FRANKLIN INSTITUTE LIBRARY 
 
 PHILADELPHIA 
 
 Class..fe3.4..5 »- Book...Pr4.2.7... Accession...3.ZS.8. 
 
 REFERENCE 
 
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/// 
 
 INTRODUCTION. 
 
 From the numerous works already published on 
 the subject of stair building it might seem useless to 
 add another. But feeling from the nature of those 
 now before the public a demand for something more 
 concise and yet complete in itself, containing the latest 
 improvements as well as introducing much which is 
 entirely new and original, I offer this to the public. 
 
 It has been the practice with most authors on this 
 subject, to treat it in so professedly a scientific man- 
 ner, as almost entirely to obscure it from the ordinary 
 mind with technicalities and unnecessary explanations, 
 thereby defeating the ostensible object of their labors. 
 
 It is therefore considered useless to give plans 
 and rules which would be of no purpose, but to exer- 
 cise the mathematical fancy of the student, who would 
 not be benefited by them in a practical way ; and as 
 those methods which require the least consideration and 
 study, and which may be executed in the shortest 
 time, are to be mostly desired by the practical me- 
 chanic, such only are given. 
 
 Bass' 
 
_ 4 — 
 
 The principal consideration in bringing out tbi-; 
 treatise has been, to make it useful, and consequently 
 no pains have been spared, to make it simple and easy 
 of comprehension. By the straightforward and nat- 
 ural manner adopted in describing the various dia- 
 grams, the expeditious mode of executing them, and 
 reducing the number of lines for each to as few as 
 possible, it is hoped this end is attained. 
 
 A multiplicity of lines always tends to confuse the 
 mind, and is an objection of the most serious char- 
 acter, and in fact, the principal complaint with work- 
 men generally, is, fixing so many lines on the memory. 
 
 Another difficulty seems to be the methods adop- 
 ted in explaining the diagrams ; for instance : 
 
 I am told to draw a line from t to ii, produce it 
 to c, bisect at o and make b d &c, &c. 
 
 But of the philosophy of these lines I am not in- 
 formed. I may be able to lay down the figures, but 
 to comprehend them in a proper manner from their 
 descriptions is entirely out of the question. 
 
 It requires a thorough mathematical knowledge 
 to understand many of the problems laid down on this 
 subject, and when fully comprehended, they only show 
 the fact, that they are merely scientific in appearance 
 and not in reality, and only demonstrate the absur- 
 dity of the premises taken, and the language used to 
 
describe them rather conceals, than reveals, their true 
 merit. 
 
 The technicalities used to decorate such pro- 
 ductions may speak well for their authors in a literary 
 sense, with a certain class, but the practical workman 
 will no doubt appreciate something better adapted to 
 his present wants. 
 
 Profiting by a knowledge of these facts, acquired 
 by observations made while teaching my plans in 
 various parts of the county, I have endeavored as much 
 as possible to avoid these difficulties, and to improve 
 this work so, as to make it acceptable to mechanics 
 generally. For this purpose an explanation of terms 
 is introduced, also an entire different style of explain- 
 ing the plates and diagrams, which give the reasons 
 for making every line. The instructions are gradual 
 and progressive in their character, from the most 
 simple Ideas on, to the more difficult of comprehen- 
 sion, and a continuous chain of thought is preserved 
 throughout, thus making it interesting and instructive 
 without tiring the mind, and it is confidently believed, 
 that if the reasons given in another part of this work 
 are carefully studied and experimentally carried out, 
 they will be adopted by every one, who may have an 
 opportunity of examining them, and soon introduced 
 to make them of great advantage to carpenters. For 
 
— 6 — 
 
 at least one half the labor ordinarily required in making 
 Spiral hand rails alone^ is dispensed with by these 
 plans. 
 
 A great variety of plans are not given, as this 
 would only enhance the price of the work, without 
 benefiting the workman, but a sufficient number and 
 variety are given to impart the principles of stair buil- 
 ding, and its modifications are left to the discretion of 
 the workman, and the circumstances necessarily atten - 
 ding this business. 
 
 In a word, it is offered to the public with a full 
 impression, that it contains information for the prac- 
 tical stair builder, which has never been published 
 and many improvements made, on the old plans laid 
 down by authors long ago, as also the methods of 
 getting the face mould &c. being entirely new. 
 
 "Without attempting to detract from the merits of 
 these authors, it would only be false modesty to refrain 
 from saying plainly, what is generally insinuated; that 
 it is offered as an improvement on works of this kind. 
 And I depend for success in the undertaking, on the 
 discriminating intelhgence of my fellow mechanics. 
 
 J. R« PERRY, Architect and Builder, 
 
— 7 — 
 
 AN EXPLANATION OF TERMS USED IN STAIR 
 BUILDING. 
 
 It might be thought by many to be unnecessary 
 to introduce this in a work of this kind, as the terms 
 are so common and generaL But it should be re- 
 membered that all who wish to become, are not stair 
 builders, let the following anecdote illustrate. 
 
 While giving lessons in Newburg, N. Y., a young 
 man, who wishing to become acquainted with this 
 branch of business, concluded to take lessons, but said, 
 he could not understand the terms and feared some 
 trouble in this respect, whereupon I agreed to make 
 all plain. In the course of the lesson I frequently 
 made use of the term stair horse, finally he could 
 stand it no longer, and enquired very earnestly, what 
 I meant by stair horse in Orange County language, 
 declaring he had never heard such a thing before in 
 all his life, and could not see the analogy between a 
 horse and a stair case. Some merriment was enjoyed at 
 his expense, but not without making him a wiser man. 
 
— 8 — 
 
 Pitch Board. 
 
 Height Rod. 
 
 Cylinder. 
 
 Hollow CYLiNDEr, 
 
 Well Hole. 
 
 Horse. 
 
 Carriage. 
 
 Is a right angled triangle, and 
 corresponds to the tread, riser 
 and pitch, or inclination of the 
 stairs. 
 
 Is that, on which is divided the 
 number of steps contained in each 
 story, or flight of stairs (in height). 
 
 Is a round solid, iiaving a circu- 
 lar base, equal and parallel. 
 
 The face string of a winding stairs 
 corresponding to well hole. 
 
 A hollow cylinder, around which 
 the steps pass and are supported. 
 
 The principal timber in a stair 
 carriage, out of which the shape 
 of the steps is cut. 
 
 All the timbers, as a whole ; that 
 which supports the stair case. 
 
— 9 — 
 
 Wall String. 
 
 Face String. 
 
 Face Mould. 
 
 Falling Mould. 
 
 Bottom Mould. 
 
 Butt Joint. 
 
 Is the plank out of which is gained 
 the shape of the steps, and fastened 
 to the wall, whether straight or 
 circular. 
 
 Is the outside, or face board of 
 the steps and connects with the 
 well hole. 
 
 Is a pattern, used to cut out the 
 rail timber, and is the principal 
 mould used. 
 
 Is a pattern of the inside or out- 
 side edge of the rail, (used in this 
 work) only to obtain the top line 
 of the rail. 
 
 Is a mould used to mark the 
 bottom of the rail, and is appli- 
 cable to this work only, not being 
 used in any other to my know- 
 ledge. 
 
 Is a joint made at right angles to 
 the top of the rail and secured by 
 a handrail screw. 
 
— 10 — 
 
 Easment. Is a curved line intersecting two 
 
 straight lines, which form an angle. 
 
 Segment. Is as much of a circle, as is cut by a 
 
 chord line. 
 
 Spiral. Is circular passing around a centre, 
 
 winding upwards, a twist line, and 
 geometrically regular in its ascent. 
 
 Geometrical. Is from Ge, the earth and Metron, the 
 measure, belonging to laid down by, 
 or disposed of according to principles 
 of Geometry, and is divided into 
 speculative and practical* 
 
 Elliptical. Is oval not from a common centre, 
 having a major and minor axis. 
 
 Stress Blocks. Are in spiral stairs, the blocks which 
 support the carriage, and in wind- 
 ing stairs, what the horse is in straight 
 ones. 
 
— 11 — 
 
 GEOMETRICAL PROBLEMS 
 
 PLATE Jl. 
 
 Fig. A. To divide a line into two equal parts 
 by a perpendicular. 
 
