good solid job will be the 
 result. 
 
 Fig. 3 is a vertical section of stair 
 steps in which the risers are shown 
 tongued into the under side of the tread, 
 as in Fig. 2, and also the tread tongued 
 into the face of the riser. This last 
 method is in general use throughout the 
 country. The stair-builder, when he has 
 steps' of this kind to construct, needs to 
 be very careful to secure the exact width 
 for tread and riser, including the tongue on each. The usual 
 method, in getting the parts prepared, is to make a pattern show- 
 ing the end section of each. The millman, with these patterns 
 to guide him, will be able to run the material through the machine 
 without any danger of leaving it either too wide or too narrow; while, 
 if he is left to himself without patterns, he is liable to make mistakes. 
 These patterns are illustrated in Figs. 4 and 5 respectively, and, as 
 shown, are merely end sections of riser and tread. 
 
 Fig. 6 is a side elevation of the steps as finished, with return 
 nosings and cove moulding complete. 
 
 A front elevation of the finished step 
 is shown in Fig. 7, the nosing and riser 
 returning against the base of the newel post. 
 Often the newel post projects past the 
 riser, in front; and when such is the case, 
 the riser and nosing are cut square against 
 the base of the newel. 
 
 Fig. 8 shows a portion of a cut and 
 mitered string, which will give an excellent 
 idea of the method of construction. - The 
 
 letter shows the nosing, F the return nosing with a bracket termi- 
 nating against it. These brackets are about r 5 T inch thick, and are 
 planted (nailed) on the string; the brackets miter with the ends of 
 the risers; the ends of the brackets which miter with the risers, are 
 
 Fig. 7. Front Elevation of 
 Finished Steps. 
 
6 
 
 STAIR-BUILDING 
 
 Fig. 8. Portion of a Cut and Mitered 
 String. Showing Method of 
 Constructing Stairs. 
 
 to be the same height as the riser. The lower ends of two, balus- 
 ters are shown at G G; and the dovetails, or mortises to receive these 
 are shown at E E. Generally two balusters are placed on each 
 
 tread, as shown; but there are some- 
 * times instances in which three are used, 
 while in others only one baluster is 
 made use of. 
 
 An end portion of a cut and 
 - mitered string is shown in Fig. 9, with 
 part of the string taken away, show- 
 ing the carriage — a rough piece of 
 lumber to which the finished string is 
 nailed or otherwise fastened. At C is 
 shown the return nosing, and the man- 
 ner in which the work is finished. A 
 rough bracket is sometimes nailed on 
 the carriage, as shown at D, to support the tread. The balusters are 
 shown dovetailed into the ends of the treads, and are either glued or 
 nailed in place, or both. On the lower edge of string, at B, is a return 
 bead or moulding. It will be noticed that the rough carriage is cut in 
 snugly against the floor joist. 
 Fig. 10 is a plan of the portion 
 of a -stairway shown in Fig. 9. 
 Here the position of the string, 
 bracket, riser, and tread can be 
 seen. At the lower step is shown 
 how to miter the riser to the 
 string; and at the second step is 
 shown how to miter it to the 
 bracket. 
 
 Fig. 11 shows a quick method 
 of marking the ends of the treads 
 
 Fig. 
 
 9. End Portion of Cut and Mitered 
 String, with Part Removed to 
 Show Carriage. 
 
 for the dovetails for balusters. 
 
 The templet A is made of some 
 
 thin material, preferably zinc or 
 
 hardwood. The dovetails are outlined as shown, and the intervening 
 
 portions of the material are cut away, leaving the dovetail portions 
 
 solid. The templet is then nailed or screwed to a gauge-block E, 
 
STAIR-BUILDING 
 
 St ™9 B mSS 
 
 Fig. 10. Plan of Portion of Stair. 
 
 when the whole is ready for use. The method of using is clearly 
 indicated in the illustration. 
 
 Strings. There are two main kinds of- stair strings — wall strings 
 
 and cut strings. These are divid- 
 ed, again, under other names, as 
 housed strings, notched strings, 
 staved strings, and rough strings. 
 Wall strings are the supporters 
 of the ends of the treads and 
 risers that are against the wall; 
 these strings may be at both ends of 
 the treads and risers, or they may be at one end only. They may be 
 housed (grooved) or left solid. When housed, the treads and risers 
 are keyed into them, and glued and blocked. When Jeft solid, they 
 have a rough string or carriage spiked or screwed to them, to lend 
 additional support to the ends of risers and treads. Stairs made after 
 this fashion are generally of a rough, strong kind, and are especially 
 adapted for use in factories, shops, and warehouses, where strength 
 and rigidity are of more importance than mere external appearance. 
 Open strings are outside strings or supports, and are cut to the 
 proper angles for receiving the ends of 
 the treads and risers. It is over a string 
 of this sort that the rail and balusters 
 range; it is also on such a string that al 
 nosings return; hence, in some localities, 
 an open string is known as a return string. 
 Housed strings are those that have 
 grooves cut in them to receive the ends of 
 treads and risers. As a general thing, wall- strings are housed. The 
 housings are made from f to f inch deep, and the lines at top of tread 
 and face of riser are made to correspond with the lines of riser and 
 tread when in position. The back lines of the housings are so 
 located that a taper wedge may be driven in so as to force the tread 
 and riser close to the face shoulders, thus making a tight joint. 
 
 Rough strings are cut from undressed plank, and are used for 
 strengthening the stairs. Sometimes a combination of rough-cut 
 strings is used for circular or geometrical stairs, and, when framed 
 
 Fig. 11. Templet Used to Mark 
 
 Dovetail Cuts for 
 
 Balusters. 
 
 together, forms the support or carriage of the stairs. 
 
8 STAIR-BUILDING 
 
 Staved strings are built-up strings, and are composed of narrow 
 pieces glued, nailed, or bolted together so as to form a portion of a 
 cylinder. These are sometimes used for circular stairs, though in 
 ordinary practice the circular part of a string is a part of the main 
 string bent around a cylinder to give it the right curve.. 
 
 Notched strings are strings that carry only treads. They are 
 generally somewhat narrower than the treads, and are housed across 
 their entire width. A sample of this kind of string is the side of a 
 common step-ladder. Strings of this sort are used chiefly in cellars, 
 or for steps intended for similar purposes. 
 
 Setting Out Stairs. In setting out stairs, the first thing to do is 
 to ascertain the locations of the first and last risers, with the height 
 of the story wherein the stair is to be placed. These points should be 
 marked out, and the distance between them divided off equally, 
 giving the number of steps or treads required. Suppose we have 
 between these two points 15 feet, or 180 inches. If we make our 
 treads 10 inches wide, we shall have 18 treads. It must be remembered 
 that the number of risers is always one more than the number of treads, 
 so that in the case before us there will be 19 risers. 
 
 The height of the story is next to be exactly determined, being 
 
 taken on a rod. Then, assuming a height of riser suitable to the place, 
 
 we ascertain, by division, how often this height of riser is contained 
 
 in the height of the story; the quotient, if there is no remainder, 
 
 will be the number of risers in the story. Should there be a remainder 
 
 on the first division, the operation is reversed, the number of inches 
 
 in the height being made the dividend, and the before-found quotient, 
 
 the divisor. The resulting quotient will indicate an amount to be 
 
 added to the former assumed height of riser for a new trial height. 
 
 The remainder will now be less than in the former division; and if 
 
 necessary, the operation of reduction by division is repeated, until 
 
 the height of the riser is obtained to the thirty-second part of an inch. 
 
 These heights are then set off on the story rod as exactly as possible. 
 
 The story rod is simply a dressed or planed pole, cut to a length 
 
 exactly corresponding to the height from the top of the lower floor 
 
 to the top of the next floor. Let us suppose this height to be 11 feet 
 
 1 inch, or 133 inches. Now, we have 19 risers to place in this space, 
 
 to enable us to get upstairs; therefor, if we divide 133 by 19, we 
 
 get 7 without any remainder. Seven inches will therefore be the 
 
STAIR-BUILDING 
 
 width or height of the riser. Without figuring this out, the workman 
 may find the exact width of the riser by dividing his story rod, by 
 means of pointers, into 19 equal parts, any one part being the proper 
 width. It may be well, at this point, to remember that the first riser 
 must always be narrower than the others, because the thickness of the 
 first tread must be taken off. 
 
 The width of treads may also be found without figuring, by 
 pointing off the run of the stairs into the required number of parts; 
 though, where the student is qualified, it is always better to obtain 
 the width, both of treads and of risers, by the simple arithmetical 
 rules. 
 
 Having determined the width of treads and risers, a pitch-board 
 should be formed, showing the angle of inclination. This is done by 
 cutting a piece of thin board or metal in the shape of a right-angled 
 triangle, with its base exactly equal to the run of the step, and its 
 perpendicular equal to 
 the height of the riser. 
 It is a general maxim, 
 that the greater the 
 breadth of a step or tread , 
 the less should be the 
 height of the riser; and, 
 conversely, the less the 
 breadth of a step, the 
 greater should be the 
 height of the riser. The 
 proper relative dimensions of treads 
 graphically, as in Fig. 12. 
 
 In the right-angle triangle ABC, make A B equal to 24 inches, 
 and B C equal to 11 inches — the standard proportion. Now, to find 
 the riser corresponding to a given width of tread, from B, set off on 
 A B the width of the tread, as B D; and from D, erect a perpendicular 
 D E, meeting the hypotenuse in E; then D E is the height of the riser; 
 and if we join B and E, the angle D B E is the angle of inclination, 
 showing the slope of the ascent. In like manner, where B F is the 
 width of the tread, F G is the riser, and B G the slope of the stair. 
 A width of tread B H gives a riser of the height of EI K; and a width 
 of tread equal to B L gives a riser equal to L M. 
 
 Fiar. 12. 
 
 Graphic Illustration of Proportional Dimen- 
 sions of Treads and Risers. 
 
 and risers may be illustrated 
 
10 ' STAIR-BUILDING 
 
 In the opinion of many builders, however, a better scheme of 
 proportions for treads and risers is obtained by the following method : 
 
 Set down two sets of numbers, each in arithmetical progression — 
 the first set showing widths of tread, increasing by inches; the other 
 showing heights of riser, decreasing by half-inches. 
 
 Treads, Inches 
 
 Risers, Inches 
 
 5 
 
 9 
 
 6 
 
 $h 
 
 7 
 
 8 
 
 S 
 
 7* 
 
 9 
 
 7 
 
 10 
 
 61 
 
 11 
 
 6 
 
 12 
 
 51 
 
 13 
 
 5 
 
 14 
 
 41 
 
 15 
 
 4 
 
 16 
 
 31 
 
 17 
 
 3 
 
 18 
 
 21 
 
 It will readily be seen that each pair of treads and risers thus obtained 
 is suitably proportioned as to dimensions. 
 
 It is seldom, however, that the proportions of treads and risers 
 are entirely a matter of choice. The space allotted to the stairs usually 
 determines this proportion ; but the above will be found a useful stand- 
 ard, to which it is desirable to approximate. 
 
 In the better class of buildings, the number of steps is considered 
 in the plan, which it is the business of the Architect to arrange; and 
 in such cases, the height of the story rod is simply divided into the 
 number required. 
 
 Pitch-Board. It will now be in order to describe a pitch-board 
 and the manner of using it; no stairs can be properly built without 
 the use of a pitch-board in some form or other. Properly speaking, 
 a pitch-board, as already explained, is a thin piece of material, 
 generally pine or sheet metal, and is a right-angled triangle in outline. 
 One of its sides is made the exact height of the rise; at right angles 
 with this line of rise, the exact width of the tread is measured off; 
 and the material is cut along the hypotenuse of the right-angled 
 triangle thus formed. 
 
 The simplest method of making a pitch-board is by using a steel 
 
STAIR-BUILDING 
 
 11 
 
 Fig. 13. Steel Square Used as a Pitch 
 
 Board in Laying Out Stair 
 
 String. 
 
 square, which, of course, every carpenter in this country is supposed 
 
 to possess. By means of this invaluable tool, also, a stair string can 
 
 be laid out, the square being applied to the string as shown in Fig. 13. 
 
 In the instance here illustrated, the 
 square shows 10 inches for the 
 tread and 7 inches for the rise. 
 
 To cut a pitch-board, after the 
 tread and rise have been deter- 
 mined, proceed as follows: Take 
 a piece of thin, clear material, and 
 lay the square on the face edge, as 
 shown in Fig. 13. Mark out the 
 
 pitch-board with a sharp knife; then cut out with a fine saw, and 
 
 dress to the knife marks; nail a piece on the largest edge of the pitch- 
 board for a gauge or fence, and it is ready for use. 
 
 Fig. 14 shows the pitch-board pure and simple; it may be half 
 
 an inch thick, or, if of hardwood, may be from a quarter-inch to a 
 
 half -inch thick. 
 
 Fig. 15 shows the pitch-board after the gauge or fence is nailed "on. 
 
 This fence or gauge may be about 1J inches wide and from f to j 
 
 inch thick . 
 
 Fig. 16 shows a sectional view of the pitch-board with a fence 
 
 nailed on. 
 
 In Fig. 17 the manner of applying the pitch-board is shown. 
 
 R R R is the string, and the line A shows the jointed or straight edge 
 
 of the string. The 
 
 pitch-board P is 
 
 shown in position, the 
 
 line 8^ represents the 
 
 step or tread, and the 
 
 line 7f shows the line 
 
 of the riser. These 
 
 two lines are of course 
 
 at right angles, or, as the carpenter would say, they are square. 
 
 This string shows four complete cuts, and part of a fifth cut for 
 
 treads, and five complete cuts for risers. The bottom of the string 
 
 at W is cut off at the line of the floor on which it is supposed to 
 
 rest. The line C is the line of the first riser. This riser is cut lower 
 
 Fig. 14. Fig. 15. Fig. 16. 
 
 Showing How a Pitch-Board is Made. 
 
 Fig. 15 shows gauge fastened to long edge; Fig. 16 is a 
 
 sectional elevation of completed board 
 
c 
 
 12 STAIR-BUILDING 
 
 than any of the other risers, because, as above explained, the thick- 
 ness of the first tread is always taken off it; thus, if the tread is 1J 
 inches thick, the riser in this case would only require to be 6J inches 
 wide, as 7| — 1J = 6J. 
 
 The string must be cut so that the line at W will be only 6£ 
 inches from the line at 8 \, and these two lines must be parallel. 
 The first riser and tread having been satisfactorily dealt with, the 
 rest can easily be marked off by simply sliding the pitch-board along 
 the line A until the outer end of the line 8J on the pitch-board 
 strikes the outer end of the line 7f on the string, when another tread 
 and another riser are to be marked off. The remaining risers and 
 treads are marked off in the same manner. 
 
 Sometimes there may be a little difficulty at the top of the stairs, 
 
 in fitting the string to the 
 
 A ^ ^ trimmer or joists; but, as it 
 
 is necessary first to become 
 expert with the pitch-board, 
 the method of trimming the 
 well or attaching the cylinder 
 to the string will be left until other matters have been discussed. 
 
 Fig. 18 shows a portion of the stairs in position. S and S show 
 the strings, which in this case are cut square; that is, the part of the 
 string to which the riser is joined is cut square across, and the butt or 
 end wood of the riser is seen. In this case, also, the end of the tread 
 is cut square off, and flush with the string and riser. Both strings 
 in this instance are open strings. Usually, in stairs of this kind, the 
 ends of the treads are rounded off similarly to the front of the tread, 
 and the ends project over the strings the same distance that the front 
 edge projects over the riser. If a moulding or cove is used under the 
 nosing in front, it should be carried round on the string to the back 
 edge of the tread and cut off square, for in this case the back edge of 
 the tread will be square. A riser is shown at R, and it will be noticed 
 that it runs down behind the tread on the back edge, and is either 
 nailed or screwed to the tread. This is the American practice, though 
 in England the riser usually rests on the tread, which extends clear 
 back to string as shown at the top tread in the diagram. It is much 
 better, however, for general purposes, that the riser go behind the 
 tread, as this tends to make the whole stairway much stronger. 
 
