*-• 
 
Digitized by the Internet Archive 
 in 2017 with funding from 
 Getty Research Institute 
 
 https://archive.org/details/elementsofhandraOOridd 
 
ELEMENTS OE HANO-RAtUNC. 
 
 DEDICATED TO TIIE 
 
 BY ROBERT RIDDELL. 
 
 SEiDNi EDITION, (REVISED AND IMPROVED. 
 
 PUBLISHED FOB THE AUTHOR. 
 
TO TUB 
 
 CARPENTERS AND JOINERS OF ENGLAND. 
 
 Gentlemen : 
 
 It is a full conviction of your favours, that has prompted mo to dedicate this volume to the 
 British Workmen, and tell the world how much I am indebted, and express the warm emotions of a 
 grateful heart. When without patron or friend, a stranger on your shores, I solicited your attention 
 and patronage to my first publication; both w T ere given with a degree of liberality and generosity, 
 that my deserts can hear no proportion to. The civility and condescension of your manners, being 
 divested of all illiberal sentiments, plainly informed me that local prejudices had no influence over 
 your minds. Thus stimulated and encouraged by your sanction and approval, my work attained a cir¬ 
 culation and notoriety, far beyond my most sanguine expectations. 
 
 Under these circumstances, gratitude becomes a duty, and I should reproach myself with that 
 ingratitude to which I hope long to remain a stranger, were I to omit the acknowledgments of your 
 friendship. But to proceed further in detailing facts would look like adulation; in proceeding I must 
 hurt your feelings, and in desisting must stifle my own,—and as I wish to be grateful, I must be silent. 
 
 To the Architects and Builders of England, I acknowledge myself particularly indebted for their 
 patronage and support. To notice all marks of attention which I received, would be to violate the 
 bounds of prudence, and to make selections, would be invidious and unjust. 
 
 To them and you a second edition is now presented, with such alterations and improvements, as to 
 justify the hope of again being the recipient of your favors. I am perfectly aware that a new 
 edition with improvements, will appear to many a direct injury to the purchasers of the former edition, 
 each copy of which becomes obviously of less value; yet it is equally obvious that even an approxi¬ 
 mation to perfection is only to be obtained by progression. It may be mentioned, that if the first 
 edition of my work had not met with encouragement, the second most certainly would never have 
 appeared. This the author hopes will lead those who have purchased his former work, to patronize 
 this ; as it is only by such means that further progress in either the development of principles or their 
 useful application, can be brought to public notice. 
 
 Workmen have long entertained the impression, that hand-railing, or a knowledge of it, constitutes 
 the summit of the joiners’ art, so that it has been looked upon by many as a separate and distinct 
 branch from carpentry, owing to its seeming intricacy. That this should be the case, is not to be 
 wmndered at, when we reflect upon the means taken by both authors and teachers to elucidate the 
 subject. In this work will be found a principle which will reduce the whole art of hand-railing to the 
 greatest simplicity, so as to make it easily comprehended, and at the same time utterly impossible to 
 be misunderstood by the ordinary carpenter or joiner. 
 
 It may be satisfactory to state that the methods herein laid down, are not theoretical or specu¬ 
 lative, but are such as the author has taught, and workmen are now in the daily habit of success¬ 
 fully applying to practice. 
 
 3, Wellington Street, Goswell Road, London. 
 

 
 
ELEMENTS OF HAND-RAILING. 
 
 PLATE 1. 
 
 No. 1. The circle and its tangent. Simple as this may appear, it is in reality not only the ground-work of 
 hand-railing, but is applicable to various other parts of carpentry. The meaning of the word “ tangent” is simply 
 a straight line touching any part of a circle. For example, let No. 1, be the circle, from A, its centre, draw a 
 line indefinitely, (say through D,) with D for a centre, and A, radius ; make the intersections B C ; from B, 
 draw the tangent, touching the circle at C. Or it may be done by joining A C ; then with a square draw the 
 line C B. 
 