 Let 1, 3, 4, 2 be a given line, and 3, 4, the part to 
 be divided, set a compass at 3 and 4 respectively and 
 describe the arcs to intersect at o, o, draw through 
 these points, which cuts the centre at c. 
 
 Fig. B. To describe any desired casmcnt 
 from a given angle. 
 
 Let 1 d and 1 c be the lines forming an angle, set 
 the compass 1, 3 any length at pleasure, also 1, 2, 
 draw a b through these points, describe from 3 and 2 
 the arcs to meet at o, set the compass at o and connect 
 3 and 2, which makes the easment> 
 
— 12 — 
 
 Figs. C and D. To find a centre, which will 
 describe the segment of a circle, touching any three 
 given points. 
 
 Let 1, 2, 3 in both figures be points set at 
 random, or intentionally, as the case maybe, then set 
 the compass at 2 and describe a circle, greater in diam- 
 eter than half the distance between the two farthest 
 points, and without altering the compass, set at 1 and 
 3, and describe arcs intersecting the circle, through 
 these intersections draw lines until they meet as at o, 
 which will be the centre. 
 
 Fig. E. To form an octagon from a square 
 jpiece of timber without laying it off on the end. 
 
 Take a common 2 feet square, lay it on the timber 
 as seen in the figure, diagonally from side to side, and 
 at 7 or 17 inches put points to which strike the lines, 
 or set a guage. *) 
 
 *) This is a very simple method, and may be done without 
 sawing off the ends of the timber, any pieces under two feet wide 
 may be laid off in this way, but when the timber is larger, double the 
 proportion, say 4 feet and 14 inches and the length will be the same. 
 The latter method may be used in laying off the foundations of octagon 
 buildings &c. 
 
— 13 — 
 
 PLATE B. 
 
 SE€TIONS OF A CYLINDER. 
 
 A cylinder, cut by any plane, through from one 
 side to the other gives sections, which are elliptical, 
 as seen in Fig. A, But a chord line of one quarter 
 circle may be traced to produce the segment of a lar- 
 ger circle, as seen in Fig. B, when the distances are 
 taken at right angles from the chord line in each case. 
 
 This latter plan applies to hand rails, and it is evi- 
 dent, the chord line should be formed in the manner 
 here laid down, from the fact of the rail passing round 
 the centre of the cylinder at equal distances from any 
 point we please to measure. 
 
 Therefore c, r, beitig the distance from the centre 
 to the inside edge of the rail, it must produce the 
 chord line r, a. 
 
 This brings the true inside line of the rail very 
 nearly, but the twist of the rail, when finished, makes 
 it exactly right, and throws the radius of the greater 
 circle on r, c, when elevated to its proper position on 
 the stairs. See Plates 19 and 20. 
 
 The figures 1, 2, 3, 4 &c. indicate the distances 
 from the chord line in each case, and are pointed off, 
 from the plan below, on the greater circle or segment. 
 
— u — 
 
 Fig. C. How to form the elliptic curve through 
 any three given points in order to describe the 
 quarter section of an ellipsis with a stick, as shoirn 
 Plate 1 Fig. C. 
 
 Let a, b, c represent tlie three points, and b, d the 
 minor circle, then a, c will be the major circle, these 
 circles corespond to the major and minor axes of the 
 ellipsis. Now it is selfevident, that if the piece x be 
 tacked on the plank to the line of the minor axis b, and 
 a stick cut, the whole length to be b, d, e, (and the notch 
 b, d,) then keeping both corners tight to the plank and 
 drawing towards the left ate, it must describe the ellip- 
 tic curve b, /, c, which is almost a perfect circle, and it 
 only begins to vary from alittle to the right off to c- the 
 distance b, h is equal to b, for, f, c, showing it to be an 
 exact quarter circle of what is required* The stick is 
 made as follows : Cut the notch the length of b, d, and 
 the whole length of it from c, J, now if a centre atg were 
 found as on PL A Fig.Z), it would show, how very close 
 to a segment of a larger circle the rail piece would come, 
 but as the spiral hne, when worked on this segment, 
 fits the circle exactly, it is the true method of making 
 them for spiral rails, for the true inside line of a hand 
 rail on these kind of stairs is neither a true segment, 
 nor an ellipsis, but a spiral curve, and which must be 
 worked from the segment of a larger circle, (as the 
 
Lith.of Bien & Sterner, 90 Fidton St Ts'T. 
 
— 15 — 
 
 spiral line runs diagonally on the inside of a segment), 
 to make the twist. 
 
 This is the problem from which a thorough 
 knowledge of hand rails can be obtained and should 
 be studied carefully; it embraces the facts and reasons 
 for adopting the plans in this treatise, it shows also, 
 when carried out, the way to describe any kind of rail, 
 whether spiral, or elliptical, to any height. The three 
 points c, b, a and the line c, a, correspond to the chord 
 line of the semi cylinder on Plate 19, to wit, h, a 
 being the points on that figure, and J, e, a the chord 
 line. 
 
 PLATE 1. 
 
 Fig. A. Is a rod including the height of the story 
 from floor to floor and as shown, makes fourteen steps. 
 
 At the top fig. C is what is called a pitch board, 
 showing the steps to be 71 inches high and 10 inches 
 wide (which would be the cut of a horse, and of course, 
 whatever would be allowed for nosing and finish would 
 be extra from this for width). This right angle tri- 
 angle gives the inclination or pitch of the stair case. 
 
 It is important to know the use, as well, as the 
 methods, of getting the inclination of stair cases. 
 Therefore let the manner of obtaing it be fiirmly fixed 
 in the mind, before proceeding. 
 
— 16 — 
 
 Fig. B. Represents a rough plank, out of which 
 is to be cut a horse, for the support of the steps, accord- 
 ing to the pitch board C. It will be seen that the plank 
 may be of unequal width as at c d. The back line of 
 the plank must be parallel to b, e, and is the line to be 
 followed in laying off the steps. 
 
 Fig. D. Is a face string fastened to the outside 
 horse. The best way to do this, is to lay off the 
 number of steps required, and then either saw out, 
 first, the face string , or fasten with nails or screws to 
 the plank, and saw out both together, in this way if it 
 springs it will not be of any importance, as they both 
 must spring alike. 
 
 It is proper to remark here, that as no person 
 can lay off two strings exactly alike with a pitch board, 
 it is best to lay off the wall string, as explained on 
 Plate 2, first, after which lay the board for the face 
 string on it and point off all the steps, then lay the 
 pitch board between every two points, and mark them 
 on the face string, for should the face string be half an 
 inch longer or shorter than the wall string, it would 
 throw the stair case out of square, and cause much 
 trouble in stepping them up. 
 
Plate 2. 
 
 Scale ^1 toi^in. 
 
 I M I I I I I ] I I I I 
 
— 17 — 
 
 PLATE 2. 
 
 Fig. A shows how to make wall strings. 
 
 First make a pattern, the exact shape of the tread 
 or nosing. Then place the pitch board c on the line o, o, 
 and the pattern under it, and so mark off all the steps 
 in the string. Then take a bit, in size to suit the thickness 
 of the step, and bore a number of holes ase, e,e, e, at the 
 bottom step, about lof an inch deep, run a guage on the 
 back of the plank to suit the depth, and after dressing- 
 out e, e, e, e, nicely to the lines, use a small back saw, 
 for cutting out the remainder, and so proceed with 
 each step. 
 
 This is the best possible method of making wall 
 strings, the old method of fitting them down after the 
 steps are on, is out of date, although some persons 
 practice this plan yet, for want of a better,* It makes 
 also a much neater job, as by keying in the steps they 
 may be made to fit exactly with scarcely any difficulty. 
 
 The treads and risers should be tounged together 
 and glued. It is not essential however to tounge the 
 back of the tread, as represented in the diagram, un- 
 less extra pains are to be taken with the work, as it 
 might as well be nailed from the back side. But the 
 riser, at the nosing, should be glued and also the 
 scocia moulding when made and piled away ready 
 for use. The space below and behind the riser and tread 
 
 2 
 
— 18 — 
 
 shows the key room, the keys should be put in with 
 glue or white lead. 
 