 Fig. 17. Showing Method of Using Pitch-Board. 
 
STAIR-BUILDING 
 
 13 
 
 Fig. 18. Portion of Stair in Position. 
 
 Housed strings are those which carry the treads and risers without 
 their ends being seen. In an open stair, the wall string only is housed, 
 the other ends of the treads and risers resting on a cut string, and the 
 
 nosings and mouldings 
 being returned as be- 
 fore described. 
 
 The manner of 
 housing is shown in 
 Fig. 19, in which the 
 treads T T and the 
 isers R R are shown 
 in position, secured in 
 place respectively by 
 means of wedges X X 
 and F F, which should 
 be well covered with 
 good glue before insertion in the groove. The housings are 
 generally made from \ to f inch deep, space for the wedge being cut 
 to suit. 
 
 In some closed stairs in which there is a housed string between the 
 newels, the string is double-tenoned into the shanks of both newels, 
 as shown in Fig. 20. The string in this example is made 12| inches 
 wide, which is a very good width 
 for a string of this kind; but the 
 thickness should never be less than 
 1 J inches. The upper newel is made 
 about 5 feet 4 inches long from drop 
 to top of cap. These strings are 
 generally capped with a subrail of 
 some kind, on which the baluster, 
 if any, is cut-mitered in. Generally 
 a groove, the width of the square 
 of the balusters, is worked on the 
 top of the subrail, and the balusters are worked out to fit into this 
 groove; then pieces of this material, made the width of the groove 
 and a little thicker than the groove is deep, are cut so as to fit in 
 snugly between the ends of the balusters resting in the groove. This 
 makes a solid job; and the pieces between the balusters may be made 
 
 Showing Method of Housing 
 Treads and Risers. 
 
14 
 
 STAIR-BUILDING 
 
 of any shape on top, either beveled, rounded, or moulded, in which 
 case much is added to the appearance of the stairs. 
 
 Fig. 21 exhibits the method of attaching the rail and string to 
 
 the bottom newel. The dotted lines 
 indicate the form of the tenons cut to 
 fit the mortises fnade in the newel to 
 receive them. 
 Fig. 22 shows 
 
 how the string fits 
 
 against the newel at the top; 
 also the trimmer E, to which the 
 newel post is fastened. The 
 string in this case is tenoned into 
 the upper newel post the same, 
 way as into the lower one. 
 
 Fig. 20. Showing Method of Con- 
 necting Housed String to 
 Newels. 
 
 Fig. 21. Method of Connect- 
 ing Rail and String to 
 Bottom Newel. 
 
 The open string shown in Fig. 23 is a portion 
 of a. finished string, showing nosings and cove 
 returned and finishing against the face of the 
 string. Along the lower edge of the string is 
 shown a bead or moulding, where the plaster 
 is finished. 
 
 A portion of a stair of the better class is 
 shown in Fig. 24. This is an open, bracketed 
 string, with returned nosings and coves and 
 scroll brackets. These brackets are made about 
 | inch thick, and may be in any desirable pat- 
 tern. The end next the riser should be mitered 
 to suit ; this will require the riser to be f inch 
 longer than the face of the string. The upper 
 part of the bracket should run under the cove 
 moulding; and the tread should project over 
 the string the full f inch, so as to cover the 
 
STAIR-BUILDING 
 
 15 
 
 mzzzzzzzzzzz 
 
 'azzzzzzzzzzzzzi 
 
 bracket and make the free even for the nosing and the cove moulding 
 to fit snugly against the end of the tread and the face of the bracket. 
 Great care must be taken about this point, or endless trouble will 
 
 follow. In a bracketed 
 stair of this kind, care 
 must be taken in plac- 
 ing the newel posts, 
 and provision must be 
 made for the extra f 
 inch due to the brack- 
 et. The newel post 
 must be set out from 
 the string f inch, and 
 it will then align with 
 the baluster. 
 We have now de- 
 scribed several methods of dealing with strings; but there are still a 
 few. other points connected with these members, both housed and 
 open, that it will be necessary to explain, before the young work- 
 man can proceed to build a fair flight of stairs. The connection of 
 the wall string to the lower and upper floors, and the manner of 
 affixing the outer or cut string to the upper joist and to the newel, 
 
 Fig. 22. 
 
 Connections of String and Trimmer at Upper 
 Newel Post. 
 
 Fig. 23. Portion of Finished String, 
 
 Showing Returned Nosings 
 
 and Coves, also Bead 
 
 Moulding. 
 
 Fig. 24. Portion of Open. Bracketed 
 String Stair, with Returned Nos- 
 ings and Coves. Scroll Bra fle- 
 ets, and Bead Moulding. 
 
 are matters that must not be overlooked. It is the intention to show 
 how these things are accomplished, and how the stairs are made 
 strong by the addition of rough strings or bearing carriages. 
 
16 
 
 STAIR-BUILDING 
 
 Fig. 25. Side Elevation of Part of 
 Stair with Open, Cut and 
 Mitered String. 
 
 Fig. 25 gives a side view of part of a stair of the better class, with 
 one open, cut and mitered string. In Fig. 26, a plan of this same stair- 
 way, W S shows the wall string; R S, the rough string, placed there 
 
 to give the structure strength; and 
 S, the outer or cut and mitered string. 
 At A A the ends of the risers are shown, 
 and it will be noticed that they are 
 mitered against a vertical or riser line 
 of the string, thus preventing the end of 
 the riser from being seen. The other 
 end of the riser is in the housing in the 
 wall string. The outer end of the tread 
 is also mitered at the nosing, and a piece 
 of material made or worked like the 
 nosing is mitered against or returned at the end of the tread. 
 The end of this returned piece is again returned on itself back to the 
 string, as shown at N in Fig. 25. The moulding, which is f-inch 
 cove in this case, is also returned on itself back to the string. 
 
 The mortises shown at B B B B (Fig. 26), are for the balusters. 
 It is always the proper thing to saw the ends of the treads ready for 
 the balusters before the treads are attached to the string; then, when 
 the time arrives to put up the rail, the back ends of the mortises can 
 be cut out, when the treads will 
 be ready to receive the balusters. 
 The mortises are dovetailed, and, 
 of course, the tenons on the balus- 
 ters must be made to suit. The 
 treads are finished on the bench; 
 and the return nosings are fitted 
 to them and tacked on, so that 
 they may be taken off to insert 
 the balusters when the rail is being 
 put in position. 
 
 Fig. 27 shows the manner in 
 which a wall string is finished at the foot of the stairs. S shows the 
 string, with moulding wrought on the upper edge. This moulding 
 may be a simple ogee, or may consist of a number of members; 
 or it may be only a bead ; or, again, the edge of the string may be 
 
 B 
 
 It 
 
 B 
 
 \t 
 
 ]ws 
 
 7RS 
 
 los 
 
 Fig. 26. 
 
 Plan of Part of Stair Shown in 
 Fig. 25. 
 
STAIR-BUILDING 
 
 17 
 
 kvkvwAvw^ 
 
 Fig. 21 
 
 Showing How Wall String is Fin- 
 ished at Foot of Stair. 
 
 left quite plain; this will be regulated in great measure by the style of 
 
 finish in the hall or other part of the house in which the stairs are 
 
 placed. B shows a portion of a baseboard, the top edge of which 
 
 has the same finish as the top edge of the string. B and A together 
 
 show the junction of the string 
 and base. F F show blocks 
 glued in the angles of the steps 
 to make them firm and solid. 
 Fig. 28 shows the manner 
 in which the wall string S is 
 finished at the top of the stairs. 
 It will be noticed that the 
 moulding is worked round the 
 ease-off at A to suit the width 
 of the base at B. The string 
 is cut to fit the floor and to 
 
 butt against the joist. The plaster line under the stairs and on the 
 
 ceiling, is also shown. 
 
 Fig. 29 shows a cut or open string at the foot of a stairway, and 
 
 the manner of dealing with it at its junction with the newel post K« 
 
 The point of the string should 
 
 be mortised into the newel 2 
 
 inches, 3 inches, or 4 inches, 
 
 as shown by the dotted lines; 
 
 and the mortise in the newel 
 
 should be cut near the center, 
 
 so that the center of the balus- 
 ter will be directly opposite 
 
 the central line of the newel 
 
 post. The proper way to 
 
 manage this, is to mark the 
 
 central line of the baluster on 
 
 the tread, and then make this 
 
 line correspond with the central line of the newel post. By careful 
 
 attention to this point, much trouble will be avoided where a turned 
 
 cap is used to receive the lower part of the rail. 
 
 The lower riser in a stair of this kind will be somewhat shorter 
 
 than the ones above it. as it must be cut to fit between the newel and 
 
 Fig. 28. Showing How Wall String is Fin- 
 ished at Top of Stair. 
 
18 
 
 STAIR-BUILDING 
 
 Square 
 
 the wall strng. A portion of the tread, as well as of the riser, will 
 also butt against the newel, as shown at W. 
 
 If there is no spandrel or wall under the open string, it may 
 run down to the floor as shown by the dotted line at 0. The piece 
 is glued to the string, and the moulding is worked on the curve. 
 If there is a wall under the string S, then the base B, shown by the 
 dotted lines, will finish against the string, and it should have a mould - 
 ing on its upper edge, the same as that on the lower edge of the string, 
 if any, this moulding being mitered into the one on the string. When 
 there is a base, the piece is of course dispensed with. 
 
 . The square of the newel should run down by the side of a joist 
 as shown, and should be firmly secured to the joist either by spiking 
 
 or by some other suitable device. 
 If the joist runs the other way, 
 try to get the newel post against 
 it, if possible, either by furring 
 out the joist or by cutting a por- 
 tion off the thickness of the newel. 
 The solidity of a stair and the 
 firmness of the rail, depend very 
 much upon the rigidity of the 
 newel post. The above sugges- 
 tions are applicable where great 
 strength is required, as in public 
 buildings. In ordinary work, the usual method is to let the newel rest 
 on the floor. 
 
 Fig. 30 shows how the cut string is finished at the.top of the stairs. 
 This illustration requires no explanation after the instructions already 
 given. 
 
 Thus far, stairs having a newel only at the bottom have been 
 dealt with. There are, however, many modifications of straight and 
 return stairs which have from two to four or six newels. In such 
 cases, the methods of treating strings at their finishing points must 
 necessarily be somewhat different from those described; but the 
 general principles/as shown and explained, will still hold good. 
 
 Well-Hole. Before proceeding to describe and illustrate neweled 
 stairs, it will be proper to say something about the well-hole, or the 
 
 Fig. 29. Showing How a Cut or Open String 
 is Finished at Foot of Stair. 
 
STAIR-BUILDING 
 
 19 
 
 opening through the floors, through which the traveler on the stairs 
 ascends or descends from one floor to another. 
 
 Fig 31 shows a well-hole, and the manner of trimming it. In 
 this instance the stairs are placed against the wall; but this is not 
 necessary in all cases, as the well-hole may be placed in any part of 
 the building. 
 
 The arrangement of the trimming varies according as the joists 
 are at right angles to, or are parallel to, the wall against which the 
 stairs are built. In the former case (Fig. 31,-4) the joists are cut short 
 and tusk-tenoned into the heavy trimmer T T , as shown in the cut. 
 This trimmer is again tusk-tenoned into two heavy joists T J and T J, 
 which form the ends of the well-hole. These heavy joists are called 
 trimming joists; and, as they have to carry a much heavier load than 
 other joists on the same Moor, 
 they are made much heavier. 
 Sometimes two or three joists 
 are placed together, side by 
 side, being bolted or spiked 
 together to give them the 
 desired unity and strength. In 
 constructions requiring great 
 strength, the tail and header 
 joists of a well-hole are sus- 
 pended on iron brackets. 
 
 If the opening runs paral- 
 lel with the joists (Fig. 31, B), the timber forming the side of the 
 well-hole should be left a little heavier than the other joists, as it 
 will have to carry short trimmers (T J and T J) and the joists run- 
 ning into them. The method here shown is more particularly 
 adapted to brick buildings, but there is no reason why the same 
 system may not be applied to frame buildings. 
 
 Usually in cheap, frame buildings, the trimmers T T are spiked 
 against the ends of tlie joists, and the ends of the trimmers are Sup- 
 ported by being spiked to the trimming joists T J , T J . This is not 
 .cry workmanlike or very secure, and should not be done, as it is not 
 early so strong or durable as the old method of framing the joists and 
 trimmers together. 
 
 Fig. o2 shows a stair with three newels and a platform. In this 
 
 Fig. 
 
 Showing How a Cut or Open String 
 is Finished at Top of Stair. 
 
20 
 
 STAIR-BUILDIXG 
 
 example, the first tread (No. 1) stands forward of the newel post 
 two-thirds of its width. This is not necessary in every case, but it is 
 sometimes done to suit conditions in the hallway. The second newel 
 is placed at the twelfth riser, and supports the upper end of the first 
 
 TJ. 
 
 JLL 
 
 Fig. 31. 
 
 Showing Ways of Trimming Well-Hole "when Joists Run in Different 
 Directions. 
 
 cut string and the lower end of the second cut string. The platform 
 (12) is supported by joists which are framed into the wall and are 
 fastened against a trimmer running from the wall to the newel along 
 the line 12. This is the case only when the second newel runs down 
 to the floor. 
 
 If the second newel does not run to the floor, the framework 
 supporting the platform will need to be built on studding. The third 
 newel stands at the top of the stairs, and is fastened to the joists of 
 the second floor, or to the trimmer, somewhat after the manner of 
 fastening shown in Fig. 29. In this example, the stairs have 1G risers 
 
STAIR-BUILDING 
 
 21 
 
 and 15 treads, the platform or landing (12) making one tread. The 
 figure 16 shows the floor in the second story. 
 
 This style of stair will require a well-hole in shape about as 
 shown in the plan; and where strength is required, the newel at the 
 top should run from floor to floor, and act as a support to the joists 
 and trimmers on which the second floor is laid. 
 
 Perhaps the best way for a beginner to go about building a stair- 
 way of this type,jwill be to lay out the work on the lower floor in the 
 exact place where the stairs are to be erected, making everything 
 
 12 
 
 o 
 
 10 9 
 
 8 
 
 5"x5' 
 
 D^ 
 
 D5"x5" 
 
 Fig. 32. Stair with Three Newels and a Platform. 
 
 full size. There will be.no difficulty in doing this; and if the positions 
 of the first riser and the three newel posts are accurately defined, 
 the building of the stairs will be an easy matter. Plumb lines can be 
 raised from the lines on the floor, and the positions of the platform 
 and each riser thus easily determined. Not only is it best to line out 
 on the floor all stairs having more than one newel; but in constructing 
 any kind of stair it will perhaps be safest for a beginner to lay out in 
 exact position on the floor the points over which the treads and risers 
 will stand. By adopting this rule, and seeing that the strings, risers, 
 and treads correspond exactly with the lines on the floor, many cases 
 of annoyance will be avoided. Many expert stair-builders, in fact, 
 adopt this method in their practice, laying out all stairs on the floor, 
 including even the carriage strings, and they cut out all the material 
 from the lines obtained on the floor. By following this method, one 
 can see exactly the requirements in each particular case, and can 
 rectify any error without destroying valuable material. 
 