 No. 2 will further illustrate the value of the tangent. Suppose No. 2 to be a circular curb or rib, and it is 
 required to have joints in the direction of A B and A C. Draw the centre line D 2 3 J ; make the tangents on 
 the mould or stufi' at right angles to each joint, the same as 2 2 2 and 3 3 3. The joints are now made with the 
 greatest nicety, without trying or fitting the work on a drawing-board, simply by placing the stock of the square 
 on the end of the joint, and the tangent line 2 2 made to agree with its blade. The wreath of a hand-rail is 
 jointed precisely the same, every joint being made at right angles to its tangent and the surface of the plank. From 
 this it will be seen that the tangent is a most important feature in the constructive principle of hand-railing. 
 
 No. 3 exhibits the semi-circle and semi-ellipse. Enclose the circle by the tangents ABODE. Suppose the 
 circle to be the base of a semi-cylinder, and this cut in the direction of A J; it is evident the section must be a 
 semi-ellipse, and its tangents form the parallelogram or oblong, the same as seen in the diagram,—the line A J 
 may be any angle or pitch. The object is the illustration of the problem, then show its application, so that it is 
 immaterial what pitch is taken. It is very clear that the straight lines or tangents which enclose the semi-ellipse, 
 will stand over those that enclose the semi-circle; a good idea may be given of this, by making the drawing on a 
 piece of card paper; then cut the line A J, so as to make a joint; cut through the line E J, also cut through the 
 upper side and the two ends of the parallelogram ; make a joint of A E: now raise the parts cut perpendicular 
 with the plane of the paper ; make P rest on B, then S will stand over C, and N over D. It would be well for 
 the pupil to try this or any other experiment with card paper, as it conveys more to the mind than words possibly 
 can do. There are a few technical words which we will have to use ; these must be understood: for example, the 
 line A J is termed the major axis, and the short line 0 S the minor axis; these terms will only be applied to 
 the semi-ellipse. Remember, that the minor axis will always be the same as the radius of the given circle. It 
 is presumed that every workman understands how to strike the semi-ellipse, with either the trammel, straight-edge 
 or string; the latter is perfectly correct in principle, and more off-handed than either of the first-named methods: 
 all that is wanted for the operation, is two common pins and a piece of thread, and to find the two focii, or places 
 to fix the pins. 
 
 No. 4 will explain this ; the figure is just the same as that at No. 3. Take S for a centre, and P or N for 
 radius; intersect the major axis at 2 2; fix a common pin in S, also in 2 2 ; fasten a thread around S, carry it 
 rround 2 2, tie the ends, (seen at V;) take out the pin at S, substitute for it a pencil; with one finger on the tie, 
 move the pencil steadily round, keeping the thread tight until the semi-ellipse is complete. This simple and me¬ 
 chanical operation is generally known ; but it must be remarked, that where the well-hole is very large, the thread 
 is not to be depended upon, owing to its stretching; in such cases use the straight-edge, by which points are obtained 
 through which the curve can be easily traced. It may be mentioned, that every wreath is nothing more or less 
 than a portion of the semi-ellipse: this is a very simple affair, and much less complicated than many other parts 
 of carpentry. The jointing of the wreath has always been considered the great difficulty ; we will show that this 
 can be done with as much certainty and accuracy as any joint in carpentry; and that every hand-rail, of what- 
 
4 
 
 ever form, can be finished on the bench. We hold that it is unmechanical, unworkmanlike, to fit or joint the 
 rail on the stairs; but before we come to an explanation of this, the elementary part must first be understood, 
 otherwise it will be impossible to comprehend our meaning; so that the progress of the pupil will depend entirely 
 on a thorough understanding of the two first plates. These are only intended as elementary lessons, yet they con¬ 
 tain most of what is required in the constructive principle of hand-railing. 
 
 No. 5 is in all respects the same as No. 3, with the exception of the width of the rail being given on the 
 ground-plan. Half the width of the rail is set off on each side of the centre line 0, and indicated by R P, the - 
 perpendiculars cutting the pitch line at S S, give the width of the mould. 
 