 Fig. B. Exhibits a general view of winding stair 
 cases. These kind although often very clumsy, are 
 nevertheless sometimes very useful, and indespen- 
 sably necessary. They may be put up in a less 
 space than is required for any other kind. First lay 
 down on the floor the exact shape and size of the 
 place to contain the stair. Then find the centre, allow- 
 ing the necessary room for doors, if any, on each side, 
 describe the circle 1, 2, 3 &c. in the centre of the treads, 
 or thereabouts, on which point off the number of 
 steps. Then draw from the centre, as at c, through the 
 points, to the walls. The shaded lines 1, 2, 3, 4, at the 
 wall are to represent boards planed off, which are to 
 project above the horses, to finish on; D, E, F are the 
 horses, cut in the following manner : 
 
 Lay the square on the board, and take the distance 
 0 0 for the first tread, then make one height, reverse 
 the square, and take again for the tread from o to p, 
 add another rise, and so on to the end. In reversing 
 the square, Judgment must be exercised or the cuts 
 will run off the board, in case they do, the same must 
 be persued until the cuts come so as to give the most 
 strength in the carriage, these horses are then nailed 
 
— 19 — 
 
 on the boards, already fastened to the wall, and the 
 steps fitted to them. 
 
 When by practice^ proficiency will suggest, the 
 modes of keying them as in straight flights, previously 
 described. 
 
 PLATE 3. 
 
 Fig. A. Exhibits a top view of a hollow cylinder 
 or well hole, the manner of making them when no 
 veneer is used, to obtain the width of the staves, and 
 the amount of curvarture in each. 
 
 A better plan however is to plane out a veneer, 
 as shown in Fig. B The veneer should be the width 
 of the face string and about I of an inch thick, it will 
 then be pliable enough to bend around a tub made 
 as shown in Figure B, Plate 4, without steaming or 
 wetting* 
 
 Fig. 5 is a cylinder or tub, d, e, f the staves, c 
 the veneer, h the staves of the tub and a its end. 
 
 PLATE 4. 
 
 Fig. A. This plate shows the manner of con- 
 structing a cylinder, B is the veneer passing over the 
 tub, the staves fedc are first fitted around the tub 
 on the veneer, and screwed to it, after they are all 
 
— 20 — 
 
 fitted number them, as shown, commence glueing from 
 one side putting each stave to its number, after stand- 
 ing about one day it will be ready for use. Many 
 persons have a fashion of wetting and steaming, the 
 veneer but this is a bad practice, as it takes twice the 
 length of time to dry, and often, it remains soft a long 
 time, and is more liable to be broken. 
 
 How to put the veneer on the tub, and have the 
 right inclination. 
 
 Take the line o, (being the axis of the cylinder) 
 and square across the bottom to the opposite side, then 
 measure up as high, on that line, as you have height 
 to over come in passing around the circle, or well hole, 
 and bend the veneer to these points. 
 
 This holds good in relation to any kind of stairs, 
 wether half a step or more are in the well hole, allways 
 being shure to have the tub long enough to suit the 
 height to be overcome.. Another method of making 
 them is shown on plate 17 figure B (which see). 
 
 PLATE 5. 
 
 Exhibits a platform or carriage and may be used 
 for either a Spiral or Elliptical rail, the only difference 
 consisting in the manner of putting in the steps. 
 
— 21 — 
 
 If the steps are put as c and a, the distance being 
 greater around the well hole than one of the treads 
 coming up below, it produces a falling, or lowering of 
 the rail at the centre of the platform g, in a well hole 
 of one foot, it becomes as seen in plate 6. Fig. A. 
 
 But to make a continued spiral rail, place the steps 
 as at / and d, the distance around the tread will then 
 be equal to any in the straight part, and of course the 
 inclination of the rail the same, and no difference in 
 the platform, except cutting the horses, at the top-, 
 where the pieces on each side of the well hole, are let- 
 tered B, B. Spike those against the platform, where a 
 spiral rail is to pass over it. 
 
 PLATE 6. 
 
 Fig. A. Shows the difference, between a spiral, 
 and an elliptical rail on a platform stair. The spiral, it 
 will be seen, runs on in a continuous manner, and in 
 consequence, would run one half step higher on the 
 same stair case, than the elliptical. (See an expla- 
 nation of the terms Plates 18, 19, 20.) But if the 
 well hole is placed differently in the platform, the 
 distance will be the same at all points from the nosings 
 to the rail. 
 
 The plans below. No. 1, and No. 2, exhibit the 
 different methods of placing them. 
 
— 22 — 
 
 PLATE 7. 
 
 Here is shown the method of obtaining the face 
 mould, or pattern of the rail, for the elliptical rail on 
 Plate 5. 
 
 Make the circle a, e, f (Fig. A) to correspond 
 exactly with the inside line of the rail, passing over 
 and around it. Take the pitch board a, h, d, and 
 measure from a, to the centre of the circle, or well 
 hole, on the pitch board, then square up from the 
 bottom at o, passing up the centre, and it will cut the 
 chord line, or pitch line, at c. 
 
 Then take o, a as the minor, and c, a as the major 
 axis of an ellipsis and by making a stick to correspond 
 to these lengths as seen in Fig. C. An elliptic curve 
 may be described in the manner laid down on PI. 14, 
 Fig which will be the exact inside line of the rail 
 as seen in Fig. a, o, c. 
 
 The reaso-n, a circle must be extended in length, 
 without increasing its width, in passing around an 
 elliptic curve, is plain, for if the distance o, be ele- 
 vated to the inclination a, c, it looses, from i to c which 
 is the same m from, i to c in the elhpsis Fig. B, and 
 the pitch line is what would be the major axis of an 
 ellipsis, were a right cylinder cut by it. This holds 
 good in all rails, which fall any below the inclination, 
 or pitch, in passing around the well hole, wether they 
 
contain one Or more steps, but is never applicable 
 where the inclination is spiral or continuous, and with- 
 out easment. 
 
 PLATE 8. 
 
 Exhibits the method of working the rail for an 
 elliptic stair case. 
 
 The rail timber being cut square through from 
 the face of the plank. 
 
 Place the pattern of the rail on the piece as seen in 
 Fig. A, the long side of the pitch board on a plain with 
 the face of the rail piece. The dotted lines, show the 
 centre and outside of the rail; the one passing through 
 its centre shows, that the pattern may be raised or 
 lowered to suit the thickness of timber, provided, the 
 same amount is taken from the other end so as to give 
 the rail the same inclination when finished, as seen in 
 the diagram. By this method a moulded rail of 2 inches 
 in thickness may be worked from a piece of timber 
 % inches thick, for a well hole of one foot diameter, 
 and a round rail requires no more than just its thick- 
 ness of timber. 
 
 A good manner of working rails and applying 
 moulds and patterns, is to screw the rail pi^ce into the 
 vice, and elevate it to the back of the pitch board by 
 
— 24 — 
 
 placing it on tlie bench, (if level) then take a spirit 
 level, and level across the end, put the rail pattern at 
 right angles, or plumb under it. 
 
 This is what corresponds to the level on the 
 landing, in passing around the well hole, the twist 
 must be worked from one end, as it always should in 
 elliptical rails, for it is evident, if the rail piece is sprung, 
 or in any way altered from its original position, it 
 alters the curvature, and can no longer follow the 
 intended circle. 
 
 To work the return twist apply the pattern the 
 reverse way and proceed as before, it will be seen also 
 that the rail, when finished, is precisely the same, as 
 though it had been worked by the old methods, ac- 
 cording to the pitch lines. 
 
 How to work the rail: 
 
 In cutting square through from the face of the 
 plank, the top edge of a falling mould is only used, 
 but for getting the thickness of the rail, a pair of com- 
 passes may be altered at the points, as represented by 
 Fig. D. Therefore when the top of the rail is worked, 
 the under side may be scribed off accurately by these 
 compasses from the top side. 
 
— 25 — 
 
 Suppose the top of the rail to be worked, accord- 
 mg to the desired twist, then place the face mould, on 
 it and mark all which is to come off, from the top 
 square the rail piece to this line, and scribe the thick- 
 ness outside and inside. 
 