22 STAIR-BUILDING 
 
 Laying Out. In order to afford the student a clear idea of what 
 is meant by laying out on the floor, an example of a simple close- 
 string stair is given. In Fig. 33, the letter F shows the floor line; 
 L is the landing or platform; and W is the wall line. The stair is to 
 be 4 feet wide over strings; the landing, 4 feet wide ; the height from 
 floor to landing, 7 feet; and the run from start to finish of the stair, 8 
 feet 8J inches. 
 
 The first thing to determine is the dimensions j}f the treads and 
 risers. The wider the tread, the lower must be the riser, as stated 
 before. No cfefinite dimensions for treads* and risers can be given, 
 as the steps have to be arranged to meet the various difficulties that 
 may occur in the working out of the construction; but a common 
 rule is this: Make the width of the tread, plus twice the rise, equal 
 to 24 inches. This will give, for an 8-inch tread, an 8-inch rise; 
 for a 9-inch tread, a 7^-inch rise; for a 10-inch tread, a 7-inch rise, 
 and so on. Having the height (7 feet) and the run of the flight (8 feet 
 8J inches), take a rod about one inch square, and mark on it the height 
 from floor to landing (7 feet), and the length of the going or run of the 
 flight (8 feet 8 J inches). Consider now what are the dimensions 
 which can be given to the treads and risers, remembering that there 
 will be one more riser than the number of treads. Mark off on the 
 rod the landing, forming the last tread. If twelve risers are desired, 
 divide the height (namely, 7 feet) by 12, which gives 7 inches as the 
 rise of each step. Then divide the run (namely, 8 feet 8J inches) by 
 11, and the width of the tread is found to be 9 \ inches. 
 
 Great care must be taken in making the pitch-board for marking 
 off the treads and risers on the string. The pitch-board may be made 
 from dry hardwood about f inch thick. One end and one side must 
 be perfectly square to each other; on the one, the width of the tread 
 is set off, and on the other the height of the riser. Connect the two 
 points thus obtained, and saw the wood on this line. The addition 
 of a gauge-piece along the longest side of the triangular piece, com- 
 pletes the pitch-board, as was illustrated in Fig. 15. 
 
 The length of the wall and outer string can be ascertained by 
 means of the pitch-board. One side and one edge of the wall string 
 must be squared; but the outer string must be trued all round. On 
 the strings, mark the positions of the treads and risers by using the 
 pitch-board as already explained (Fig. 17). Strings are usually 
 
STAIR-BUILDIXG 
 
 23 
 
 made 11 inches wide, but may be made 12V inches wide if necessary 
 for strength. 
 
 After the widths of risers and treads have been determined, and 
 the string is ready to lay out, apply the pitch-board, marking the 
 
 <r 
 
 
 
 ♦ i 
 
 
 
 — 
 
 i—r 
 :> [ 
 
 r'j 
 
 
 1 
 
 i 
 
 
 
 — 
 
 i 
 
 |§|r 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Fig. 
 
 Method of Laying Out a Simple, Close-String Stair. 
 
 first riser about 9 inches from the end ; and number each step in succes- 
 sion. The thickness of the treads and risers can be drawn by using 
 thin strips of hardwood made the width of the housing required. 
 Now allow for the wedges under the treads and behind the risers, and 
 thus find the exact width of the housing, which should be about f inch 
 
24 STAIR- BUILDING 
 
 deep; the treads and risers will require to be made 1J inches longer 
 than shown in the plan, to allow for the housings at both ends. 
 
 Before putting the stair together, be sure that it can be taken 
 into the house and put in position without trouble. If for any reason 
 it cannot be put in after being put together, then the parts must be 
 assembled, wedged, and glued up at the spot. 
 
 It is essential in laying out a plan on the floor, that the exact 
 positions of the first and last risers be ascertained, and the height of 
 the story wherein the stair is to be placed. Then draw a plan of the 
 hall or other room in which the stairs will be located, including sur- 
 rounding or adjoining parts of the room to the extent of ten or twelve 
 feet from the place assigned for the foot of the stair. All the door- 
 ways, branching passages, or windows which can possibly come in 
 contact with the stair from its commencement to its expected ter- 
 mination or landing, must be noted. The sketch must necessarily in- 
 clude a portion of the entrance hall in one part, and of the lobby or 
 landing in another, and on it must be laid out all the lines of the 
 stair from the first to the last riser. 
 
 The height of the story must next be exactly determined and 
 taken on the rod ; then, assuming a height of risers suitable to the place, 
 a trial is made by division in the manner previously explained, to 
 ascertain how often this height is contained in the height of the story. 
 The quotient, if there is no remainder, will be the number of risers 
 required. Should there be a remainder on the first division, the opera- 
 tion is reversed, the number of inches in the height being made the 
 dividend and the before-found quotient the divisor; and the operation 
 of reduction by division is carried on till the height of the riser is 
 obtained to the thirty-second part of an inch. These heights are then 
 set off as exactly as possible on the story rod, as shown in Fig. 33. 
 
 The next operation is to show the risers on the sketch. This 
 the workman will find no trouble in arranging, and no arbitrary rule 
 can be given. 
 
 A part of the foregoing may appear to be repetition; but it is not, 
 for it must be remembered that scarcely any two flights of stairs are 
 alike in run, rise, or pitch, and any departure in any one dimension 
 from these conditions leads to a new series of dimensions that must 
 be dealt with independently. The principle laid down, however, 
 applies to all straight flights of stairs; and the student who has followed 
 
STAIR-BUILDING 25 
 
 closely and retained the pith of what has been said, will, if he has a 
 fair knowledge of the use of tools, be fairly equipped for laying out 
 and constructing a plain, straight stair with a straight rail. 
 
 Plain stairs may have one platform, or several; and they may 
 turn to the right or to the left, or, rising from a platform or landing, 
 may run in an opposite direction from their starting point. 
 
 When two flights are necessary for a story, it is desirable that 
 each flight should consist of the same number of steps; but this, of 
 course, will depend on the form of the staircase, the situation and 
 height of doors, and other obstacles to be passed under or over, as 
 the case may be. 
 
 In Fig. 32, a stair is shown with a single platform or landing and 
 three newels. The first part of this stair corresponds, in number of 
 risers, with the stair shown in Fig. 33; the second newel runs down 
 to the floor, and helps to sustain the landing. This newel may simply 
 by a 4 by 4-inch post, or the whole space may be inclosed with the 
 spandrel of the stair. The second flight starts from the platform just 
 as the first flight starts from the lower floor, and both flights may be 
 attached to the newels in the manner shown in Fig. 29. The bottom 
 tread in Fig. 32 is rounded off against the square of the newel post; 
 but this cannot well be if the stairs start from the landing, as the tread 
 would project too far onto the platform. Sometimes, in high-class 
 stairs, provision is made for the first tread to project well onto the 
 landing. 
 
 If there are more platforms than one, the principles of construc- 
 tion will be the same; so that whenever the student grasps the full 
 conditions governing the construction of a single-platform stair, he 
 will be prepared to lay out and construct the body of any stair having 
 one or more landings. The method of laying out, making, and setting 
 up a hand-rail will be described later. 
 
 Stairs formed with treads each of equal width at both ends, are 
 named straight flights; but stairs having treads wider at one end than 
 the other are known by various names, as winding stairs, dog-legged 
 stairs, circular stairs, or elliptical stairs. A tread with parallel sides, 
 having the same width at each end, is called a flyer; while one having 
 one wide end and one narrow, is called a winder. These terms will 
 often be made use of in what follows. 
 
26 
 
 STAIR-BUILDING 
 
 The elevation and plan of the stair shown in Fig. 34 may be 
 called a dog-legged stair with three winders and six flyers. The flyers, 
 however, may be extended to any number. The housed strings to 
 receive the winders are shown. These strings show exactly the manner 
 of construction. The shorter string, in. the corner from \ to 4, which 
 is shown in the plan to contain the housing of the first winder and 
 
 half of the second, is put 
 up first, the treads being 
 leveled by aid of a spirit 
 level ; and the longer upper 
 string is put in place after- 
 wards, butting snugly 
 against the lower string in 
 the corner. It is then 
 fastened firmly to the wall. 
 The winders are cut snugly 
 around the newel post, and* 
 well nailed. Their risers 
 will stand one above 
 another on the post; and 
 the straight string above 
 the winders will enter the 
 post on a line with the top 
 edge of the uppermost 
 winder. 
 
 Platform stairs are often 
 constructed so that one 
 flight will run in a direc- 
 tion opposite to that of the 
 other flight, as shown in Fig. 35. In cases of this kind, the landing or 
 platform requires to have a length more than double that of the treads, 
 in order that both flights may have the same width. Sometimes, 
 however, and for various reasons, the upper flight is made a little 
 narrower than the lower; but this expedient should be avoided when- 
 ever possible, as its adoption unbalances the stairs. In the example 
 before us, eleven treads, not including the landing, run in one direction; 
 while four treads, including the landing, run in the opposite direction ; 
 or, as workmen put it, the stair "returns on itself." The elevation 
 
 Fig. 34. Elevation and Plan of Dog-Legged Stair 
 with Three Winders and Six Fivers. 
 
STAIR-BUILDING 
 
 27 
 
 12 
 
 Lomdinq 
 
 10 
 
 2 
 
 13 
 
 \A 
 
 Newel 
 
 16 
 
 Wall 
 
 Fig. 35. Plan of Platform Stair Returning on Itself. 
 
 shown in Fig. 36 illustrates the manner in which the work is executed, 
 The various parts are shown as follows: 
 
 Fig. 37 is a section of the top landing, with baluster and rail. 
 
 Fig. 3S is part of the long newel, showing mortises for the strings. 
 
 Fig. 36. Elevation Showing Construction of Platform Stair of which Plan is 
 Given in Fig. 35. 
 
28' 
 
 STAIR-BUILDING 
 
 Fig. 39 represents part of the bottom newel, showing the string, 
 moulding on the outside, and cap. 
 
 Fig. 40 is a section of the top string enlarged. 
 
 Fig. 41 is the newel at the bottom, as cut out to 
 receive bottom step. It must be remembered that 
 there is a cove under each tread. This may be nailed 
 in after the stairs are put together, and it adds greatly 
 to the appearance. 
 
 We may state that stairs should have carriage pieces 
 
 of F To 37 Landin° n ^ xe< ^ ^ rom ^ OOY to floor, under the stairs, to support 
 Baiuster.andRaii! them. These may be notched under the steps; or 
 rough brackets may be nailed to the side of the car- 
 riage, and carried under each riser and tread. 
 
 There is also a framed spandrel which helps materially to carry 
 the weight, makes a sound job, and 
 adds greatly to the appearance. This 
 spandrel may be made of lj-inch 
 material, with panels and mouldings 
 on the front side, as shown in Fig. 36. 
 The joint between the top and bottom 
 rails of the spandrel at the angle, 
 should be made as shown in Fig. 42 
 with a cross-tongue, and glued and 
 fastened with long screws. Fig. 43 is 
 simply one of the panels showing the 
 miters on the moulding and the shape Mortises m iSSf 
 
 Newel. 
 
 of the sections. As there is a conven- 
 ient space under the landing, it is commonly used for a closet. 
 
 In setting out stairs, not only the proportions of treads and risers 
 must be considered, but also the material available. 
 As this material runs, as a rule, in certain sizes, it is 
 best to work so as to conform to it as nearly as 
 possible. In ordinary stairs, 11 by 1-inch common 
 stock is used for strings and treads, and 7-inch by 
 f-inch stock for risers; in stairs of a better class, 
 wider and thicker material may be used. The rails 
 eduction of top are set ftt YSly[qus heigntS ; 2 feet 8 inches may be 
 
 Fig. 39. Mortises 
 in Lower Newel 
 for String. Out- 
 sideMoulding.and 
 Cap. . 
 
STAIR-BUILDIXG 
 
 29 
 
 taken as an average height on the stairs, and 3 feet 1 inch on landings, 
 with two balusters to each step. 
 
 In Fig. 36, all the newels and balusters are shown square; but 
 it is much better, and is the more common practice, to have them 
 
 ^ 
 
 Newel 
 
 V 
 
 Fig. 41. Newel Cut 
 to Receive Bottom 
 Step. 
 
 Fig. 42. Showing Method of Joining 
 Spandrel Rails, with Cross-Tongue 
 Glued and Screwed. 
 
 turned, as this gives the stairs a much more artistic appearance. 
 The spandrel under the string of the stairway shows a style in which 
 many stairs are finished in hallways and other similar places. Plaster 
 is sometimes used instead of the panel work, but is not nearly so good 
 as woodwork. The door under the landing may open into a closet, 
 or may lead to a cellarway, or through to some other room. 
 
 In stairs with winders, the width of a winder should, if possible, 
 be nearly the width of the regular tread, at 
 a distance of 14 inches from the narrow 
 end, so that the length of the step in 
 walking up or down the stairs may not 
 be interrupted; and for this reason and 
 several others, it is always best to have 
 three winders only in each quarter-turn. 
 Above all, avoid a four-winder turn, as 
 this makes a breakneck stair, which 
 more difficult to construct and 
 venient to use. 
 
 Bullnose Tread. No other stair, perhaps, looks so well at the 
 starting point as one having a bullnose step. In Fig. 44 are shown a 
 plan and elevation of a flight of stairs having a bullnose tread. The 
 method of obtaining the lines and setting out the body of the stairs, 
 
 is 
 incon- 
 
 Mouldin 
 
 Fig. 43. Panel in Spandrel, Sho-w 
 
 ing Miters on Moulding, and 
 
 Shape of Section. 
 
30 
 
 STAIR-BUILDING 
 
 is the same as has already been explained for other stairs, with the 
 exception of the first two steps, which are made with circular ends, 
 as shown in the plan. These circular ends are worked out as here- 
 after described, and are attached to the newel and string as shown. 
 
 Scale of& 
 
 ±== 
 
 Feet 
 
 ^ 
 
 Fig. 44. Elevation and Plan of Stair with Bullnose Tread. 
 
 The example shows an open, cut string with brackets. The spandrel 
 under the string contains short panels, and makes a very handsome 
 finish. The newels and balusters in this case are turned, and the latter 
 have cutwork panels between them. 
 
STAIR-BUILDING 
 
 31 
 
 Fig. 45. 
 through 
 Step. 
 
 Bullnose steps are usually built up with a three- 
 piece block, as shown in Fig. 45, which is a sec- 
 tion through the step indicating the blocks, tread, 
 and riser. 
 
 Fig. 46 is a plan showing how the veneer of the 
 riser is prepared before being bent into position. The block A indi- 
 cates a wedge which is glued and driven home after the veneer is 
 put in place. This tightens up the work and makes it sound and 
 clear. Figs. 47 and 48 show other methods of forming bullnose steps. 
 Fig. 49 is the side elevation of an open-string stair with bullnose 
 steps at the bottom; 
 while Fig. 50 is a view 
 showing the lower end 
 of the string, and the 
 manner in which it is 
 prepared for fixing to 
 the blocks of the step. 
 Fig. 51 is a section 
 through the string, showing the bracket, cove, and projection of tread 
 over same. 
 
 Figs. 52 and 53 show respectively a plan and vertical section of 
 the bottom part of the stair. The blocks are shown at the ends of the 
 steps (Fig. 53), with the veneered parts of the risers going round them; 
 also the position where the string is fixed to the blocks (Fig. 52) ; and 
 
 Fig. 46. 
 
 Plan Showing Preparation of Veneer before 
 Bending into Position. 
 
 Newel 
 
 Fig. 47. 
 
 Fig. 48. 
 
 Methods of Forming Bullnose Steps. 
 
 the tenon of the newel is marked on the upper step. The section (Fig, 
 53) shows the manner in which the blocks are built up and the newel 
 tenoned into them. 
 
32 
 
 STAIR-BUILDING 
 
 Fig. 49. Side Elevation of Open-Strin 
 Stair with Bullnose Steps. 
 