 No. 6 is the same as No. 5. This shows how the width of any mould may be accurately obtained by a 
 
 proportional; for example: on each side of O, the minor axis, set-off half the width of the rail indicated by P R; 
 
 also on the perpendiculars at A and J, set-off half the width of the rail indicated by 2 2 and 3 3. Lay a straight 
 edge on P 2 and R 2; mark the major axis at S S, by the same method N N is obtained. The width of the 
 mould at its extremities is now the same as No. 5. The minor axis, as has been stated, is in all cases the same 
 as the given ground-plan ; there being two curves here, repeat the method for adjusting the pins, in order to strike 
 them with a string ; take outside S or N in the compasses ; with this distance, and P for centre, intersect the 
 major axis on each side of the minor axis : points are thus found to fix the pins for the outside curve. For the 
 inside, take the distance Y S, and R for a centre; make an intersection on each side of V. Points are now given 
 to fix the pins for striking both the curves. Apply the thread and pencil by the method which has already been 
 stated. 
 
 No. 7 is a perspective view of two blocks cut on the same pitch as that at No. 3. The sides of the blocks 
 
 B C D E, are the same as the sides of the squares at No. 3. This diagram truly represents the tangents which 
 
 enclose the elliptic curve. 
 
 PLATE 2. 
 
 No 1 is a perspective view of the wreath resting on a block which has been cut by the pitch-board; the in¬ 
 tention of this is to show the wreath landing on a level floor, in which case the shank is perfectly square, or in 
 other words, having no spring. It will be noticed that if the slab A B is cut off at right angles to the joint, 
 then the upper part of the wreath must be level with the floor, whilst the shank remains on the same pitch as the 
 stairs. The pupil must understand that no falling moulds are used ; in no case are they wanted, from the fact that 
 every wreath, or rather the stuff, when cut, makes its own easing: this can easily be explained; suppose the slab 
 A B cut off in the way mentioned; it is clear that the corner, or external angle B C, gives the most beautiful 
 curve that can be desired. The thickness of the straight rail on the shank is gauged from the upper surface of 
 the plank, and the slab on the lower side cut off near the springing; but on the upper end, the section of square 
 rail is made in the centre of the plank. This wreath answers equally well for starting, simply by reversing it. 
 
 No. 2 exhibits the wreath-piece cut square through the plank ; this is a great saving in time and stuff—but it 
 must not be supposed for a moment that the plank being cut square through, changes the cylindrical or oblique 
 cut; such is not the case. A glance at the end of the joint No. 2 will explain this. Through the centre of the 
 stuff square over P J again through the centre, draw the pitch 2 3; this will be the centre line, on each side of 
 which set off half the width of the rail; produce these lines to N N, and we have the end view of the oblique cut. 
 It is very plain that N N forms no part of the rail, so that it is useless to cut through more plank than what will 
 square it. The application of the face-mould is easily understood; for example, suppose the upper surface of the wreath- 
 piece to be the mould, and the line P J squared over its edge ; now shift the mould until P stands over 2 ; then the 
 outer edge will be at N. The inner edge having moved to its proper place, a direction is thus given to mark the sur¬ 
 face of the plank for the superfluous wood. The application to the under side is the same ; J is made to stand over 3. 
 It will be noticed throughout this system, that the application of the moulds and their construction, are from centres. 
 
 No. 3. This will clearly illustrate the whole secret of hand-railing, and in such manner that any workman will 
 understand it. All that is required, is simply to find the section of a cube, or a square block, when cut by two pitches. 
 But to speak more plainly, we put the question, what shape is the end of a jack-rafter, when cut by the 
 side bevel, and down bevel ? The proper understanding of this solves all mystery connected with hand-railing. 
 Then the cutting of a square block on two given pitches, and its section, will be the bases from which we shall prove, 
 in the most simple and undisguised manner, rest the whole of this art. The pupil who is really desirous to be 
 acquainted with the true principles of hand-railing, must give his earnest attention to the practical illustration of 
 this simple problem. Let No. 3 be a square piece of stuff or a block of any length, its sides make equal, say 1-| 
 or 2 inches. On two of its sides mark any two unequal pitches, similar to A B C; we must now find on 
 a plain surface, what shape the end of this block will be, when cut by the two pitches already named.- Let 
 C 2, No. 4, equal one side of the block P R, or 3 3 ; draw the perpendiculars C A and 2 0 ; make C B and B A to 
 equal the two pitches on the block; draw A 0 3 parallel with C 2; produce C B cutting at 3 ; also produce A B ; 
 make E 0 equal to 0 A ; observe that 3 is a point determined by producing the lines C B and A 0, (this is mentioned to 
 show the importance of the ordinate.) Then E and 3 are points that give a direction to draw this; from 0 and A, 
 