 Cut another mould to correspond to the bottom 
 of the rail, as seen in Plate 13, marked apply it to 
 the bottom in the same manner as the top one, work 
 to these lines, and it gives a rail shaped as Fig. C, 
 Plate 13, after which any desired shape may be given. 
 
 Fig. B exhibits the manner of making easments 
 by intersectional lines, the retrogressive steps, on a 
 platform stairs, form an angle as in this figure, and 
 the rail should always run one half step higher on the 
 landing, or be made to suit the height of the long 
 balusters. 
 
 Fig. C represents the easment on a newel post. 
 
 PLATE 9. 
 
 How to draw falling moulds. 
 
 Fig. A gives the shape of the rail, when placed 
 over the circle, or what is commonly called a falUng 
 mould. 
 
— 26 — 
 
 Let «, h, c represent the exact inside, or outside 
 line of the rail, according to the kind of mould to be 
 obtained, set a compass from a to c (the diameter of 
 the circle) and describe the dotted lines from c to d, 
 and from a to d, draw from d through a and c, to e and 
 /; make e,/ parallel to a, c, and at right angles erect 
 the height to be overcome in passing around the well 
 hole or circle of the rail, as g, then draw the line 
 g,f, place the pitch boards at right angles to e, g, and 
 e, f, when any desired easment may be drawn by the 
 intersection of lines, or by compasses to suit the eye. 
 Make the butt joint at right angles from g, / in the 
 centre. 
 
 The dotted line shows what is denominated the 
 spiral line, wherein there is no easment, but a con- 
 tinual twist. 
 
 When the rail passes on a landing or floor, where 
 the flight runs from floor to floor, a small easment 
 should be made at the centre, which is one half step 
 higher than the rail coming up from below. 
 
 Fig. B. Another method is to lay ofi" the 
 steps around the inside or outside of the rail, this is 
 where more than one step is in the circle, as seen in 
 the figure. 
 
 Care must be taken, in laying it down to have 
 the exact pitch of the steps for the inside of the rail, 
 
^ 27 — 
 
 when getting an inside mould, and for the outside 
 when getting an outside mould. This is a very natural 
 and comprehensive way of getting a mould ; the true 
 pitch should be ascertained, and a pitch board made, 
 when it may be passed along a board and the number 
 of steps marked on it; also the different pitches eased 
 into each other, and the mark for the holes pointed 
 6ff on the mould, for boring the rail. 
 
 Boring the Rail. 
 
 As a general thing two balusters are placed on a 
 step, and to find the distance from centre to centre, 
 divide the base hne of the pitch board equally, then 
 square up from the bottom and the pitch line will be 
 cut in the centre also; therefore half the length of the 
 pitch line is the distance between the holes for the 
 balusters on the rail. 
 
 Points should be taken on a rod, both to make the 
 rail and also to divide off the holes, but by experience 
 it may be avoided, as a good stair builder would make 
 an entire stair case, without even seeing the building 
 had he only the pitch and number of steps required. 
 But for beginners this is the best method, the rail may 
 be then bored, by dividing the balusters along the rail 
 between these points. 
 
— 28 — 
 
 Sometimes the rail may be laid on the nosings 
 and the holes marked on it by squaring up from the 
 steps. 
 
 A good plan however for the twist part is, to bore 
 it after it is strung over the circle, when it may be 
 mariied correctly by plumbing up from the steps. 
 
 Newel Posts. 
 PLATE 10. 
 
 Exhibits part of a stair including the newel post. 
 The proper method of making them, where a good 
 solid one can not be obtained, and also where they 
 may be preferred, on account of beauty and durability: 
 
 The height rod at the side of the post, shows the 
 different parts of which it is made up; the base below 
 is generally about 9 inches, the mouldings between it 
 and the spire, as also between the spire and top, are 
 simply two pieces of the rail plank glued together, and 
 turned in a lathe to suit the fancy. 
 
 The spire and base are veneered with the kind 
 of wood of which the rail and balusters are made, a 
 screw, passing through the rail cap and post below the 
 joist, is fastened in the manner seen on the diagram. 
 
— 29 — 
 
 By this means the post may be fastened much 
 firmer than by keys, and should it at any time become 
 loose, may be screwed up at pleasure. 
 
 A good way to cut the dovetails in the steps is also 
 here shown, by cutting one side square, a nail may 
 be driven in and the step firmly secured to the face 
 string without showing it as the baluster covers it 
 when in. 
 
 The face string should be finished down in the 
 manner here described, where it is practicable, as it 
 is much neater, than when connecting the base with- 
 out an easment. *) 
 
 PLATE 11. 
 
 I am now about to explain the method of getting 
 out rails by a plan never before published, and which 
 
 *) As stated in. the introduction, it is not deemed necessary to 
 cr\ve the manner of making curtail steps and rails in this volume, as 
 it would be a repetition only and of no benefit. Nearly all the nu- 
 merous works published' oa this subject, contain the manner of con- 
 structing them. 
 
— 30 — 
 
 is contrary to all the ideas, it has been my fortune to 
 examine, by all authors I have met with, being also, 
 as before stated, the principal reason for offering this 
 book to the public. 
 
 Fig. A, By this plan the falling mould is first 
 obtained, or at least the outstretch of th« circle taken 
 and the pitch applied, in order to ascertain the exact 
 height, to be overcome in going around the circle, or 
 inside line of the rail. 
 
 Therefore let fl, b, c be the -exact line of the well 
 hole. Then divide half the step, or base line of the 
 pitch board, each way from the centre or plumb line, 
 which is indicated by the shaded part o, o. Find the 
 stretchout as on Plate 9. Place the pitch board, as 
 usual, at right angles from e and f, continue the pitch 
 line, then erect the perpendicular e, g. 
 
 This gives a line from which to construct the fall- 
 ing mould, also the exact height the rail will attain in 
 passing over and around the well hole. 
 
 At right angles from the pitch line, and in the 
 centre, draw the thickness of the rail, then measure 
 
— oi — 
 
 on each side half the width of the rail. Connect these 
 lines with the pitch board, and it gives the falling 
 mould inside and outside. , 
 
 The easment on the rail is so slight, that any 
 judgment on the part of the workman would dispense 
 with the use of a falling mould, except for the purpose 
 of marking the joint on the rail. 
 
 Fig. B. How to find the face mould for a 
 spiral rail. 
 
 Let a, b, c be the exact inside line of the rail, 
 found by the falling mould, draw the chord line in the 
 circle c, b, erect d in its centre. 
 
 Erect the perpendicular c, e, equal in height to the 
 spiral line at g, in Fig. k. Draw the chord line from 
 e to a, plumb up from the centre of the well hole b, h, 
 to the chord line e, «, and at right angles make f equal 
 in length to half the diameter of the circle, draw a 
 chord line from y to a, in the centre of which and at 
 right angles to it make g, equal to d in the plan 
 below. 
 
— 32 — 
 
 This then gives the points f, g, a. Set a compass 
 at the point g, and describe a circle around it, about 
 3 the distance from a and f, then without moving the 
 compasses put the foot at a and f, and describe circles 
 to intersect, now draw through these intersections 
 lines to the centre at o, from whence describe the inside 
 line of the rail, a, g,f. To make the butt joints draw 
 lines from o through a and /. From o, a at right angles 
 extend the length of the straight part of the rail at 
 pleasure. The mould should be made a little longer, 
 in order to have wood to make the joint exact. 
 
 From the same centre may be described, a si- 
 milar mould to ^, but as it is the segment of a larger 
 circle, the same pattern may be used continuously 
 right and left. 
 
 It will be seen, that the mould falls below the 
 point e at i. This is owing to the twist required in 
 the rail, as each piece revolves on the points a SLudf, 
 and when it is worked will throw the rail to its proper 
 height, (see Plate 13, Figs. A, B, C, for a full expla- 
 nation ; also Plates 18, 19 and 20.) 
 
 The bevel taken from lines b,. h and /to work the 
 twist is applied on the plank from the inside and out- 
 
_ 33 _ 
 
 side of the timber, on both ends, which is cut square 
 through from its face, as on Plate 13 (which now 
 read carefully) . 
 
 PLATE 12. 
 
 Exhibits a Spiral or Geometrical Stairs, a con- 
 tinuation of winders from bottom to top. 
 