 The newel, Fig. 49, is rather an 
 elaborate affair, being carved at the 
 base and on the body, and having 
 a carved rosette planted in a small, 
 sunken panel on three sides, the rail 
 butting against the fourth side. 
 
 Open-Newel Stairs. Before leav- 
 ing the subject of straight and dog- 
 legged stairs, the student should be 
 made familiar with at least one 
 example of an open-newel stair. As 
 the same principles of construction 
 govern all styles of open-newel 
 stairs, a single example will be sufficient. The student must, of 
 course, understand that he himself is the greatest factor in planning 
 stairs of this type ; that the setting out and design- 
 ing will generally devolve on him. By exercising 
 a little thought and foresight, he can so arrange 
 his plan that a minimum of both labor and material 
 will be required. 
 
 Fig. 54 shows a plan of an open-newel stair 
 
 having two landings and closed strings, shown in 
 
 elevation in Fig. 55. The dotted lines show the 
 
 carriage timbers and trimmers, also the lines of 
 
 risers; while the treads are shown by full lines. 
 
 It will be noticed that the strings and trimmers 
 
 at the first landing are framed into the shank of the second newel 
 
 post, which runs down to the floor; while the top newel drops below 
 the fascia, and has a turned and carved drop. This drop 
 hangs below both the fascia and the string. The lines 
 of treads and risers are shown by dotted lines and 
 crosshatched sections. The position of the carriage 
 timbers is shown both in the landings and in the runs 
 Fig. 51. section of the stairs, the projecting ends of these timbers being 
 supposed to be resting on the wall. A scale of the plan 
 
 and elevation is attached to the plan. In Fig. 55, a story rod is 
 
 shown at the right, with the number of risers spaced off thereon. 
 
 The design of the newels, spandrel, framing, and paneling is shown. 
 
 Fig. 50. Lower End 
 of String to Connect 
 with Bullnose Step. 
 
STAIR-BUILDING 
 
 33 
 
 Fig. 52. Plan of Bottom Part 
 of Bullnose Stair 
 
 Fig. 53.- Vertical Section through 
 Bottom Part of Bullnose Stair. 
 
 Only the central carriage timbers are shown in Fig. 54; but in a 
 stair of this width, there ought to be two other timbers, not so heavy, 
 perhaps, as the central one, yet strong enough to be of service in lend- 
 ing additional strength to the stairway, and also to help carry the laths 
 and plaster or the paneling which may be necessary in completing 
 the under side or soffit. The strings being closed, the butts of their 
 balusters must rest on a subrail which caps the upper edge of the 
 outer string. 
 
 % 
 
 #fl 
 
 a 
 
 4 
 
 ^ 
 
 w 
 
 
 // 
 
 ^ 
 
 ^ 
 
 -^ 
 
 m 
 
 - j\- 
 
 S!' 
 
 
 Well -Hole 
 
 m 
 
 ili 
 
 I 
 
 IIP 
 
 i^ 
 
 I Car 
 
 ?. a 2 
 
 r'^^ 
 
 €\ 
 
 7 Feet 
 
 Fig. 54. .flan of Open-Newel Stair, with Two Landings and Closed Strings. 
 
34 
 
 STAIR-BUILDING 
 
 The first newel should pass through the lower floor, and, to 
 insure solidity, should be secured by bolts to a joist, as shown in the 
 elevation. The rail is attached to the newels in the usual manner, 
 with handrail bolts or other suitable device. The upper newel should 
 be made fast to the joists as shown, either by bolts or in some other 
 
 Fig. 55. Elevation of Open-Newel Stair Shown in Plan in Fig. 54. 
 
 efficient manner. The intermediate newels are left square on the 
 shank below the stairs, and may be fastened in the floor below either 
 by mortise and tenon or by making use of joint bolts. 
 
 Everything about a stair should be made solid and sound; and 
 every joint should set firmly and closely; or a shaky, rickety, squeaky 
 stair will be the result, which is an abomination. 
 
 Stairs with Curved Turns. Sufficient examples of stairs having 
 angles of greater or less degree at the turn or change of direction, to 
 
STAIR-BUILDING 
 
 35 
 
 enable -the student to build any stair of this class, have now been 
 given. There are, however, other types of stairs in common use, 
 whose turns are curved, and in which newels are employed only at 
 the foot, and sometimes at the finish of the flight. These curved turns 
 may be any part of a circle, according to the requirements of the case, 
 but turns of a quarter-circle or half-circle are the more common. 
 The string forming the curve is called a cylinder, or part of a cylinder, 
 as the case may be. The radius of this circle or cylinder may be any 
 length, according to the space assigned for the stair. The opening 
 around which the stair winds is called the well-hole. 
 
 Fig. 56 shows a portion of a stairway having a well-hole with 
 a 7-inch radius. This stair is rather peculiar, as it shows a quarter- 
 space landing, and a quarter-space having 
 three winders. The reason for this is the 
 fact that the landing is on a level with the 
 floor of another room, into which a door 
 opens from the landing. This is a problem 
 very often met with in practical work, 
 where the main stair is often made to do 
 the work of two flights because of one floor 
 being so much lower than another. 
 
 A curved stair, sometimes called a 
 geometrical stair, is shown in Fig. 5.7, 
 containing seven winders in the cylinder 
 or well -hole, the first and last aligning with 
 
 Pig. 56. Stair Serving for Two 
 
 Flights, with Mid-Floor 
 
 Landing. 
 
 the diameter. 
 
 In Fig. 58 is shown another example of this kind of stair, con- 
 taining nine winders in the well-hole, with a circular wall-string. 
 It is not often that stairs are built in this fashion, as most stairs having 
 a circular well-hole finish against the wall in a manner similar to that 
 shown in Fig. 57. 
 
 Sometimes, however, the workman will be confronted with a 
 plan such as shown in Fig. 58; and he should know how to lay out 
 the wall-string. In the elevation, Fig. 58, the string is shown to be 
 straight, similar to the string of a common straight flight. This results 
 from having an equal width in the winders along the wall-string, and, 
 as we have of necessity an equal width in the risers, the development 
 of the string is merely a straight piece of board, as in an ordinary 
 straight flight. In laying out the string, all we have to do is to make 
 
36 
 
 STAIR-BUILDING 
 
 a common pitch-board, and, with it as a templet, mark the lines of 
 the treads and risers on a straight piece of board, as shown at 1, 2, 3, 
 4, etc. 
 
 If you can manage to bend the string without kerfing (grooving), 
 it will be all the better; if not, the kerfs (grooves) must be parallel to 
 the rise. You can set out with a straight edge, full size, on a rough 
 platform, just as shown in the diagram; and 
 when the string is bent and set in place, the 
 risers and winders will have their correct 
 positions. 
 
 To bend these strings or otherwise prepare 
 them for fastening against the wall, perhaps 
 the easiest way is to saw the string with a fine 
 saw, across the face, making parallel grooves. 
 This method of bending is called kerfing, 
 above referred to. The kerfs or grooves 
 must be cut parallel to the lines of the risers, so as to be vertical when 
 the string is in place. This method, however — handy though it may 
 be — is not a good one, inasmuch as the saw groove will show more or 
 less in the finished work. 
 
 Another method is to build up or stave the string. There are 
 
 Fig. 57. Geometrical Stair 
 with Seven Winders. 
 
 Fig. 58. Plan of Circular Stair and Layout of Wall String 
 for Same. 
 
 several ways of doing this. In one, comparatively narrow pieces are 
 cut to the required curve or to portions of it, and are fastened together, 
 edge to edge, with glue and screws, until the necessary width is 
 obtained (see Fig. 59). The heading joints may be either butted or 
 beveled, the latter being stronger and should be cross-tongued. 
 
 Fig. 60 shows a method that may be followed when a wide string 
 is required, or a piece curbed in the direction of its width is needed 
 
STAIR-BUILDING 
 
 37 
 
 for any purpose. The pieces are stepped over each other to suit the 
 desired curve; and though shown square-edged in the figure, they are 
 usually cut beveled, as then, by reversing them, two may be cut out 
 of a batten. 
 
 Panels and quick sweeps for similar purposes are obtained in the 
 manner shown in Fig. 61, by joining up narrow boards edge to edge 
 
 Fig. 59. 
 
 Fig. 60. 
 
 Methods of Building Up Strings. 
 
 at a suitable bevel to give the desired curve. The internal curve is 
 frequently worked approximately, before gluing up. The numerous 
 joints incidental to these methods limit their uses to painted or unim- 
 portant work. 
 
 In Fig. 62 is shown a wreath-piece or curved portion of the 
 outside- string rising around the cylinder at the half-space. 
 This is formed by reducing a short piece of string to a veneer 
 between the springings; bending it upon a cylinder made to fit the 
 plan; then, when it is secured in position, filling up the back of the 
 veneer with staves glued across it; and, finally, gluing a piece of canvas 
 over the whole. The appearance of the 
 wreath-pi ce after it has been built up and 
 removed L*om the cylinder is indicated in 
 Fig. 63. The canvas back has been omitted 
 to show the staving; and the counter- wedge 
 key used for connecting the wreath-piece 
 with the string is shown. The wreath- 
 piece is, at this stage, ready for marking 
 the outlines of the steps. 
 
 Fig. 62 also shows the drum or shape around which strings may 
 be bent, whether the strings are formed of veneers, staved, or kerfed. 
 Another drum or shape is shown in Fig. 64. In this, a portion of a 
 cylinder is formed in the manner clearly indicated; and the string, 
 being set out on a veneer board sufficiently thin to bend easily, is la*id 
 
 Fig. 61. Building Up a Curved 
 Panel or Quick Sweep. 
 
38 
 
 STAIR-BUILDING 
 
 down round the curve, such a number of .pieces of like thickness beino- 
 then added as will make the required thickness of the string. In 
 working this method, glue is introduced between the veneers, which 
 
 Fig. 62. Wreath- 
 Piece Bent 
 around Cylinder. 
 
 Fig. 63. CompletedWreath- 
 Piece Removed from 
 Cylinder. 
 
 . 64. Another Drum or 
 ?hape for Building 
 Curved Strings. 
 
 are then quickly strained down to the curved piece w T ith hand screws. 
 A string of almost any length can be formed in this way, by gluing 
 a few feet at a time, and when that dries, removing the cylindrical 
 curve and gluing dow r n more, until the whole is completed. Several 
 other methods will suggest themselves to the workman, of building up 
 good, solid, circular strings. 
 
 One method of laying out the treads and risers around a cylinder 
 or drum, is shown in Fig. 65. The line D shows the curve of the rail. 
 The lines showing treads and risers may be marked off on the cylinder, 
 or they may be marked off after the veneer is bent around the drum or 
 cylinder. 
 
 There are various methods of making inside cylinders or wells, 
 and of fastening same to strings. One method is shown in Fig. 66. 
 This gives a strong joint when properly made. It will be noticed that 
 the cylinder is notched out on the back; the two blocks shown at the 
 back of the offsets are wedges driven in to secure the cylinder in place, 
 and to drive it up tight to the strings. Fig. 67 shows an 8-inch well- 
 hole with cylinder complete; also the method of trimming and finish- 
 ing same. The cylinder, too, is shown in such a manner that its con- 
 struction will be readily understood. 
 
 Stairs having a cylindrical or circular opening always require 
 a weight support underneath them. This support, which is generally 
 made of rough lumber, is called the carriage, because it is supposed 
 
STAIR-BUILDING 
 
 39 
 
 to carry any reasonable load that may be placed upon the stairway. 
 Fig. 68 shows die under side of a half-space stair having a carriage 
 beneath it. The timbers marked S are of rough stuff, and may be 
 2-inch by 6-inch or of greater dimensions. If they 
 are cut to fit the risers and treads, they will require 
 to be at least 2-inch by 8-inch. 
 
 In preparing the rough carriage for the 
 winders, it will be best to let the back edge of the 
 tread project beyond the back of the riser so that it 
 forms a ledge as shown under C in Fig. 69. Then 
 fix the cross-carriage pieces under the winders, 
 with the back edge about flush with the backs 
 of risers, securing one end to the well with screws, 
 and the other to the wall string or the wall. Xow 
 cut short pieces, marked (Fig. 68), and fix them tightly in between 
 the cross-carriage and the back of the riser as at B B in the section, 
 Fig. 69. These carriages should be of 3-inch by 2-inch material. 
 Xow get a piece of wood, 1-inch by 3-inch, and cut pieces C C to fit 
 tightly between the top back edge of the winders (or the ledge) and 
 the pieces marked B B in section. This method makes a very 
 sound and strong job of the winders; and if the stuff is roughly 
 planed, and blocks are glued on each side of the short cross-pieces 
 0, it is next to impossible for the winders ever to spring or 
 squeak. When the weight is carried in this manner, the plasterer will 
 
 Fig. 65. Laying Out 
 
 Treads and Risers 
 
 around a Drum. 
 
 Fig. 66. One Method 
 
 of Making an Inside 
 
 Well. 
 
 Fig. 67. Construction and 
 
 Ti'imming of 8-Inrli 
 
 Well-Hole. 
 
 have very little trouble in lathing so that a graceful soffit will be made 
 under the stairs. 
 
 The manner of placing the main stringers of the carriage s N . 
 is shown at A, Fig. 69. Fig. 68 shows a complete half-space stair; 
 
40 
 
 STAIR-BUILDIXG 
 
 one-half of this, finished as shown, will answer well for a quarter-space 
 stair. 
 
 Another method of forming a carriage for a stair is shown in 
 Fig. 70. This is a peculiar but very handsome stair, inasmuch as the 
 first and the last four steps are parallel, but the remainder balance or 
 dance. The treads are numbered in this illustration; and the plan of 
 
 the handrail is shown ex- 
 tending from the scroll, at 
 the bottom of the stairs to 
 the landing on the second 
 story. The trimmer T at 
 the top of the stairs is also 
 shown ; and the rough strings 
 or carriages, R S,R S,R S, 
 are represented by dotted 
 lines. 
 
 This plan represents a 
 stair with a curtail step, 
 and a scroll handrail rest- 
 ing over the curve of the 
 curtail step. This type of 
 stair is not now much in 
 vogue in this country, 
 though it is adopted occa- 
 sionally in some of the larger cities. The Use of heavy newel posts 
 instead of curtail steps, is the prevailing style at present. 
 
 In laying out geometrical stairs, the steps are arranged on prin- 
 ciples already described. The well-hole in the center is first laid down 
 and the steps arranged around it. In circular stairs with an open well- 
 hole, the handrail being on the inner side, the width of tread for the 
 steps should be set off at about 18 inches from the handrail, this 
 giving an approximately uniform rate of progress for anyone ascending 
 or descending the stairway. In stairs with the rail on the outside, as 
 sometimes occurs, it will be sufficient if the treads have the proper 
 width at the middle point of their length. 
 
 Where a flight of stairs will likely be subject to great stress and 
 wear, the carriages should be made much heavier than indicated in 
 
 Fig. 68. 
 
 Under Side of Half- Space Stair, with 
 Carriages and Cross-Carriages. 
 
STAIR-BUILDING 
 
 41 
 
 Fig. 69. Method of Reinforcing Stair. 
 
 the foregoing figures; and there may be cases when it will be necessary 
 
 to use iron bolts in the sides of the rough strings in order to give them 
 
 greater strength. This necessity, however, will arise only in the case 
 
 of stairs built in public buildings, 
 churches, halls, factories, ware- 
 houses, or other buildings of a simi- 
 lar kind. Sometimes, even in house 
 stairs, it may be wise to strengthen 
 the treads and risers by spiking 
 pieces of board to the rough string, 
 ends up, fitting them snugly against 
 the under side of the tread and the 
 
 back of the riser. The method of doing this is shown in Fig. 71, in 
 
 which the letter shows the pieces nailed to the string. 
 
