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Stair-building and the steel square cover

Stair-building and the steel square

Chapter 3: Definitions.
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About This Book

A practical manual that teaches the measurement, layout, and construction of stairways and the use of the steel square in carpentry. The first part defines rise, run, and pitch and gives step-by-step methods for setting out straight, winding, closed- and open-string stairs, well-holes, curved turns, handrail design and fitting, and the geometrical procedures for wreaths and tangent systems, with guidance on riser and tread proportions. The second part presents steel-square specifications and many applied problems for roof and framing work, including polygon miters, common rafters, hips, valleys, and related cutting and layout techniques.

PART I
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 connected with the art of building, is probably the subject least understood 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 seldom be totally eradicated by commendable features that may be noted elsewhere. 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 by the staircase, which is the space allowed for the stairway; but, as a general rule, the tread should not be less than nine inches wide, and the riser should not be over eight inches high. Seven-inch riser 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 deviation from the rule; for instance, in large buildings, such as hotels, railway depots, or other public buildings, treads are often made 18 inches wide, having risers of from 2½ inches to 5 inches depth.

Definitions.

Before proceeding 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.[A] 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 sides, a practice not 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 1¼ 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 ⅞-inch stuff.

Riser. This is the vertical height of the step. The riser is generally 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 indicate 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 × 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 9½ inches width and ⅞-inch thickness. In the first-class stairways the thickness is usually 1⅛ inches, for both front and wall strings.

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; O and O, 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 about ⅜-inch long, and may be ⅜-inch or ½-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.

Fig. 4. End Section of Riser. Fig. 5. End Section of Tread.

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 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 showing 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 O shows the nosing, F the return nosing with a bracket terminating against it. These brackets are about 516-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 to be the same height as the riser. The lower ends of two balusters 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 sometimes 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, showing 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 manner 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 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, 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 divided, 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 left 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 all 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 ⅝ to ¾ 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 together, forms the support or carriage of the stairs.

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.

[A] 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.

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; therefore, if we divide 133 by 19, we get 7 without any remainder. Seven inches will therefore be the 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 and risers may be illustrated graphically, as in Fig. 12.

In the right-angle triangle A B C, 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 H K; and a width of tread equal to B L gives a riser equal to L M.

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    8½
  7 8
  8    7½
  9 7
10    6½
11 6
12    5½
13 5
14    4½
15 4
16    3½
17 3
18    2½

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 standard, 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 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 determined, 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 1½ inches wide and from ⅜ to ¾ 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 8⅓ represents the step or tread, and the line 7¾ 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 than any of the other risers, because, as above explained, the thickness of the first tread is always taken off it; thus, if the tread is 1½ inches thick, the riser in this case would only require to be 6¼ inches wide, as 7¾-1½ = 6¼.

The string must be cut so that the line at W will be only 6¼ inches from the line at 8⅓, 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 8⅓ on the pitch-board strikes the outer end of the line 7¾ 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 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.

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 before described.

The manner of housing is shown in Fig. 19, in which the treads T T and the risers 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 ½ to ⅝ 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 12¾ inches wide, which is a very good width for a string of this kind; but the thickness should never be less than 1½ 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 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 made 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.

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 ⅜ inch thick, and may be in any desirable pattern. The end next the riser should be mitered to suit; this will require the riser to be ⅜ 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 ⅜ inch, so as to cover the bracket and make the face 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 placing the newel posts, and provision must be made for the extra ⅜ inch due to the bracket. The newel post must be set out from the string ⅜ inch, and it will then align with the baluster.



We have now described 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 workman 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, 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.


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 stairway, W S shows the wall string; R S, the rough string, placed there to give the structure strength; and O 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 ⅝-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 balusters 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 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 baluster 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 the wall string. 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 O. The piece O 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 moulding 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 O 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 portion 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 suggestions 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.