 The numbers 32 indicate the number of steps 
 in the circle, the shaded part the rail ; o,o,o are stress 
 blocks, and are the principal pieces in the construction 
 of the carriage ; c, d, a show the chord line of one 
 quarter part of the circle, from which is found (by the 
 previous method) the rail, one mould being sufficient 
 for all the segments in the circle. See Plate 17 how 
 to build the carriage and wall string *) 
 
 The carriage, rail, wall string, &c. are invariably 
 got in the same manner, as described on the plates 
 refered to above. 
 
 *) This plate contains the principles of all spiral stairs and 
 rails, and any alteration is only a variation from the general rule. 
 
 3 
 
— 34 — 
 
 PLATE 13. 
 
 How to find the face mould of a stair rail in 
 the easiest possible manner, for spiral stairs. 
 
 Let a, e, f, Fig. A be the exkct inside line of the 
 rail, draw the chord hne e, h,f and at the centre square 
 out the hne h, to the circle. Erect a perpendicular 
 from the axis of the circle on a, e, equal in height to 
 half the number of steps in coming around the circle, 
 over which the rail is to pass. (1, 2, 3, 4 or o, being 
 heights in the quarter circle) Then draw the line to a. 
 At right angles from o, produce c, equal in length to 
 half the axis a, e, from c draw the line to a, which 
 corresponds to e, f in the plan, make b also in the 
 same manner as below. 
 
 This gives the points a, b, c; then take any thing 
 more than one half the distance between b and a, or c, 
 and describe a circle, placing the foot of the com- 
 passes respectively at c and a, making intersecting 
 circles, and through these points draw lines to the 
 centre G, from where describe the inside line of the face 
 mould a, b, c. This is the same method as Plate A Fig. 
 C and D. 
 
— 35 — 
 
 The lines represented on the mould marked x, 
 make a mould from the same centre for the bottom 
 of the rail, c, d, is the width of the mould. 
 
 Make both joints by drawing hues from G through 
 a and c, and any length of timber required for an 
 easment, extend at right angles from G, «, indicated 
 by E. 
 
 The bevel taken from the diagram is applied as 
 seen on Fig. C. 
 
 Fig. B exhibits a piece of rail timber, from the 
 saw, perfectly square, and just the width of the rail, 
 except of an inch allowed for smoothing up. 
 
 H, is the straight part attached to the twist for 
 the easment. a,h, c, the inside line, c, d its width, and 
 c, e the depth of it. is a piece of paste board which 
 represents the falHng mould (but for continuous twists, 
 all that IS used is a piece straight on its edge.) 
 
 Fig. C exhibits, only the inside and ends of a si- 
 milar piece, the square ends shown by the pattern of 
 
— 36 - 
 
 the rail, and the bevel taken from Fig. A, applied on 
 the inside of one end and the outside of the other. 
 
 There is no straight part to this, and therefore 
 would be such as is made for continuous winders, each 
 successive piece being but a continuation of the same 
 pattern. 
 
 It will be observed, that the line across the tim- 
 ber representing the shape of the rail, is elevated 
 somewhat more than the face mould naturally throws 
 it, this is owing to the twist which must be worked 
 on the timber, and when the rail is placed in its po- 
 sition over the well hole, will be exactly right in height 
 and otherwise. 
 
 By refering to Plates 11 and 19 it will be seen 
 also, that the circle of the inside line of the rail, when 
 continued around the cylinder seems less in height 
 than the number of steps would require, but this is 
 owing to the manner of viewing the line, as it cannot 
 be represented on paper exactly. For if the circle 
 were drawn through the right angled point of the 
 chord line (which represents the axis of the cylinder 
 
— 37 — 
 
 in those figures) it would appear too narrow at the 
 centre of the quarter circle. 
 
 The doted lines are the plumb lines, supposing it 
 were cut according to the pitch, which it is not but 
 still show it to be the same when finished as though it 
 were cut in that way. 
 
 How to work a twist for a spiral rail. 
 
 Dress the rail timber perfectly square from its 
 face, just the width of the rail, (allowing a little to 
 smooth up) apply the falling moulds or mold, only 
 to obtain the top of the rail, and easment if any. 
 
 Apply the bevel on the outside and inside edge 
 of the rail, as in Fig. C according (to wether it is to 
 run right or left handed) work off the top to the top 
 lines of the rail piece, the rail remains square in the 
 middle of the piece and the twist runs both ways, but 
 still the middle will be reduced by the inside and out- 
 side lines. 
 
 Then take the face mould again and lap it on the 
 rail piece marking all on the outside, and being shure 
 to keep it on the inside edge of the timber, or as the 
 
— 38 — 
 
 patterns on the ends of the piece require. Then work 
 of this wood at right angles from the top of the rail. 
 Now take the compasses described on Plate 8, and set 
 them to the desired thikness of the rail, and scribe off 
 the inside and outside, Work to these lines. Then place 
 the bottom mould in its proper position, (the centre 
 of the rail) and mark both sides, work of these to 
 lines, and it gives the shape of the rail as at a. Plate 
 13, Fig. C. 
 
 After which any other shaped rail may be worked 
 out of it to suit the fancy. 
 
 For a round rail the corners may be guaged off 
 from the square piece, and worked as if it were a 
 straight rail. 
 
— 39 — 
 
 [NTRODUCTORY REMARKS CONCERN- 
 ING SPIRAL AND ELLIPTICAL LINES 
 FOR HAND RAILS. 
 
 <*' I have mentioned before, that in some cases it is 
 
 necessary to cut out the face moulds on the eUiptical 
 plan, (introduced by Peter Nicholson many years ago) 
 but nothing can be more void of principle, than many 
 of the plans laid down, in regard to spiral rails. And 
 it seems as though no pains have been taken by any 
 later authors to correct the mistake, as they have 
 based their investigations on the theory of cutting a 
 cylinder to the required pitch, supposing the elliptical 
 section, thereby given, to be the true inside line of 
 the rail, in passing over and around the well hole. 
 
 The only difficulty with those authors, seems to 
 have been, that, of disputing the correctness of the 
 above named theory, thereby coming in contact with 
 estabhshed rules and opinions, but I would ask; 
 How is it possible to advance in the arts and siences, 
 without coming in contact, and successfully removing 
 from the mind, erroneous theories, it matters not by 
 whom, or how long established. 
 
— 40 — 
 
 It is true many books have been published set- 
 ing forth improvements made in handrails, but still, 
 being based on the same old' theory, to me at least, 
 it has been a different reading of the same book. 
 
 Therefore I assert there have been no real im. 
 provement since to my knowledge, and this being the 
 proper place, I will endeavour to explain (in a short 
 way) the difference between a spiral and an ellipti- 
 cal line. 
 
 The spiral line passing around, the cylinder is 
 regular and continuous in its inclination, whereas the 
 elliptic shortens and quickens around its major axis, 
 and while the spiral line continues to run on up like 
 the screw of an auger, the elhptical line, after passing 
 its major axis, actually runs down the opposite side, 
 of the cylinder as it necessarily must, in forming the 
 elliptical section. 
 
 Therefore where an easment is wanted, as on a 
 landing, the elliptical line is just the thing required. 
 
— dl — 
 
 PLATE 14. 
 
 How to describe one fourth of an ellipse with 
 a stick as shown on Plate 7. 
 
 This stick represents half the major and minor 
 axes of the eUipse. 
 
 It will be seen that the well hole here laid down 
 contains 4 steps to the centre, and but 3 from it to 
 the end of the circle, therefore it is plain, the rail 
 should drop a little, to correspond with the nosings in 
 height, but as the long balusters are always used on 
 the landing, it is raised one half step, makingit 3] steps 
 high. Make the stick in Fig. B from the end to the 
 extreme length, equal to b, in Fig. b below, and 
 for the short diameter, from a to c, Fig. b. 
 
 Fig JB shows the manner of describing the 
 face mould ; the paste board which is intended for 
 it, is laid on the plank or workbench, and a small 
 stick tacked at right angles from the edge, the stick is 
 then slipped tight to the angle and moved to the left 
 or right according to the way the rail is to run; a, c, d 
 show the distances on the stick, a, c the minor axis 
 
— 42 — 
 
 and to d the width of the rail, e shows the end of the 
 stick passing below the strips, tacked on the plank, 
 therefore when the stick is moved, its whole length is 
 brougt into the circle, and makes the quarter ellipse. 
 