 Types of Stairs in Common Use. In order to make the student 
 
 familiar with types of stairs in general use at the present day, plans 
 
 of a few of those most likely 
 
 to be met with will now be 
 
 given. 
 
 Fig. 72 is a plan of a 
 
 straight stair, with an ordi- 
 nary cylinder at the top 
 
 provided for a return rail 
 
 on the landing. It also 
 
 shows a stretch-out stringer 
 
 at the starting. 
 
 Fig. 73 is a plan of a 
 
 stair with a landing and 
 
 return steps. 
 
 Fig. 74 is a plan of a 
 
 stair with an acute angular 
 
 landing and cylinder. 
 
 Fig. 75 illustrates the 
 
 same kind of stair as Fig. 74, the angle, however, being obtuse. 
 Fig. 76 exhibits a stair having a half-turn with two risers on land- 
 
 Fig. 
 
 70. Plan Showing One Method of Constructing 
 Cari'iage and Trimming Winding Stair. 
 
 ings. 
 
 Fig. 77 is a plan of a quarter-space stair with four winders. 
 Fig. 78 shows a stair similar to Fig. 77, but with six winders. 
 
42 
 
 STAIK-BUILDIXG 
 
 - 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 Fig. 71. Reinforcing Treads and Risers 
 by Blocks Nailed to String. 
 
 Fig. 72. Plan of Straight Stair with 
 Cylinder at Top for Return Rail. 
 
 Fig. 79 shows a stair having five 
 dancing winders. 
 
 Fig. 80 is a plan of a half-space 
 stair having five dancing winders 
 and a quarter-space landing. 
 Fig. 81 shows a half-space stair with dancing winders all around 
 the cylinder. 
 
 Fig. 82 shows a geometrical stair having 
 winders all around the cylinder. 
 
 Fig. 83 shows the plan and elevation of 
 stairs which turn around a central post. This 
 kind of stair is frequently used in large stores 
 and in clubhouses and other similar places, 
 and has a very graceful appearance. It is not 
 very difficult to build if properly planned. 
 
 The only form of stair not shown which the 
 student may be called upon to build, would 
 very likely be one having an elliptical plan; 
 but, as this form is so seldom used— being 
 found, in fact, only in public buildings or 
 great mansions — it rarely falls to the lot of 
 the ordinary workman to be called upon to design or construct a 
 stairway of this type. 
 
 
 ) 
 
 
 
 
 
 
 
 
 
 
 
 
 ' ^ 
 
 
 
 
 Fig. 73. Plan of Stair with 
 Landing and Return Steps. 
 
 Fig. 74. Plan of Stair with Acute- Angle 
 Landing and Cylinder. 
 
 Fig. 75. Plan of Stair with Obtuse- Angle 
 Lariding and Cylinder. 
 
STAIR-BFILDIXO 
 
 43 
 
 
 u 
 
 
 
 
 
 
 
 
 
 " -\ 
 
 
 
 
 
 
 
 
 
 Fig. 77 
 
 Quarter-Space Stair with 
 Four Winders. 
 
 Fig. 76. Half -Turn Stair with 
 Two Risers on Landings. 
 
 Fig. 79. Stair with Five Dancing Winders. 
 
 Quarter-Space Stair with Six- 
 Winders. 
 
 
 ■ / 
 
 17 
 
 
 
 
 
 
 
 
 
 
 
 
 ^sl 
 
 
 
 
 ~^~> 
 
 Fig. 81. Half-Space Stair with 
 
 Dancing Winders all 
 
 around Cvlinder. 
 
 GEOMETRICAL STAIRWAYS AND 
 HANDRAILING 
 
 Fig. 80. Half-Space Stair with 
 
 Five Dancing Winders and 
 
 Quarter-Space Landing. 
 
 The term geometrical is applied to stair- 
 ways having any kind of curve for a plan. 
 The rails over the steps are made con- 
 tinuous from one story to another. The resulting winding or 
 twisting pieces are called wreaths. 
 
 Wreaths. The construction of wreaths is based on a few 
 geometrical problems — namely, the projection of straight and curved 
 lines into an oblique plane; and the finding of the angle of inclination 
 3f the plane into which the lines and curves are projected. This angle 
 
44 
 
 STAIK-HU1LDING 
 
 Fig. 83. Plan and Eleva- 
 tion of Stairs Turning 
 around a Central 
 Post. 
 
 Fig. 82. Geometrical Stair with 
 Winders all Around Cylinder. 
 
 is called the bevel, and by its use 
 the wreath is made to twist. 
 
 In Fig. 84 is shown an obtuse- 
 angle plan; in Fig. 85, an acute-angle 
 plan ; and in Fig. 86, a semicircle en- 
 closed within straight lines. 
 
 Projection. A knowledge of how 
 to project the lines and curves in each 
 of these plans into an oblique plane, 
 and to find the angle of inclination of 
 the plane, will enable the student to 
 construct any and all kinds of wreaths. 
 
 The straight lines a, b, c, d in the plan, Fig. 86, are known as 
 tangents; and the curve, the central line of the plan wreath. 
 
 The straight line across from n to n is the diameter; and the 
 perpendicular line from it to the lines c and b is the radius. 
 
 A tangent line may be defined as a line touching a curve without 
 cutting it, and is made use of in handrailing to square the joints of the 
 wreaths. 
 
 Tangent System. The tangent system of handrailing takes its 
 name from the use made of the tangents for this purpose. 
 
 In Fig. 86, it is shown that the joints connecting the central line 
 of rail with the plan rails w of the straight flights, are placed right at 
 the springing; that is, they are in line with the diameter of the semi- 
 circle, and square to the side tangents a and d. 
 
 The center joint of the crown tangents is shown to be square to 
 tangents b and c. When these lines are projected into an oblique 
 plane, the joints of the wreaths can be made to butt square by applying 
 the bevel to them. 
 
STAIR-BUILDIXG 
 
 45 
 
 All handrail wreaths are assumed to rest* on an oblique plane 
 while ascending around a well-hole, either in connecting two flights 
 
 ,Tancjent 
 
 Joint 
 
 CenteT Line of Rail 
 Fig. 84. Obtuse-Angle Plan. 
 
 Joint 
 
 Joint 
 
 or in connecting one flight to a 
 landing, as the case may be. 
 
 In the simplest cases of 
 construction, the wreath rests 
 on an inclined plane that in- 
 clines in one direction only, to 
 
 either side of the well-hole ; while in other cases it rests on a plane 
 that inclines to two sides. 
 
 Fig. 87 illustrates what is meant by a plane inclining in one 
 
 direction. It will be noticed 
 that the lower part of the figure 
 is a reproduction of the quad- 
 rant enclosed by the tangents 
 a and b in Fig. 86. The 
 quadrant, Fig. 87, represents a 
 central line of a wreath that is 
 to ascend from the jomt on the 
 plan tangent a the height of h 
 above the tangent b. 
 
 In Fig. 88, a view of Fig. 87 
 is given in which the tangents c 
 and b are shown in plan, and also the quadrant representing the plan 
 central line of a wreath. The curved line extending from a to h in 
 this figure represents the development of the central line of the plan 
 wreath, and, as shown, it rests on an oblique plane inclining to one 
 side only — namely, to the side of 
 the plan tangent a. The joints 
 are made square to the devel- 
 oped tangents a and m of the in- 
 clined plane; it is for this 
 purpose only that tangents are 
 made use of in wreath construc- 
 tion. They are shown in the 
 figure to consist of two lines, 
 a and m, which are two adjoining 
 sides of a developed section (in 
 
 Fig. 85. Acute- Angle Plan. 
 
 
 
 
 
 Joint 
 
 
 
 
 
 b 
 
 V 
 
 a 
 
 
 
 " 1 ^ 
 
 la 
 \\ 
 
 
 d 
 
 n 
 
 y Joint 
 
 
 1 
 
 Joint 
 
 n 
 
 i 
 
 
 
 Diameter 
 
 
 
 vy 
 
 
 
 
 
 w 
 
46 
 
 STAIR-BUILDIXG 
 
 Joint 
 
 Illustrating Plane 
 Inclined in One Direction 
 Only. 
 
 this case, of a square prism), the section being the assumed inclined 
 
 plane whereon the wreath rests in its ascent from a to h. The joint at h, 
 
 if made square to the tangent m, will be a true, square butt-joint; so 
 
 also will be the joint at a, if made square to 
 
 the tangent a. 
 
 In practical work it will be required to find 
 the correct goemetrical angle between the two 
 developed tangents a and m; and here, again, 
 it may be observed that the finding of the 
 correct angle between the two developed 
 tangents is the essential purpose of every 
 tangent system of handrailing. 
 
 In Fig. 89 is shown the geometrical solu- 
 tion — the one necessary to find the angle 
 between the tangents as required on the face- 
 mould to square the joints of the wreath. 
 The figure is shown to be similar to Fig. 87, 
 except that it has an additional portion 
 marked " Section." This section is the true shape of the oblique plane 
 whereon the wreath ascends, a view of which is given' in Fig. 88. It 
 will be observed that one side of it is the developed tangent m; another 
 side, the developed tangent a!' (— a). 
 The angle between the two as here 
 presented is the one required on the face- 
 mould to square the joints. 
 
 In this example, Fig. 89, owing to 
 the plane being oblique in one direction 
 only, the shape of the section is found by 
 merely drawing the tangent a" at right 
 angles to the tangent ra, making it equal 
 in length to the level tangent a in the 
 plan. By drawing lines parallel to a" Tanqent a 
 and ra respectively, the form of the section Fig . 8 g. pian Line of Rail Pro- 
 
 •ii u <? j -x j.1' l " • j.i_ jected into Oblique Plane Inclined 
 
 will be tound, its outlines being the por- to one side only, 
 
 jections of the plan lines; and the angle 
 
 between the two tangents, as already said, is the angle required on 
 the face-mould to square the joints of the wreath. 
 
 The solution here presented will enable the student to find the 
 
STAIR- BUILDING 
 
 47 
 
 Joint 
 
 correct direction of the tangents as required on the face-mould to 
 square joints, in all cases of practical work where one tangent of a 
 wreath is level and the other tangent is inclined, a condition usually 
 met with in level-landing stairways. 
 
 Fig. 90 exhibits a condition of tangents where the two are equally 
 inclined. The plan here also is taken from Fig. 86. The inclination 
 of the tangents is made equal 
 to the inclination of tangent b 
 in Fig. 86, as shown at m in 
 Figs. 87, 88, and 89. 
 
 In Fig. 91, a view of Fig. 90 
 is given, showing clearly the 
 inclination of the tangents c" 
 and d" over and above the plan 
 tangents c and d. The central 
 line of the wreath is shown 
 extending along the sectional 
 plane, over and above its plan 
 lines, from one joint to the 
 other, and, at the joints, made 
 square to the inclined tangents 
 c" and d". It is evident from 
 the view here given, that the 
 
 Joint 
 Fig. 89. Finding Angle between Tangenis. 
 
 condition necessary to square the joint at each end would be to find 
 the true angle between the tangents c" and d ff , which would give the 
 correct direction to each tangent. 
 
 In Fig. 92 is shown how to find this angle correctly as required 
 on the face-mould to square the joints. In this figure is shown the 
 same plan as in Figs. 90 and 91 , and the same inclination to the 
 tangents as in Fig. 90, so that, except for the portion marked "Section," 
 it would be similar to Fig;. 90. 
 
 To find the correct angle for the tangents of the face-mould, 
 draw the line m from d, square to the inclined line of the tangents 
 c' d"j revolve the bottom inclined tangent & to cut line m in n, where 
 the joint is shown fixed ; and from this point draw the line c" to w. The 
 intersection of this line with the upper tangent d" forms the correct 
 angle as required on the face-mould. By drawing the joints square 
 to these two lines, they will butt square with the rail that is to connect 
 
48 
 
 STAIR-BUILDIXG 
 
 
 V 
 
 b 
 
 •S- 
 
 \ C 
 
 / Plan 
 
 Fig. 90. Two Tangents Equally 
 Inclined. 
 
 Fig. 91. Plan Lines Projected 
 
 into Oblique Plane Inclined to 
 
 Two Sides. 
 
 with them, or to the joint of another wreath that may belong to the 
 
 cylinder or well-hole. 
 
 Fig. 93 is another view of 
 these tangents in position 
 placed over and above the 
 plan tangents of the well- 
 hole. It will be observed 
 that this figure is made up 
 of Figs. 88 and 91 com- 
 bined. Fig. 88, as here 
 presented, is shown to con- 
 nect with a level - landing 
 rail at a. The joint having 
 been made square to the 
 level tangent, a will butt 
 square to a square end of 
 the level rail. The joint at 
 h is shown to connect the 
 two wreaths and is made 
 
 Fig. 92. Finding Angle between Tangents. Square to the inclined tan- 
 
STAIR-BUILDING 
 
 49 
 
 gent m of the lower wreath, and also square to the inclined tangent c" 
 of the upper wreath; the two tangents, aligning, guarantee a square 
 butt-joint. The upper joint is made square to the tangent d", which 
 is here shown to align with the rail of the connecting flight ; the joint 
 will consequently butt square to the end of the rail of the flight above. 
 The view given in this diagram is that of a wreath starting from 
 a level landing, and winding around a well-hole, connecting the 
 landing with a flight of stairs leading to a second story. It is presented 
 to elucidate the use made of tangents to square the joints in wreath 
 
 construction. The wreath is shown to 
 be in two sections, one extending from 
 the level-landing rail at a to a joint in 
 the center of the well-hole at h, this 
 section having one level tangent a and 
 one inclined tangent m; the other sec- 
 tion is shown to extend from h to n, 
 where it is butt-jointed to the rail of the 
 flight above. 
 
 This figure clearly shows that the 
 joint at a of the bottom wreath — owing 
 to the tangent a being level and there- 
 fore aligning with the level rail of the 
 landing — will be a true butt-joint; and 
 that the joint at h, which connects the 
 two wreaths, will also be a true butt- 
 
 N\ joint, owing to it being made square to 
 
 \ • / the tangent m of 
 
 Fig. 93. Laying Out Line of Wreath to Start from Level-Land- 
 ing Rail, Wind around Well-Hole, and Connect at Landing with 
 Flight to Upper StoYv. 
 
 the bottom 
 wreath and to the 
 tangent c" of the 
 upper wreath, 
 both tangents 
 having the same 
 inclination; also 
 the joint at /twill 
 butt square to 
 the rail of the 
 flight above, 
 
50 
 
 STAIR-BUILDING 
 
 owing to it being made square to the tangent d" , which is shown to 
 have the same inclination as the rail of the flight adjoining. 
 
 As previously stated, the use made of tangents is to square the 
 joints of the wreaths; and in this diagram it is clearly shown that the 
 way they can be made of use is by giving each tangent its true direc- 
 tion. How to find the true direction, or the angle between the tangents 
 
 Landing- 
 
 Fig. 94. Tangents Unfolded to Find Their Inclination. 
 
 a and m shown in this diagram, was demonstrated in Fig. 89 ; and how 
 to find the direction of the tangents c" and d" was shown in Fig. 92. 
 
 Fig. 94 is presented to help further toward an understanding 
 of the tangents. In this diagram they are unfolded; that is, they 
 are stretched out for the purpose of finding the inclination of each 
 one over and above the plan tangents. The side plan tangent a 
 is shown stretched out to the floor line, and its elevation a' is a level 
 line. The side plan tangent d is also stretched out to the floor line, 
 as shown by the arc n r m'. By this process the plan tangents are now 
 in one straight line on the floor line, as shown from w to ra'. Upon 
 each one, erect a perpendicular line as shown, and from m' measure 
 to n, the height the wreath is to ascend around the well-hole. In 
 
STAIR-BITLDIXG 
 
 51 
 
 practice, the number of risers in the well-hole will determine this 
 height. 
 