 The pattern is then applied at right angles from 
 the short side of the pitch board, as described on 
 Plate 8, which it is presumed, the reader has ac- 
 quainted himself with ere this. 
 
 Any of the moulds may be applied for any rails 
 herein treated of, as well by the pitch lines, as by 
 cutting square through from the face of the plank, 
 but there is no danger of any one resorting to the old 
 method of cutting out rails with a whipsaw, when they 
 may be cut out by a jigsaw, in half the time, and be- 
 sides, afterward worked in less time, than it would re- 
 quire, even to cut them out by the old method. The 
 dotted line on the outside of this mould shows what 
 it should be to cut the pitch. 
 
 The curvature of any part of an ellipse is altered 
 by twisting it out of its original position, therefore it 
 will not answer to work the twist from both ends, as 
 on a spiral rail piece, at least to be consistent with 
 
— 43 — 
 
 principle, if the inside of a rail were but the double 
 section, cut by a given plane. 
 
 PLATE 15. 
 
 How to get a falling mould, showing the con- 
 nections of straight rail, wether the steps arc equal 
 in number or the treads alike in width. 
 
 Lay off the plan of the rail a, h, c, if for the out- 
 side, and a, q, if the inside is required. 
 
 Obtain the stretchout of the semi circle, as given 
 on Plate 9, then erect a perpendicular on the left hand 
 side of the stretchout point, equal in height, to all the 
 steps in the semi circle, counting from the bottom up- 
 ward. From this point draw a hue to the right hand 
 point of the stretchout at / Make the pitch board 
 below (if any straight connects) at right angles from 
 e, b,f and the easments, by intersection of lines, or 
 by making points m, I on the pitch lines, and setting 
 the foot of the compasses to these points respectively 
 describing n, from which make the easment. The 
 letters g, A, q show the rail joints. 
 
— 44 — 
 
 Care should be taken to make the easments as 
 graceful, as the thickness of thuber and other circum- 
 stances will admit, however the judgment of the 
 workman has all to do in this matter, as it regards 
 taste. 
 
 The easment at the top, it will be seen, is made 
 by glueing the block k on the bottom of the straight 
 part, and is a very good method, provided a little care 
 be taken in working the rail piece exact, and also let- 
 ting in the bolt. 
 
 It saves also, a good deal of trouble in making 
 the upper twist. 
 
 It applies particularly to the kind on Plate 16, 
 where the upper part of the rail is elKpticah But even 
 on these the upper part may be made from the lower 
 mould, by dropping the rail sHghtly, if it is preferred. 
 
 The straight part usually attached to the circular 
 part of a rail, is from 3 to 8 inches, where it is 
 proper to make the easment very long however, part 
 of it should be made on the straight rail, as this saves 
 thickness of timber in making the twist. 
 
— 46 — 
 
 If the rail starts from a newel post to wind con- 
 tinuously, the first piece should be got out, as shown 
 on Plate 14, Fig. & and B. 
 
 It would not be essential to mark the steps on 
 the diagram as here represented, but it is merely to 
 show the similarity between this, and a plan for getting 
 the same on Plate 9. 
 
 PLATE 16. 
 
 Exhibits a stair carriage showing the manner of 
 constructing carriages of this kind generally. 
 
 Lay down on the floor the necessary lines, over 
 which to build the stair carriage, as regards the 
 number of steps, size of the well hole, position of the 
 steps, rail, wall string, studding and stress blocks. 
 
 How to construct the stairs. 
 
 If a part of the carriage is straight, as in the dia- 
 gram, commence putting up first, by placing the wall 
 string of the straight part to its place and fastening it. 
 
— 46 — 
 
 To this spike up the first rough riser of the 
 carriage as marked No. 10, or fasten it in the wall as 
 the case may be, place also the studding to their places 
 as shown at x, x, x, x, and prop up the rough riser 
 at the well hole exactly plumb over the line on 
 the floor. 
 
 Then put up the next rough riser, one step 
 higher in the circle than the first, and make the stress 
 blocks the tops of which are, a, a, a, &c. and the sides, 
 cut as in Fig. A, Plate 17, (the sides of the blocks are 
 marked h, b, showing the rough risers as they run one 
 above an other) then spike them into their places as 
 seen here also. 
 
 The rough risers should run into the circle so as 
 to cut them off plumb with the well hole in order to 
 nail the hollow cylinder at each step, as it increases 
 the strength of the carriage very much when finished, 
 and so proceed round spiking the rough risers to the 
 studding and letting them run on to the wall as seen 
 here. It is better on this account to have studding 
 placed here, than if a circular wall were built. 
 
 The studding generally should be left run to the 
 full bight of the building, sometimes however this 
 
47 — 
 
 would not answer as the plan of the building might re- 
 quire the stairs to run to the hight of one story only. 
 
 Where they are left run the full height, a segment 
 of the same circle should be placed at the top joists, 
 and nailed through into the tops of the studding, but 
 where they only run one story, the floor may be cut 
 to the same circle, and the nosing and bulasters con- 
 tinued around as on landings. 
 
 The way to get the depth of the rough false riser 
 is seen in Plate IT, Fig. A, where the straight part 
 coming up from below is attached to it, viz : By cutting 
 down through the horse, and adding to this length one 
 rise in height. The bottom edge is afterward trimmed 
 off to make the easment in the carriage, a, a, a, shows 
 the rough risers in the carriage and b, h, are the stress 
 blocks. «, c being the depth of the risers. 
 
 How to put down the wall string. 
 
 PLATE 17, Fig. B. 
 
 Shows the manner of making wall strings by 
 keying them out of a plank. 
 
 The dove tails are cut diagonally across the plank 
 according to a pitch board found from this line of the 
 
— 48 — 
 
 carriage, a plow bit is generally run on the top edge of 
 the plank about l inch deep and from | to 2 inch from 
 its face, which is intended to receive a moulding, when 
 plastered. 
 
 The keys should be cut as far through, as to the 
 bottom of this groove, as seen in the figure. 
 
 How to get the pitch line. 
 
 Divide off on the inside line of the keys, into 
 spaces of about one inch, the distance from the face of 
 one riser to the face of the next, in the floor plan. 
 
 Take this distance as a base line, and square up 
 one step, draw the Hypothenuse line, of the right 
 angle, which gives the exact pitch of the string, as on 
 the figure which is marked C. 
 
 It will be seen the keys are driven alternately 
 from each side, this is in order to obviate the difficult}^ 
 of springing one side too much. 
 
 A bevel may be set to the pitch board, and the 
 centre lines marked on the plank about three inches 
 apart, when the bevel should be again altered slightly, 
 
— 49 — 
 
 and the taper of the keys again marked, then saw 
 out to the bottom of the groove on these hnes. 
 
 The keys should be made about 4 inches longer 
 than the dovetail, to allow for driving, and nearly 
 square, for when the plank is sprung it makes the 
 dovetails square, as marked on the Plate 16. Spring 
 the plank to the studding, when it is ready for cutting 
 down to its place, if the plank is moistened with hot 
 water it will spring all the better, but requires time 
 again to dry, befor fastening the joints. 
 
 How to cut it down. 
 
 Keep the wall string at both ends equal distance, 
 when sprung, from the false risers, against the studd- 
 ing or wall, and mark plumb all the faces of the risers 
 and joints to be made, then take down the string and 
 cut them out, as marked, when it is ready to be placed 
 in its position on the carriage. 
 
 In most cases when stairs are built in this way, 
 the steps and risers are scribed up neatly to the 
 wall string and so fastened permanently, but they may 
 
 4 
 
— 60 — 
 
 be fitted to the string and marked, after which the 
 string is taken down and the steps gained out, or with 
 care, the pitch board may be run on the wall string 
 before being sprung, and the steps laid off, the same 
 as on a straight piece. 
 
 Well Holes. 
 
 May be made also by ascertaning the exact pitch in 
 the manner described on Plate 17, and by finding the 
 exact height they are to travel in passing around any 
 circle, for small cylinders or well holes, it is an inferior 
 method to the one laid down on Plate 4, and should 
 not be used, but for large well holes, it is preferable 
 on account of the shortness of time required in mak- 
 ing them. 
 
 In well holes from 3 to 8 feet diameter, the keys 
 come from 3 to 6 inches apart, and the string may be 
 sprung to the carriage, thereby saving the time required 
 to make a well tub, generally a cutting thrust, or dado 
 plane, is used in cutting the depth of the gaines, and 
 afterward dressed out to receive the keys. *) 
 
 *) This kind of stair are preferable to any other kind for private 
 dwellings on account of their graceful appearance and adaptation to a 
 
— 51 — 
 
 Many different methods are laid down for the 
 construction of stair carriages, but as the method just 
 described is considered the best as well, as the most 
 expeditious for this kind, it is given, leaving the work- 
 man to consult his own judgment for variety. 
 
 Sometimes straight horses are used to run across 
 the carriage instead of stress blocks, when these are 
 used they may be cut by the same rule given on 
 Plate 2, but to give an opinion, they are not near so 
 permanent as the blocks. 
 
 front hall, also for economy in room, and by landing at once on the 
 second floor, thereby forming no obstruction in passing to any room 
 from the upper landing either way, front or back, and affording a 
 passage way below in either direction, which a platform, would not 
 admit, besides requiring much less room on the first floor. 
 
— 62 — 
 
 Reasons For Adopting These Methods 
 In Making Hand Rails And The Phi- 
 losophy Of The System, Explained 
 Comparatively With Models. 
 
 Although it might not be essentially necessary to 
 have a complete knowledge of the principles involved 
 in the preceeding rules, to succeed in working hand 
 rails (from the plainess of the diagrams accompanying 
 them). Yet, as the investigating mind demands a 
 satisfactory explanation of the Why and Wherefore, 
 it is thought proper to give these additional reasons, 
 and as no better way exist to fasten conviction upon 
 the mind, than by models, it is asked from those wish- 
 ing to pursue the investigation further, to provide 
 themselves with a small model, as follows : 
 
 PLATE 18. 
 
 Make a right cylinder about eight inches long 
 and three inches in diameter, draw on both ends 
 
— 53 — 
 
 the axis lines, so as to divide it into two equal 
 parts, then draw lines down each side connecting the 
 axes, space off, say six steps high up one line, and 
 divide half the cylinder in six parts also, this when 
 the lines are drawn up and around it will form steps. 
 Then take a strip of paper perfectly straight on 
 its edge, and lap around the semi cylinder from the 
 first step to the top, as seen on the figure from a to h. 
 It will be seen, that this paper will follow all the 
 points of the steps ae 1, 2, 3, 4, 5 and 6, therefore this 
 must be the spiral line and which a hand rail should 
 follow. 
 
 Now if the line A, B, were cut through from side 
 to side, it would pass 2, 3 and 4, but would fall short 
 between 1, 2 and 4, 5, and if a line from o to 6, were 
 cut it would touch o, 3, 6. It is evident this could not 
 be the line of the rail. It is equally plain that no cut 
 of a cylinder from any pitch, will suit a spiral line, 
 for as already stated the section thus obtained must 
 be elliptical, (therefore it is not true, that a hand rail 
 is a double section of a cylinder cut by a given pitch) 
 when used for spiral stairs, as contended for by P. 
 Nicholson and later authors. For instead of being 
 the double section of a cylinder it must be worked 
 from the segment of a larger circle. 
 
— 64 — 
 
 On page 13 of the new carpenters guide, may be 
 found the following remarks : 
 
 "Upon these figures, meaning the cut of a cylin- 
 der any direction to make an obstuse angle with the 
 plane of a segment". Depends the whole principles of 
 hand rails for stairs, "The reader ought to understand 
 how to form the sections of a cylinder in any case 
 whatever, for the face or raking mould of a hand rail, 
 is nothing but the double section of a cylinder, ^c. 
 
 Contrary however to this general opinion here 
 Quoted. I assert, that although by cutting a right 
 cylinder to any pitch, from one side to another, its 
 sections being elliptical, it does not follow that such 
 sections are the true line of a spiral rail in passing 
 around it, and more than this, it is a contradiction of 
 terms to say, that the spiral line of a hand rail is ellip- 
 tical, because, spiral is not elliptical. 
 
 I do not dispute the fact, that to cut a cylinder 
 by any pitch its sections will be elliptical. But that 
 an ellipsis although it fit a circle, will not pass v&gw- 
 larly over the stairs and be an equal distance from the 
 nosings, as it evidently should. On Plates 19 and 20 
 
— 55 — 
 
 • will be seen a further demo^stration of these ideas 
 and the falacy of the elliptical theory of hand rails. 
 
 PLATE 19. 
 
 Shows a semi cyhnder perspectively and corres- 
 ponds to a well hole around which a hand rail passes. 
 
 Now let d, h, be the exact inside line of the 
 rail, then b, e, a, would be the chord line, if the cyl- 
 inder were cut by the pitch, and it will be admitted, 
 that the rail passing around and over the well hole 
 should be equal distance, from a plumb line passing 
 up to the ceiling from the centre of the well hole, this 
 line would correspond to g, e, c, and b, i, shows the 
 spiral line passing around. Therefore the distance 
 c, d, must be made at right angles from the chord hne 
 of one quarter circle, as the rail is made in two peices 
 for a semi circle. 
 
 Is it not evident then, that a, e, cannot be the 
 right length of a chord line for one quarter circle, as 
 the rail does not curve to the centre of the cyhnder, 
 but keeps half the diameter of the inside line from it 
 in passing up and around. 
 
— 56 ~ 
 
 PLATE 20. • 
 
 Exhibits the same by ordinates, it will be obser- 
 ved that the distance h, a, is the same as c, J in PI. 19- 
 
 By dividing the chord line of the quarter circle 
 below into 8 parts or more, and plumbing up to the 
 chord line h, e, and squaring from thence to the 
 chord line of the cylinder d, a, and squaring from that 
 again at random, then applying the distances from the 
 quarter circle below on these lines, it gives points, 
 which if connected will be the same as seen on Plate 
 13, and proven to be a segment of a larger circle by 
 placing a compass at f. 
 
 This tjierefore is the true method of getting a rail 
 piece by ordinates, wether the plan be elliptical or 
 circular, but for the inside of an elliptical rail, it is the 
 best method, and for the spiral mould take Plate 13. 
 Where an easment is required as at a landing on 
 spiral stairs, the above method is recommended, ex- 
 cept, that the plan should be laid down as on Plate 14 
 or by the small stick on Plate 7, Fig. C7, and Plate B, 
 Fig. C. 
 
 Again, suppose as an illustration, a common 
 Screw Pump be taken. The outside of the shaft around 
 which the spiral line runs, is just the same as shown 
 
— 67 - 
 
 on Plate 19, and the straight strip which is used to lay 
 off, the gaines or the twisted groove, is identical with 
 the falling mould of a rail for the continuous part of 
 the flight. A pump maker would laugh at the idea of 
 stricking out these flights or parts of the twist, with 
 a trammel, or by ordinates, and yet it would be no 
 more absurd, than to use the same instrument, for a 
 rail which eridently runs precisely the same on these 
 kind of stairs. 
 
 A twist cut rifle will illustrate what I mean also, 
 and has led me to introduce a problem, and a ma- 
 thematical Theorem, for the solution of all such 
 questions, I do this to gratify a class of individuals 
 who may probably feel the necessity of a mathema- 
 tical demonstration. 
 
— 58 — 
 
 Question. 
 
 Suppose a rifle ball one half inch in diameter to twist, 
 once round in passing 6 feet, the barrel being 3 feet 
 long, and the distance to travel 100 yards. What dis- 
 tance would a mark travel on the outside of the ball. 
 
 Solution. 
 
 Take the circumferance of the semi diameter of 
 the ball, then suppose a right angle triangle, the base 
 hne to be the length of this semi circumference, and 
 its perpendicular the length of the barrel, now by 
 drawing the hypothenuse the figure is complete, then 
 by multiplying the hypothenuse line by 100 yards it 
 must give the exact distance the mark would travel, 
 hence the following theorem. 
 