 Now, from point n, draw a few treads and risers as shown; and 
 along the nosing of the steps, draw the pitch-line; continue this line 
 over the tangents d" , c" ', and m, down to where it connects with the 
 bot ora level tangent, as shown. This gives the pitch or inclination 
 to the tangents 
 over and above 
 the well-hole. 
 The same line is 
 shown in Fig. 93, 
 folded around 
 the well-hole, 
 from n, where it 
 connects with the 
 flight at the up- 
 per end of the 
 well-hole, to a, 
 where it connects 
 with the level- 
 landing rail at 
 the bottom of 
 the well-hole. It 
 will be observed 
 that the upper 
 portion, from 
 joint n to joint h, 
 over the tangents 
 
 c" and d" , coincides with -the pitch-line of the same tangents as 
 presented in Fig. 92, where they are used to find the true angle between 
 the tangents as it is required on the face-mould to square the ioints 
 of the wreath at h. 
 
 In- Fig. 89 the same pitch is shown given to tangent m as in Fig. 
 94; and in both figures the pitch is shown to be the same as that over 
 and above the upper connecting tangents c" and d", which is a neces- 
 sary condition where a joint, as shown at h in Figs. 93 and 94, is to 
 connect two pieces of wreath as in this example. 
 
 In Fig. 94 are shown the two face-moulds for the wreaths, placed 
 
 Fig. 95. Well-Hole Connecting Two Flights, with Two Wreath- 
 Pieces, Each Containing Portions of Unequal Pitch. 
 
52 STAIR-BUILDIXG 
 
 upon the pitch-line of the tangents over the well-hole. The angles 
 between the tangents of the face-moulds have been found in this 
 figure by the same method as in Figs. 89 and 92, which, if compared 
 with the present figure, will be found to correspond, excepting only 
 the curves of the face-moulds in Fig. 94. 
 
 The foregoing explanation of the tangents will give the student 
 a fairly good idea of the use made of tangents in wreath construction. 
 The treatment, however, would not be complete if left off at this 
 point, as it shows how to handle tangents under only two conditions — 
 namely, first, when one tangent inclines and the other is level, as at 
 a and w; second, when both tangents incline, as shown at c" and d" . 
 
 In Fig. 95 is shown a well-hole connecting two flights, where two 
 
 .Joint 
 
 Joint 
 
 Tangent' Tangent I h 6 4 Tangent I 5 
 
 Fig. 96. Finding Angle be- Fig. 97. Finding Angle be- 
 
 tween Tangents for Bottom tween Tangents for Upper 
 
 Wreath of Fig. 95. Wreath of Fig. 95. 
 
 portions of unequal pitch occur in both pieces of wreath. The first 
 piece over the tangents a and b is shown to extend from the square 
 end of the straight rail of the bottom flight, to the joint in the center 
 of the well-hole, the bottom tangent a" in this wreath inclining more 
 than the upper tangent- b" . The other piece of wreath is shown to 
 connect with the bottom one at the joint h" in the center of the well- 
 hole, and to extend over tangents c" and d" to connect with the rail of 
 the upper flight. The relative inclination of the two tangents in this 
 wreath, is the reverse of that of the two tangents of the lower wreath. 
 In the lower piece, the bottom tangent a", as previously stated, 
 inclines considerably more than does the upper tangent b" \ while 
 in the upper piece, the bottom tangent c" inclines considerably less 
 than the upper tangent d". 
 
 The question may arise: What causes this? Is it for variation 
 in the inclination of the tangents over the well-hole? It is simply 
 owing to the tangents being used in handrailing to square the joints. 
 
 The inclination of the bottom tangent a" of the bottom wreath 
 
STAIR-BUILDING 
 
 53 
 
 is clearly shown in the diagram to be determined by the inclination 
 of the bottom flight. The joint at a!' is made square to both the straight 
 rail of the flight and to the bottom tangent of the wreath; the rail and 
 tangent, therefore, must be equally inclined, otherwise the joint will 
 not be a true butt-joint. The same remarks apply to the joint at 5, 
 where the upper wreath is shown jointed to the straight rail of the 
 upper flight. In this case, tangent d" must be fixed to incline conform- 
 ably to the in- Jomt _^ 
 
 clination of the 
 upper rail ; other- 
 wise the joint at 
 5 will not be a 
 true butt-joint. 
 
 The same 
 principle is ap- 
 plied in deter- 
 mining the pitch 
 or inclination 
 over the crown 
 tangents b" and 
 c". Owing to the 
 necessity of j oint- 
 ing the two 
 wreaths, as 
 shown at h, these 
 two tangents 
 must have the 
 
 same inclination, and therefore must be fixed, as shown from 2 
 to 4, over the crown of the well-hole. 
 
 The tangents as here presented are those of the elevation, not 
 of the face-mould. Tangent a" is the elevation of the side plan tan- 
 gent a; tangents b" and c" are shown to be the elevations of the plan 
 tangents b and c; so, also, is the tangent d" the elevation of the side 
 plan tangent d. 
 
 If this diagram were folded, as Fig. 94 was shown to be in Fig. 
 93, the tangents of the elevation — namely, a", b", c" , d" — would stand 
 over and above the plan tangents a, b, c, d of the well-hole. In prac- 
 tical work, this diagram must be drawn full size. It gives the correct 
 
 2X\ 
 
 \ 
 
 V 
 
 \ 
 
 Joint 
 
 / \ <T\ 
 
 d 
 
 5 
 
 
 Tangent 
 
 
 y Face Si <§fl 
 
 ° \MouW^y 
 
 Landing 
 Rail 
 
 Face Mouldy 
 Joint I-— 
 
 JointvV/' X 
 
 s4v 
 
 w b 
 
 c 
 
 
 
 
 \ a 
 
 r 
 
 ■\ 
 
 d / 
 
 
 •y 
 
 V 
 
 *»^ 
 
 ' 
 
 y 
 
 Fig. 98. 
 
 Diagram of Tangents and Face-Mould for Sta:.r with 
 Well-Hole at Upper Landing. 
 
54 
 
 STAIR-BUILDING 
 
 Joint 
 
 Fig. 99. Draw- 
 ing Mould when 
 One Tangent is 
 Level and One 
 Inclined over 
 Right -Angled 
 Plan. 
 
 length to each tangent as required on the face-mould, and furnishes 
 also the data for the lay-out of the mould. 
 
 Fig. 96 shows how to find the angle between the tangents of the 
 face-mould for the bottom wreath, which, as shown in Fig. 95, is to 
 span over the first plan quadrant a b. The elevation 
 Joi-nt tangents a" and b n ', as shown, will be the tangents of the 
 mould. To find the angle between the tangents, draw 
 the line a h in Fig. 96 ; and from a, measure to 2 the 
 length of the bottom tangent a" in Fig. 95; the 
 length from 2 to h, Fig 96, will equal the length of 
 the upper tangent b" ', Fig. 95. 
 
 From 2 to 1, measure a distance equal to 2-1 in Fig. 
 95, the latter being found by dropping a perpendicular 
 from w to meet the tangent b" extended. Upon 1, erect 
 a perpendicular line; and placing the dividers on 2, 
 extend to a; turn over to the perpendicular at a"; con- 
 nect this point with 2, and the line will be the bottom tangent as 
 required on the face-mould. The upper tangent will be the line 2-h, 
 and the angle between the two lines is shown at 2. Make the joint 
 at h square to 2-h, and at a" square to a" -2. 
 
 The mould as it appears in Fig. 96 is complete, except the curve, 
 which is comparatively a 
 small matter to put on, as 
 will be shown further on. 
 The main thing is to find 
 the angle between the tan- 
 gents, which is shown at 2, 
 to give them the direction to 
 square the joints. 
 
 In Fig. 97 is shown how 
 to find the angle between 
 the tangents c" and d" 
 shown in Fig. 95, as required 
 on the face-mould. On the 
 
 line h-5, make h-4 equal to the length of the bottom tangent of the 
 wreath, as shown at &"-4 in Fig. 95; and 4-5 equal to the length of 
 the upper tangent &" . Measure from 4 the distance shown at 4-6 
 in Fig 95, and place it from 4 to 6 as shown in Fig. 97; upon 6 erect a 
 
 Newel 
 
 Fig. 100. 
 
 Plan of Curved Steps and Stringer at 
 Bottom of Stair. 
 
STAIR-BUILDING 
 
 55 
 
 perpendicular line. Now place the dividers on 4; extend to h; turn 
 over to cut the perpendicular in h"; connect this point with 4, and the 
 angle shown at 4 will be the angle required to square the joints of the 
 wreath as shown at h" and 5, where the joint at 5 is shown drawn 
 square to the line 4-5, and the joint at h! f square to the line 4 h" '. 
 
 Fig. 98 is a diagram of* tangents and face-mould for a stairway 
 having a well-hole 
 at the top landing. 
 The tangents in this 
 example will be two 
 equallyinclined tan- 
 gents for the bot- 
 tom wreath ; and for 
 the top wreath, one 
 inclined andonelev- 
 el, the latter align- 
 ing with the level 
 rail of the landing. 
 The face-mould, 
 as here presented, 
 will further help 
 toward an under- 
 standing of the lay- 
 out of face-moulds 
 as shown in Figs. 96 
 and 97. It will be observed that the pitch of the bottom rail is con 
 
 Level Tangent 
 
 Floor Line'-' 
 
 Fig. 101. 
 
 Newel 
 
 Finding Angle between Tangents for Squaring 
 Joints of Ramped Wreath. 
 
 tinued from a" to b", a condition caused by the necessity of jointing the 
 wreath to the end of the straight rail at a" , the joint being made square 
 to both the straight rail and the bottom tangent, a" '. From b" a line is 
 drawn to d" , which is a fixed point determined by the number of risers 
 in the well-hole. From point d", the level tangent d" 5 is drawn in line 
 with the level rail of the landing; thus the pitch-line of the tangents 
 over the well-hole is found, and, as was shown in the explanation of 
 Fig, 95, the tangents as here presented will be those required on the 
 face-mould to square the joints of the wreath. 
 
 In Fig. 98 the tangents of the face-mould for the bottom wreath 
 are shown to be a" and b". To place tangent a" in position on the 
 face-mould, it is revolved, as shown by the arc, to m, cutting a line 
 
56 
 
 STAIR-BUILDING 
 
 Fig. 102. 
 
 Newel 
 
 Bottom Steps with Obtuse- 
 Angle Plan. 
 
 previously drawn from w square to the tangent b" extended. Then, 
 by connecting m to b" , the bottom tangent is placed in position on the 
 face-mould. The joint at m is to be made square to it; and the joint 
 at c, the other end of the mould, is to be made square to the tangent b". 
 
 The upper piece of wreath in this 
 example is* shown to have tangent c" 
 inclining, the inclination being the same 
 as that of the upper tangent b" of the 
 bottom wreath, so that the joint at c", 
 when made square to both tangents, 
 will butt square when put together. 
 The tangent d" is shown to be level, so 
 that the joint at 5, when squared with 
 it, will butt square with the square end 
 of the level-landing rail. The level tangent is shown revolved to its 
 position on the face-mould, as from 5 to 2. In this last position, it 
 will be observed that its angle with the inclined tangent c" is a right 
 angle ; and it should be remembered that in every similar case where 
 one tangent inclines and one is level 
 over a square-angle plan tangent, the 
 angle between the two tangents will 
 be a right angle on the face-mould. 
 A knowledge of this principle will en- 
 able the student to draw the mould 
 for this wreath, as shown in Fig. 99, 
 by merely drawing two lines perpen- 
 dicular to each other, as d" 5 and d" c" ', 
 equal respectively to the level tangent 
 d" 5 and the inclined tangent c"in Fig. 
 98. The joint at 5 is to be made 
 square to d" 5; and that at c", to d" c" '. 
 Comparing this figure with the face- 
 mould as shown for the upper wreath in Fig. 98, it will be observed 
 that both are alike. 
 
 In practical work the stair-builder is often called upon to deal 
 with cases in which the conditions of tangents differ from all the 
 examples thus far given. An instance of this sort is shown in Fig. 100, 
 in which the angles between the tangents on the plan are acute. 
 
 Face Mould^c / 
 
 MyTA Pitch- 
 \yr board 
 
 
 z/y 
 
 — Riser 
 
 4r^^ 
 
 r\ 
 
 = — Riser 
 
 V.'\w 
 
 b 
 
 Floor Line 
 
 v< 
 
 Plan 
 
 
 Newel > 
 
 
 
 Fig. 103. Developing Face -Mould, 
 Obtuse-Angle Plan. 
 
STAIR-BUILDING 
 
 57 
 
 In all the preceding examples, the tan- 
 gents on the plan were at right angles; 
 that is, they were square to one another. 
 Fig. 100 is a plan of a few curved 
 steps placed at the bottom of a stairway 
 with a curved stringer, which is struck from 
 a center o. The plan tangents a and b 
 are shown to form an acute angle with each 
 other. The rail above a plan of this 
 design is usually ramped at the bottom end, where it intersects the 
 newel post, and, when so treated, the bottom tangent a will have 
 to be level. 
 
 Fig. 104. Cut tine Wreath from 
 Plank. 
 
 / 
 
 Fig. 105. Wreath Twisted, Ready to be Moulded. 
 
 In Fig. 101 is shown 
 how to find the angle be- 
 tween the tangents on the 
 face-mould that gives them 
 the correct direction for 
 squaring the joints of the 
 
 wreath when it is determined to have it ramped. This figure must 
 be drawn full size. Usually an ordinary drawing-board will answer 
 the purpose. Upon the board, reproduce the plan of the tangents and 
 curve of the center line of rail as shown in Fig. 100. Measure the height 
 
 of 5 risers, as shown in 
 Fig. 101, from the floor line 
 to 5 ; and draw the pitch of 
 the flight adjoining the 
 wreath, from 5 to the floor 
 line. From the newel, 
 draw the dotted line to w, 
 square to the floor line; 
 from iv, draw the \inew m, 
 square to the pitch-line b". 
 Now take the length of the 
 bottom level tangent on a 
 trammel, or on dividers if 
 large enough, and extend 
 it from n to m, cutting the 
 
 106. Twisted Wreath Raised to Position, with line drawn previously from 
 
 Fig. 
 
58 
 
 STAIR-BUILDING 
 
 w, at m. Connect m to n as shown by the line a" . The intersection 
 of this line with b" determines the angle between the two tangents a rt 
 and b" of the face-mould, which gives them the correct direction as 
 required on the face-mould for squaring the joints. The joint at m is 
 made square to tangent a"; and the joint at 5, to tangent b" . 
 
 In Fig. 102 is presented an example of a few steps at the bottom 
 of a stairway in which the tangents of the plan form an obtuse angle 
 with each other. The curve of the 
 central line of the rail in this case 
 will be less than a quadrant, and, 
 as shown, is struck from the center 
 o, the curve covering the three first 
 steps from the newel to the springing. 
 
 In Fig. 103 is shown how to 
 develop the "tangents of the face- 
 mould. Reproduce the tangents and 
 
 Fig. 107. Finding Bevel, Bot- 
 tom Tangent Inclined, Top 
 One Level. 
 