 The hypothenous of a right angle triangle is equal 
 to the spiral line of a semi cylinder, the outretch of which 
 is talcenfor the base line of the triangle. {See Plate 21.) 
 
 Again, as the difference between a spiral and 
 elliptical line is considerable, I here give the way to 
 get the length of each, which shows conclusively, that 
 they cannot be taken for the same in any case whatever. 
 
— 69 - 
 
 Rule for the spiral line. 
 
 The hypothenuse of a right angle triangle is equal 
 to the square root of the sum of the squares of the 
 Base and perpendicular lines, or thus by formula, 
 
 Rule for the elliptical line or arc. 
 
 The square root of half the sum of the squares of 
 the major and minor axes, multiplied by 3, 1416, 
 equals the circumference, or the ellipse, therefore one 
 half of this must be the length of the arc, or semi sec- 
 tion, and is thus expressed, 
 
 ^^! + ^X 3,1416 = arc, -5 
 
 But perhaps the common auger affords the best 
 illustration of these principles, as it embraces both the 
 spiral and elliptical curves, and forever settles the 
 question, in relation to both theories, showing the 
 
 *) The letters in these Algebraic expressions refer thus : H for 
 hpothemise B for base, and P for ^perpendicular also, M for major and 
 M for minor axis of the ellipse. 
 
— 60 — 
 
 utility of each, at a glance. Observe, that from 
 the bottom upward passing around from the bits 
 about half its circumference, it is not regular in ascen- 
 ding, but increases gradually until it obtains a regular 
 ascent. This corresponds exactly to the elliptical curve. 
 But after it has attained (by constantly increasing its 
 inclination) to regularity, it is then what is termed 
 the spiral line. This shows, that any part of a rail 
 may be obtained (in order to form an easment on a 
 landing), out of the least possible quantity of stuff in 
 thickness, by describing a similar curve to that ex- 
 hibited by turning an auger upside down, or the bits 
 upward, which are elliptical, and correspond to Plate 
 14, also, the absurdity of useing that kind of a curve 
 for a continuous flight. 
 
 PLATE 21. 
 
 Exhibits the method of getting a falling mould 
 by dividing the circle into any number of parts and 
 pointing them ofi' on a line parallel to its base or axis. 
 By this method the pitch of a wall string may be found 
 as the one on Plate 17. 
 
 PLATE 22. 
 
 Exhibits a plan for a stair the well hole being the 
 frustrum of a cone. 
 
it 
 
 — 61 — 
 
 Let the small square in the centre of the dia- 
 gram, 1, 2, 3, 4, represent the increasing width of the 
 circle as it passes upward, determine the size desired, 
 and set the compass at 1, make the circle to o, move 
 the point to 2, and thus pass round to 4, when the 
 inside of the string or handrail as the case may be is 
 completed. It will be seen that each part corres- 
 ponds to one quarter of the circle, therefore proceed 
 in getting the rail just as in Plate 13 for each quarter 
 circle, adding the correct height to be overcome in 
 the same. 
 
 The wall string may be found also as usual, and 
 either glued or keyed up to the wall properly. 
 
 PLATE 23. 
 
 Exhibits a platform stair the steps running at right 
 angles from the platform. 
 
 In laying off this kind, the well hole or face string 
 should be so arranged as to be equal to one of the 
 treads, then it would require no easment in the string 
 and very little in the rail. The rail for these kind of 
 stairs must be got out as on Plate 13 or at least by 
 
•a 
 
 — 62 - 
 
 that principle, as it will be the segment of a larger 
 circle. 
 
 c, d, shows a newel post made in the same way 
 as on Plate 10. 
 
 PLATE 24. 
 
 Shows the method of fastening the rail and cap, 
 of an ogee hand rail. Fig. ^ is a top view, the circle 
 at b is the hole turned in the cap to hide the bolt 
 head, and a, the circle of the ornament to cover it, 
 see Plates 10 and 23. 
 
 Fig. B shows the bottom, the dotted bolt secur- 
 ing the rail and cap thogether. 
 
 The rail should not be worked at the easment 
 until the cap is fitted on it, when it may be dressed to 
 suit it exactly as it makes a much neater job than to 
 work it before hand. 
 
 PLATE 25. 
 
 This plate sfiows the method of making the rail 
 pass nearly an equal height from the progressive and 
 retrogressive steps, although the steps may have been 
 wrongly placed in the platform. 
 
i 
 
— 63 — 
 
 Let Fig. A be an example, the face of one riser 
 on the axis hne of the circle, and the other 3 or 4 
 inches from the other side, when it is evident, if the 
 rail is worked out in the regular way the balusters 
 must be shorter on the retrogressive flight. 
 
 The method of finding the line of the rail in such a 
 case, is shown on Fig. C, which is the mould for Fig. A. 
 Fig. 5 and i) are found in the same way. 
 
 Take the outstretch of the circle, the exact inside 
 line of the rail, then make the pitch boards correspond 
 to the height of the rail from o, passing round to a, in 
 the platform^. Draw the lines in each case on the out- 
 stretch circle the same as in the plan, and erect per- 
 pendiculars from the outstretch line, as x, x, to cut the 
 chord line, this gives the angles from which to make 
 the easment and the top line of the rail. 
 
 Now as the rail must twist more and raise faster 
 from c to 0 on the left than from o to c, coming up on 
 the right hand side, the moulds for the face of the rail 
 must be got out as on Plates 8 and 11, as the left hand 
 one requires to be an elliptical piece and the right 
 hand one spiral. The spiral piece should be worked 
 from both ends with the bevel taken from the dia- 
 
— 64 — 
 
 gram, and the elliptical piece worked as laid down 
 and described on Plate 8. 
 
 The propriety of this method will be seen at once, 
 as by it, the balusters will be of their proper length, 
 or nearly so, and will overcome a difficulty very often 
 experienced by incompetent workmen. 
 
 PLATE 26. 
 
 Fig. A exhibits an elliptical well hole and the 
 method of obtaining the face mould for the rail by 
 ordinates, which is the best way of getting it. Lay ofiP 
 the square 1, 2, 8, 4 cutting the ellipse into four parts, 
 making a chord line for each, at right angles from 
 which make the plumb lines 1, 2, 3, 4, 5, 6, &c. &c. 
 Make the parallel line a, and space up the last plumb line 
 the number of steps as 1, 2, 3, 4, 6, 6, 7, 8, 9, 10, 
 draw the hypothenuse line, and at right angles, make 
 the distances from the chord line in the plan, draw 
 through these points for the inside line of the rail, and 
 proceed with each piece in the same manner. Let o, 
 in the plan, represent the width of the rail, and plumb 
 up in the manner here shown or guage from the in- 
 side. The bevel to work the twist must be taken from 
 the pitch board or the hypothenuse line on the dia- 
 gram. This face mould may be found also by applying 
 Problem C, Plate B. 
 
— 65 — 
 
 Fig. B exhibits a segment of a larger circle and 
 is the same as on Plate 13, Fig. A. Showing 5 steps 
 in height to be overcome in the quarter circle, the 
 plumb lines below show that all the other distances 
 might be taken as the one in the centre, and that they 
 are at right angles to the chord line. 
 
 This is if any thing easier than the foregoing me- 
 thods, the principle however being precisely the same. 
 
INDEX 
 
 Introduction ^^'^Kes 3- 6 
 
 Explanation of Technical terms " 7 — 10 
 
 Geometrical Problems "II 
 
 Sections of a cylinder "13 
 
 How to make well tubs " 19— 
 
 How to work rail pieces • " 24 — o i 
 
 How to make falling moulds " 25—4.3 
 
 How to bore hand rails "27 
 
 How to make newel posts "28 
 
 How to find the face moulds for spiral rails . . . . " 31-34 
 
 Remarks on the spiral and eUiptical Unes "39 
 
 How to describe one fourth of an ellipse " 41 
 
 How to construct spiral stair carriages "45 
 
 How to make wall strmgs . "47 
 
 How to cut down wall strings ......... "49 
 
 Reasons for adopting these methods ....... "52 
 
 Mathematical demonstrations "58—59 
 
 How to put on a rail where the steps are wrongly placed 
 
 in the platform . " 62-64