 Fig. 108. Application of Bevels in Fitting Wreath to 
 Rail. 
 
 curve of the plan in full size. Fix point 3 at a height equal to 3 
 risers from the floor line; at this point place the pitch-board of the 
 flight to determine the pitch over the curve as shown from 3 through 
 b" to the floor line. From the newel, draw a line to w, square to. 
 the floor line; and from w, square to the pitch-line b' f , draw the line 
 w m; connect m to n. This last line is the development of the bottom 
 plan tangent a; and the line b" is the development of the plan tangent 
 
STAIR-BUILDING 
 
 59 
 
 b; and 
 its true 
 
 a 
 
 -« l ^ 
 
 the angle between the two lines a" and b" will give each line 
 direction as required on the face-mould for squaring the joints 
 
 of the wreath, 
 as shown at 
 m to connect 
 square with 
 the newel, and 
 at 3 to con- 
 nect square to 
 the rail of the 
 c o n nee ting 
 flight. 
 
 The wreath 
 in- this e x- 
 ample follows 
 
 Fig. 109. Face-Mould and Bevel for Wreath, Bottom Tangent Level, i.L„ n/^In-Kn^ 
 
 Top one inclined. tne nosing line 
 
 of the steps 
 without being ramped as it was in the examples shown in Figs. 100 
 and 101. In those figures the bottom tangent a was level, while in 
 Fig. 103 it inclines equal to the pitch of the upper tangent b" and of the 
 flight adjoining. In 
 other words, t h e 
 method shown in 
 Fig. 101 is applied 
 to a construction in 
 which the wreath is 
 ramped; while in 
 Fig. 103 the method 
 is applicable to a 
 wreath following 
 the nosing line all 
 along the curve to 
 the newel. 
 
 The stair-build- 
 er is supposed to 
 know how to con- 
 struct a wreath under both conditions 
 determined bv the Architect. 
 
 Fig. 110. 
 
 Finding Bevels for Wreath with Two Equally 
 Inclined Tangents. 
 
 as the conditions are usually 
 
60 
 
 STAIR-BUILDING 
 
 The foregoing examples cover all conditions of tangents that 
 
 are likely to turn up in practice, and, if clearly understood, will enable 
 
 the student to lay out the 
 
 face-moulds for all kinds 
 
 of curves. 
 
 Bevels to Square the 
 
 Wreaths. The next 
 
 process in the construc- 
 tion of a wreath that the 
 
 handrailer will be called 
 
 upon to perform, is to find 
 
 the bevels that will, by 
 
 being applied to each end 
 
 of it, give the correct angle 
 
 to square or twist it when 
 
 winding around the well- 
 hole from one flight to 
 
 another flight, or from 
 
 a flight to a landing, as 
 
 the case may be. 
 
 The wreath is first 
 
 cut from the plank square to its surface as shown in Fig. 104. 
 
 After the application of the bevels, it is twisted, as shown 
 
 in Fig. 105, ready 
 to be moulded; 
 and when in 
 position, ascending 
 from one end of the 
 curve to the other 
 
 Fig. 111. Application of Bevels to Wreath Ascending 
 on Plane Inclined Equally in Two Directions. 
 
 r* end, 
 
 over 
 
 the 
 
 in- 
 
 clined plane of the 
 section around the 
 well-hole, its sides 
 will be plumb, as 
 shown in Fig. 106 
 at b. In this fig- 
 ure, as also in Fig. 105, . the wreath a lies in a horizontal position 
 in which its sides appear to be out of plumb as much as the bevels 
 
 Fig. 112. 
 
 Finding Bevel Where Upper Tangent Inclines 
 More Than Lower One. 
 
STAIR-BUILDING 
 
 61 
 
 Fig. 113. Finding Bevel Where Upper Tangent Inclines Less 
 Than Lower One. 
 
 are out of plumb. In the upper part of the figure, the wreath 
 
 b is shown placed in its position upon the plane of the section, 
 
 where its sides are seen to be plumb. It is evident, as 
 
 shown in the 
 
 relative posi- 
 
 tion of the 
 
 wreath in this 
 
 figure, that, if 
 
 the bevel is the 
 
 correct angle 
 
 of the plane of 
 
 the section 
 
 whereon the 
 
 wreath b rests 
 
 in its ascent 
 
 over the well- 
 
 hole, the 
 
 wreath will in 
 
 that case have its sides plumb all along when in position. It is for this 
 
 purpose that the bevels are needed. 
 
 A method of finding the bevels for all wreaths (which is considered 
 rather difficult) will now be explained : 
 
 First Case. In Fig. 107 is shown a case where the bottom 
 tangent of a wreath is inclining, and the top one level, similar to the 
 top wreath shown in Fig. 98. It has already been noted that the plane 
 of the section for this kind of wreath inclines to one side only; therefore 
 one bevel only will be required to square it, which is- shown at d, 
 Fig. 107. A view of this plane is given in Fig. 108; and the bevel d, 
 as there shown, indicates the angle of the inclination, which also is 
 the bevel required to square the end d of the wreath. The bevel is 
 shown applied to the end of the landing rail in exactly the same manner 
 in which it is to be applied to the end of the wreath. The true bevel 
 for this wreath is found at the upper angle of the pitch-board. At the 
 end a, as already stated, no bevel is required, owing to the plane 
 inclining in one direction only. Fig. 109 shows a face-mould and 
 bevel for a wreath with the bottom tangent level and the top tangent 
 inclining, such as the piece at the bottom connecting with the landing 
 rail in Fig. 94. 
 
62 
 
 STAIR-BUILDING 
 
 Second Case. It may be required to find the bevels for a wreath 
 having two equally inclined tangents. An example of this kind also 
 is shown in Fig. 94, where both the tangents c" and d" of the upper 
 
 Fig. 1 14. Finding Bevel 
 Where Tangents In- 
 cline Equally over 
 Obtuse- Angle Plan. 
 
 Fig. 115. Same Plan as in Fig. 
 
 114, but with Bottom Tangent 
 
 Level. 
 
 wreath incline equally. Two bevels are required in this case, because 
 the plane of the section is inclined in two directions; but, owing to the 
 inclinations being alike, it follows that the two will be the same. 
 They are to be applied to both ends of the wreath, and, as shown in 
 Fig. 105, in the same direction — namely, 
 toward the inside of the wreath for the bot- 
 tom end, and toward the outside for the upper 
 end. 
 
 In Fig. 110 the method of finding the bevels 
 is shown. A line is. drawn from w to c", square 
 to the pitch of the tangents, and turned over 
 to the ground line at h, which point is con- 
 nected to a as shown. The bevel is at h. 
 To show that equal tangents have equal 
 bevels, the line m is drawn, having the same 
 inclination as the bottom tangent c" , but in another direction. Place 
 the dividers on o', and turn to touch the lines d n and m, as shown by 
 the semicircle. The line from o' to n is equal to the side plan tangent 
 
 Fig. 116. Finding Bevels 
 for Wreath of Fig. 115. 
 
STAIR-BUILDING 
 
 63 
 
 w a, and both the bevels here shown are equal to the one already 
 found. They represent the angle of inclination of the plane where- 
 on the wreath ascends, a view of which is given in Fig. Ill, where 
 the plane is shown to incline equally in two directions. At both ends 
 is shown a section of a rail; and the bevels are applied to show how, 
 by means of them, the wreath is squared or twisted when winding 
 around the well-hole and ascending upon the plane of the section. 
 The view given in 
 
 m Level Tancrent 
 
 Ground^tTine 
 
 this figure will en- 
 able the student to 
 understand the 
 nature of the bevels 
 found in Fig. 110 
 for a wreath having 
 two equally inclined 
 tangents; also for 
 all other wreaths of 
 equally inclined 
 tangents, in that 
 every wreath in 
 such case is assumed 
 to rest upon an in- 
 clined plane in its 
 ascent over the well- 
 hole, the bevel in 
 every case being the angle of the inclined plane. 
 
 Third Case. In this example, two unequal tangents are given. 
 the upper tangent, inclining more than the bottom one. The method 
 shown in Fig. 110 to find the bevels for a wreath with two equal tan- 
 gents, is applicable to all conditions of variation in the inclination of 
 the tangents. In Fig. 112 is shown a case where the upper tangent 
 d" inclines more than the bottom one c" . The method in all cases is 
 to continue the line of the upper tangent d" ' , Fig. 112, to the ground 
 line as shown at n; from n, draw a line to a, which will be the horizon- 
 tal trace of the plane. Now, from o, draw a line parallel to a n, as 
 shown from o to d, upon d, erect a perpendicular line to cut the tangent 
 d", as shown, at m; and draw the line m u o". Make u o" equal to 
 the length of the plan tangent as shown by the arc from o. Put one 
 
 Fig. 117. 
 
 Upper Tangent Inclined. Lower Tangent Level. 
 Over Acute-Angle Plan. 
 
64 STAIR-BUILDING 
 
 leg of the dividers on u; extend -to touch the upper + angent d", and 
 turn over to 1 ; connect 1 to o" ; the bevel at 1 is to be applied to tangent 
 d". Again place the dividers on u; extend to the line h, and turn over to 
 2 as shown; connect 2 to o" ', and the bevel shown at 2 will be the one 
 
 to apply to the bottom tangent c". 
 It will be observed that the line h 
 represents the bottom tangent. It 
 is the same length and has the same 
 inclination. An example of this 
 kind of wreath was shown in Fig. 
 95, where the upper tangent d" is 
 shown to incline more than the bot- 
 tom tangent c" in the top piece ex- 
 Fig. 118. Finding Bevels for Wreath i. » 7 „ , r -p, i-ic i 
 
 oi Plan, Fig. 117. tending from h" to o. Bevel 1, round 
 
 in. Fig. 112, is the real bevel for the 
 end 5 ; and bevel 2, for the end h" of the wreath shown from h" to 5 
 in Fig. 95. 
 
 Fourth Case. In Fig. 113 is shown how to find the bevels for a 
 wreath when the upper tangent inclines less than the bottom tangent. 
 This example is the reverse of the preceding one; it is the condition 
 of tangents found in the bottom piece of wreath shown in Fig. 95. 
 To find the bevel, continue the upper tangent b" to the ground line, 
 as shown at n; connect n to a, which will be the horizontal trace of 
 the plane. From o, draw a line parallel to n a, as shown from o to d; 
 upon d, erect a perpendicular line to cut the continued portion of the 
 upper tangent b" in m; from m, draw the line m u o" across as shown. 
 Now place the dividers on u; extend to touch the upper tangent, and 
 turn over to 1 ; connect 1 to o" '; the bevel at 1 will be the one to apply 
 to the tangent b" at h, where the two wreaths are shown connected in 
 Fig. 95. Again place the dividers on u; extend to touch the line c; 
 turn over to 2 ; connect 2 to o"; the bevel at 2 is to be applied to the 
 bottom tangent a" at the joint where it is shown to connect with the 
 rail of the flight. 
 
 Fifth Case. In this case we have two equally inclined tangents 
 over an obtuse-angle plan. In Fig. 102 is shown a plan of this kind ; 
 and in Fig. 103, the development of the face-mould. 
 
 In Fig. 114 is shown how to find the bevel. From a, draw a line 
 to a! , square to the ground line. Place the dividers on a' '; extend to 
 
STAIR-BUILDIXG 
 
 65 
 
 touch the pitch of tangents, and turn over as shown to m; connect m 
 to a. ' The bevel at m will be the only one required for this wreath, 
 but it will have to be applied to both ends, owing to the two tangents 
 being inclined. 
 
 Sixth Case. In this case we have one tangent inclining and one 
 tangent level, over an acute-angle plan. 
 
 In Fig. 115 is shown the same plan as in Fig. 114; but in this 
 
 Directing Ordinate 
 Of Base 
 
 • Fig. 119. Laying Out Curves on Face-Mould with Pins and String. 
 
 case the bottom tangent a" is to be a level tangent. Probably this 
 condition is the most commonly met with in wreath construction at 
 the present time. A small curve is considered to add to the appear- 
 ance of the stair and rail; and consequently it has become almost a 
 "fad" to have a little curve or stretch-out at the bottom of the stairway i 
 and in most cases the rail is ramped to intersect the newel at right; 
 angles instead of at the pitch of the flight. In such a case, the bottom 
 tangent a" will have to be a level tangent, as shown at a" in Fig. 115, 
 the pitch of the flight being over the plan tangent b only. 
 
6<j 
 
 STAIR-BUILDING 
 
 Fig. 120. Simple Method of Drawing Curves 
 on Face-Mould. 
 
 . To find the bevels when tangent b" inclines and tangent a" is 
 level, make a c in Fig. 116 equal to a c in Fig. 115. This line will be 
 
 the base of the two bevels. 
 Upon a, erect the line a w m 
 at right angles to a c; make a 
 w equal to o w in Fig. 115; con- 
 nect w and c; the bevel at w 
 will be the one to apply to tan- 
 gent b" at n where the wreath 
 is joined to the rail of the flight. 
 Again, make a m in Fig. 116 
 equal the distance shown in Fig. 
 115 between w and m, which is 
 the full height over which tan- 
 gent b" is inclined ; connect m to 
 c in Fig. 116, and at m is the bevel to be applied to the level tangent a". 
 
 Seventh Case. 
 In this case, illus- 
 trated in Fig. 117, 
 the upper tangent 
 b" is shown to in- 
 cline, and the bot- 
 tom tangent a" to 
 be level, over an 
 acute - angle plan. 
 The plan here is 
 the same as that in 
 Fig. 100, where a 
 curve is shown to 
 stretch out from the 
 line of the straight 
 stringer at the bot- 
 tom of a flight to a 
 newel, and is large 
 
 •, , . Fig. 121. Tangents, Bevels. Mould-Curves, etc., from Bottom 
 
 enough to Contain Wreath of Fig. 95, in which Upper Tangent Inclines Less 
 „ . . than Lower One. 
 
 five treads, which 
 
 are gracefully rounded to cut the curve of the central line of rail in 
 
 1, 2, 3, 4. This curve also may be used to connect a landing rail to a 
 
 <#■■ 
 
 LOfC. 
 
STAIR-BUILDING 
 
 67 
 
 flight, either at top or bottom, when the plan is acute-angled, as will 
 be shown further on. 
 
 To find the bevels — g'L_ _Majar_ 
 
 for there will be two 
 bevels necessary for this 
 wreath, owing to one 
 tangent b" being inclined 
 and the other tangent a" 
 being level — make a c, 
 Fig. 118, equal to a c in 
 Fig. 117, which is a line 
 drawn square to the 
 ground line from the 
 newel and shown in all 
 preceding figures to have 
 been used for the base 
 of a triangle containing 
 the bevel. Make a w in 
 Fig. 11§ equal to w o in 
 
 Fig. 117, which is a line drawn square to the inclined tangent b" from 
 w; connect w and c in Fig. 118. The bevel shown at w will be the one 
 to be applied to the joint 5 on tangent b", Fig. 117. Again, make am 
 
 Fig. 122. 
 
 Developed Section of Plane Inclining Un- 
 equally in Two Directions. 
 
 Fig 123. Arranging Risers around Well-Hole on Level-Landing Stair, 
 with Radius of Central Line of Rail One-Half Width of Tread. 
 
 in Fig. 118 equal to the distance shown in Fig. 117 between the line 
 representing the level tangent and the line w! 5, which is the height that 
 
68 
 
 STAIR-BUILDING 
 
 tangent b" is shown to rise; connect m to c in Fig. 1 18; the bevel shown 
 at m is to be applied to the end that intersects with the newel as shown 
 at m in Fig. 117. 
 
 The wreath is shown developed in Fig. 101 for this case; so that, 
 with Fig. 100 for plan, Fig. 101 for the development of the wreath, 
 and Figs. 117 and 118 for finding the bevels, the method of handling 
 any similar case in practical work can be found. 
 
 How to Put the Curves on the Face- Mould 
 
 Joint; 
 
 It has been shown 
 how to find the 
 angle between the 
 tangents o f the 
 face-mould, and 
 that the angle is 
 for the purpose of 
 squaring the joints 
 at the ends of the 
 wreath. In Fig. 
 119 is shown how 
 to lay out the 
 curves by means 
 of pins and a 
 string — a very 
 common practice 
 among stair-build- 
 ers. In this 
 example the face- 
 mould has equal 
 tangents as shown 
 at c" and d". The angle between the two tangents is shown at m as it 
 will be required on the face-mould. In this figure a line is drawn 
 from m parallel to the line drawn from h, which is marked in the diagram 
 as "Directing Ordinate of Section/' The line drawn from m will 
 contain the minor axes; and a line drawn through the corner of the 
 section at 3 will contain the major axes of the ellipses that will consti- 
 tute the curves of the mould. 
 
 The major is to be drawn square to the minor, as shown. Place, 
 from point 3, the circle shown on the minor, at the same distance as 
 the circle in the plan is fixed from the point o. The diameter 
 
 Pig. 124. 
 
 Arrangement of Risers Around Well-Hole with Rad- 
 ius Larger Than One-Half Width of Tread. 
 
STAIR-BUILDING 
 
 69 
 
 of this circle indicates the width of the curve at this point. The width 
 at each end is determined by the bevels. The distance a b, as shown 
 
 Fig. 125. Ai-rangement of Risers around Well-Hole, with Risers Spaced 
 Full Width of Tread. 
 
 upon the long edge of the bevel, is equal to J the width of the mould, and 
 is the hypotenuse of a right-angled triangle whose base is J the width of 
 the rail. By placing this dimension on each side of n, as shown at b 
 
 Rlaer 
 
 Fig. 126. Plan of Stair 
 Shown in Fig. 123. 
 
 Fig. 127. Plan of Stair 
 Shown in Fig. 124. . 
 
 Fig. 128. Plan of Stair 
 Shown in Fig. 125. 
 
 and b, and on each side of h" on the other end of the mould, as shown 
 also at b and 6, we obtain the points b 2 b on the inside of the curve, and 
 
70 
 
 STAIR-BUILDING 
 
 the points b 1 b on the outside. It will now be necessary to find the 
 elliptical curves that will contain these points; and before this can be 
 
 done, the exact length of the minor and 
 major axes respectively must be deter- 
 mined. The length of the minor axis 
 for the inside curve will be the dis- 
 tance shown from 3 to 2 ; and its length 
 for the outside will be the distance 
 shown from 3 to. 1. 
 
 To find the length of the major axis 
 -^Bbar d for the inside, take the length of half the 
 minor for the inside on the dividers: 
 place one leg on b, extend to cut the 
 major in z, continue to the minor as 
 shown at k. The distance from b to k 
 will be the length of the semi-major axis for the inside curve. 
 
 To draw the curve, the points or foci where the pins are to be 
 fixed must be found on the major axis. To find these points, take 
 the length of b k (which is, as previously found, the exact length of 
 
 Fig. 129. Drawing Face-Mould 
 for Wreath from Pitch-Board. 
 
 Landing Rail 
 
 Fig. 130. Development of Face-Mould for Wreath Connecting Rail 
 of Flight with Level-Landing Rail. 
 
 the semi-major for the inside curve) on the dividers; fix one leg at 2, 
 and describe the arc Y, cutting the major where the pins are shown 
 fixed, at o and o. Now take a piece of string long enough to form a 
 
STAIR-BUILDING 
 
 71 
 
 loop around the two and extending, when tight, to 2, where the pencil 
 is placed ; and, keeping the string tight, sweep the curve from b to b. 
 
 EE 
 
 Step 
 
 Step 
 
 Step 
 
 Step 
 
 Platform 
 
 Joint 
 
 Fig. 181. Arranging Risers in 
 Quarter-Turn between ° 
 
 Two Flights. 
 
 Joint 
 
 Step 
 
 Step | 
 
 The same method, for finding the major and foci for the outside 
 curve, is shown in the diagram. The line drawn from b on the outside 
 of the joint at n, to w, is the semi-major for the outside curve; and the 
 
 %s 
 
 
 
 • 
 
 N 
 
 
 ^ 
 
 
 
 
 N<C 
 
 
 
 
 
 
 \^ 
 
 j& 
 
 
 
 
 
 
 
 "\ 
 
 
 X 
 
 
 ^Risers-; 
 
 : 1 
 
 
 
 V: 
 
 
 
 / 
 
 ' '' / 
 
 
 ^\. Xy > 
 
 
 
 /^S 
 
 ' 
 
 ^*s 
 
 ^Ov 
 
 
 
 
 y * 
 
 ^x?N 
 
 
 •—* — mser 
 
 X, 
 
 
 jS 
 
 
 
 
 
 
 L— =. 
 
 -'r\'s 
 
 er 
 
 
 
 Fig. 132. Arrangement of Risers around Quarter-Turn Giv- 
 ing Tangents Equal Pitch with Connecting Flight. 
 
 points where the outside pins are shown on the major will be the foci. 
 To draw the curves of the mould according to this method, which 
 
72 
 
 STAIR-BUILDING 
 
 E\ 
 
 1 
 
 Trr 
 
 is a scientific one, may seem a complicated problem; but once it is 
 understood, it becomes very simple. A simpler way to draw them, 
 however, is shown in Fig. 120. 
 
 The width on the minor and at each end 
 will have to be determined by the method just 
 explained in connection with Fig. 119. In 
 Fig 120, the points b at the ends, and the points 
 in which the circumference of the circle cuts 
 the minor axis, will be points contained in 
 the curves, as already explained. Now take a flexible lath; bend it 
 to touch b, z, and b for the inside curve, and b, w, and b for the outside 
 curve. This method is handy where the curve is comparatively flat, 
 as in the example here shown ; but where the mould has a sharp curva- 
 
 Fig. 133. Finding Bevel 
 
 for Wreath of Plan, 
 
 Fig. 132. 
 
 Fig. 134. Well-Hole with Riser in Center. Tangents of Face-Mould, and Central Line 
 
 of Rail, Developed. 
 
 ture, as in case of the one shown in Fig. 101, the method shown in Fig. 
 119 must be adhered to. 
 
 With a clear knowledge of the above two methods, the student 
 will be able to put curves on any mould. 
 
 The mould shown in these two diagrams, Figs. 119 and 120, is 
 for the upper wreath, extending from h to n in Fig. 94 A practical 
 handrailer would draw only what is shown in Fig. 120. He would 
 
STAIR-BUILDIXG 
 
 'Z 
 
 take the lengths of tangents from Fig. 94, and place them as shown 
 at h m and m n. By comparing Fig. 120 with the tangents of the 
 upper wreath in Fig. 94, it will be easy for the student to understand 
 
 . 135. Arrangement of Risers in 
 itair with Obtuse- Angle Plan. 
 
 Fig. 136. Arrangement of Risers in Obtuse- 
 Angle Plan, Giving Equal Pitch. over Tan- 
 gents and Flights. Face-Mould Developed. 
 
 the remaining lines shown in Fig. 120. The bevels are shown applied 
 
 to the mould in Fig. 105, to give it the twist. In Fig. 106, is shown how, 
 
 after the rail is twisted and 
 
 placed in position over and 
 
 above the quadrant c d in 
 
 Fig. 94, its sides will be 
 
 plumb. 
 
 In Fig. 121 are shown 
 the tangents taken from 
 the bottom wreath in Fig. 
 95 It was shown how to 
 develop the section and 
 find the angle for the tan- 
 gents in the face-mould, fi 
 in Fig. 113. The method 
 shown in Fig. 119 for putting on the curves, would be the most suitable. 
 
 Fig. 121 is presented more for the purposes of study than as a 
 method of construction. It contains all the lines made use of to find 
 
 137. 
 
 Arrangement of Risers in Flight with 
 Curve at Landing. 
 
74 
 
 STAIR-BUILDING 
 
 Fig. 138. 
 
 Development of Face-Moulds 
 fox- Plan, Fig. 137 
 
 the developed section of a plane inclining unequally in two different 
 directions, as shown in Fig. 122. 
 
 Arrangement of Risers in and around Well-Hole. An important 
 matter in wreath construction is to have a knowledge of how to 
 
 arrange the risers in and around a 
 well-hole. A great deal of labor 
 and material is saved through it; 
 also a far better appearance to the 
 finished rail may be secured 
 
 In level-landing stairways, the 
 easiest example is the one shown 
 in Fig. 123, in which the radius of 
 the central line of rail is made 
 equal to one-half the width of a tread. In the diagram the radius is 
 shown to be 5 inches, and the treads 10 inches. The risers are placed 
 in the springing, as at a and a. The elevation of the tangents by this 
 arrangement will be, as shown, one level and one inclined, for each" 
 piece of wreath. When in this position, there is no trouble in finding 
 the angle of the tangent as required on the face-mould , owing to that 
 angle, as in every such case, being a right angle, as shown at w; also 
 no special bevel will have to be found, because the upper bevel of the 
 pitch-board contains the angle required. 
 
 The same results are obtained in the example shown in Fig. 
 124, in which the radius of the well-hole is larger than half the width 
 of a tread, by placing the riser a at a distance from c equal to half 
 the width of a tread, instead of at the springing as in the preceding 
 example. 
 
 In Fig, 125 is sncwn a case where the risers are placed at s dis- 
 tance from c equal to a full tread, the effect in respect to the tangents 
 of the face-mould and bevel being the same as in the two preceding 
 examples. In Fig. 126 is shown the plan of Fig. 123; in Fig. 127. 
 the plan of Fig. 124; and in Fig. 128, the plan of Fig. 125. For the 
 wreaths shown in all these figures, there will be no necessity of spring- 
 ing the plank, which is a term used in handrailing to denote the 
 twisting of the wreath; and no other bevel than the one at the upper 
 end of the pitch-board will be required. This type of wreath, also, 
 is the one that is required at the top of a landing when the rail of the 
 flight intersects with a level-landing rail. 
 
STAIR-BUILDING 
 
 i o 
 
 I-n Fig. 129 is shown a very simple method of drawing the face- 
 mould for this wreath from the pitch-board. Make a c equal to the 
 radius of the plan central line of rail as shown at the curve in Fig. 130. 
 From where line c c" cuts the long side of the pitch-board, the 
 line c" a" is drawn at right angles to the long edge, and is made 
 equal to the length of the plan tangent a c, Fig. 130. The curve is 
 drawn by means of pins and string or a trammel. 
 
 In Fig. 131 is shown a quarter-turn between two flights. The 
 correct method of placing the risers in and around the curve, is to put 
 the last one in the first flight one-half a step from springing c, and 
 the first one in the second flight one-half a step from a, leaving a space 
 in the curve equal to a full tread. By this arrangement, as shown 
 in Fig. 132, the pitch-line of the tangents will equal the pitch of the 
 connecting flight, thus securing the second easiest condition of tan- 
 gents for the face-mould — namely, as shown, two equal tangents. 
 For this wreath, only one bevel will be needed, and it is made up of 
 the radius of the plan central line of the rail o c, Fig. 131, for base, 
 and the line 1-2, Fig. 132, for altitude, as shown in Fig. 133. 
 
 The bevel shown in this figure has been previously explained in 
 Figs. 105 and 106. It is to be applied to both ends of the wreath. 
 
 The example shown in Fig. 134 is of a well-hole having a riser 
 in the center. If the radius of the plan central line of rail is made 
 equal to one-half a tread, the pitch of tangents will be the same as 
 of the flights adjoining, thus securing two equal tangents^for the two 
 sections of wreath. In this figure the tangents of the face-mould are 
 developed, and also the central line of the rail, as shown over and 
 above each quadrant and upon the pitch-line of tangents. 
 
 The same method may be employed in .stairways having obtuse- 
 angle and acute-angle plans, as shown in Fig. 135, in which two flights 
 are placed at an obtuse angle to each other. If the risers shown at 
 a and a are placed one-half a tread from c, this will produce in the 
 elevation a pitch-line over the tangents equal to that over the flights 
 adjoining, as shown in Fig. 136, in which also is. shown the face-mould 
 for the wreath that will span over the curve from one flight to another. 
 
 In Fig. 137 is shown a flight having the same curve at a landing. 
 The same arrangement is adhered to respecting the placing of the 
 risers, as shown at a and a. In Fig. 138 is shown how to develop the 
 face-moulds- 
 
EXAMINATION PAPER 
 
STAIR-BUILDING 
 
 Read Carefully: Place your name and full address at the head of the 
 paper. Any cheap, light paper like the sample previously sent you may 
 be used. Do not crowd your work, but arrange it neatly and legibly. Do 
 not copy the answers from the Instruction Paper; use your own words, so 
 that we may be sure you understand the subject. 
 
 1. Define staircase and stairway. 
 
 2. What is meant by the rise and run of a stairway? How 
 measured? 
 
 3. Define tread and riser. 
 
 4. How do treads and risers compare as to number? Why? 
 
 5. What is a string or string-board 1 ? Describe the various 
 kinds of strings. 
 
 6. How are treads and risers fitted together and fastened in 
 housed strings? 
 
 7. Describe the construction and use of a fitch-board. 
 
 8. How are the relative dimensions of treads and risers deter- 
 mined ? 
 
 9. Are all the risers in a flight of stairs cut of uniform height? 
 
 10. Describe the use of flyers, winders, and dancing steps. 
 
 11. How are balusters fastened on strings? 
 
 12. How are strings fastened to newel-posts? 
 
 13. Describe methods of constructing bullnose steps and risers 
 for same. 
 
 14. What is the difference between a quarter-space landing 
 and a half -space landing? 
 
 15. Define the terms: well-hole; drum; cylinder; kerfing; 
 geometrical stairway; carriage timber; wreath; tangent; croivn 
 tangent; springing oj a well-hole; ground-line; sivan-neck; face- 
 mould; nosing; return nosing; spandrel; cove-moulding. 
 
 16. Describe the use of the face-mould. 
 
 17. When the face-mould is applied, and material for the 
 wreath cut from the plank, how is the wreath-piece given its final 
 shape? 
 
STAIR-BUILDING 
 
 18. What, is the use of tangents in handrailing? What do the 
 bevels represent? 
 
 19. What is an oblique plane? 
 
 20. Are all wreaths assumed to be resting on an oblique plane? 
 
 21. In referring to an oblique plane, what do you understand 
 by the expressions inclined in one direction only and inclined in two 
 directions? 
 
 22. What is meant when t#o wreath tangents are said to be 
 equally inclined? What, when unequally inclined? 
 
 23. When an oblique plane is inclined in one direction only, 
 how many bevels will be needed to twist the wreath? 
 
 24. When the plane inclines in two directions, how many bevels 
 are required? 
 
 25. When the inclination is equal in two directions, how many 
 bevels are needed? 
 
 26. When the plane is unequally inclined in two directions, 
 how many bevels are needed? 
 
 27. How can a stairway be reinforced? 
 
 28. How should a scroll bracket be terminated against the 
 riser? 
 
 29. When a plane is equally inclined in two directions, how are 
 the bevel or bevels to be applied to twist the wreath resting upon it 
 in its ascent around the well-hole? 
 
 30. What is the difference between the plan tangents, pitch-line 
 of tangents, and tangents of the face-mould? 
 
 31. Why is it necessary to determine with exactness the angle 
 between the tangents on the face-mould ? 
 
 32. What is the width of the face-mould to be, when laid but on 
 the minor axis? 
 
 33. How is the width of the mould at the ends determined? 
 
 34. How do you find the minor axis and major axis of the mould 
 curves? 
 
 35. Show how to find the thickness of the plank that will be 
 required for the wreath. 
 
 After completing the work, add and sign the following statement: 
 
 I hereby certify that the above work is entirely my owu. 
 
 (Signed) 
 
JAN 30 WOO 
 
 y 
 
LIBKAKY Ul- UUNUKtbb 
 
 021 218 403 2