Troveribfd by R Ric 
 
 bokn, libk. RolwulStr London 
 
draw lines parallel with the ordinate. Through 0, draw F S at right angles to the ordinate ; make F N equal to 
 C A ; join N S ; from N S draw lines at right angles to N S ; make N Y equal to F E; join Y P ; make S T equal 
 to S A ; join T P. Two sides of a parallelogram are now obtained ; complete the other two sides, by drawing V 
 H parallel to P T, and T H parallel with P Y. Now the block No. 3, being cut through ABC, its ends will be 
 parallelograms, or precisely the same shape as the figure just drawn. If the two pieces thus cut are put to¬ 
 gether, so that the pitches are reverse to each other, this will give a good and correct idea of the wreath. On the 
 square ends strike a semi-circle, the radius to equal P R, No. 3, or A 0, No. 4. On the other ends sketch an ellip¬ 
 tic curve similar to that seen at No. 4, of which VTH are its tangents. These, when in position, stand over 
 the tangents S P R, No. 3, and the elliptic curve over the quarter circle. It is presumed that the cutting of 
 the block is sufficiently explained to be understood; if so, the value and importance of the tangents will be clearly 
 seen. The corners on the blocks truly represent these, and also represent the centre of the rail.* A bevel for 
 each of the pitches at No. 4 will be required. 
 
 That for A B is found by taking 2 for a centre, and for a radius, a tangent curve to the produced line A B, 
 cutting at E; join E C ; in the angle is the bevel. That for the pitch C B, is found by taking 0 for centre, 
 and for a radius a tangent curve to B 3, cutting at J; join J A ; in the angle is the bevel. The truth of these 
 bevels can be tested by the block, when cut. To make our meaning fully understood, take a piece of card paper ; 
 on this make a drawing similar to No. 4; cut through the line 0 P; also cut through the lines P Y II T S; then 
 cut lightly into the lines S P and S 0, so as to make a hinge, or joint. Now turn up the parts cut on 
 the base S 0; make T rest on A. Then will T P stand over A 0, and P Y over 0 E. The surface of the paper 
 wfill represent the surface of the plank on the two pitches, the same as the block. The use of the bevels will 
 also be seen. Remember that the line S P N is in all cases the major axis. This completes the problem which, 
 we have already stated, embodies the whole art of hand-railing; and it only remains to put it to a practical use, 
 by drawing the face-mould, for which take a thin board, lay its edge on the line S P N; these square over its 
 edge and surface. No. 5 shows the board with the parallelogram, formed the same as No. 4. Let S P W be a 
 gauge line any distance from the edge of the board, so that the shank will be sufficiently long ; this represents the 
 major axis, the same as S P N, No. 4. Make S A and W C, equal to A S and F E, No. 4; from P draw 
 through A and C ; draw C B parallel to P A, and B A produced parallel with P C. (This is but a repetition of the 
 figure drawn at No. 4.) Find the proportions of the mould, by making P R equal to C 2, No. 4 ; on each side 
 of R, set off half the width of the rail, indicated by Y. D ; on each side of A and C, set off half the width of 
 the rail indicated by 2 3 and e J ; lay a straight-edge on D and 2 ; mark N ; again on Y and 3 ; mark Y ; 
 then Y N are points which determine the width of the shank. This draw parallel with A B ; lay the 
 straight-edge on D J ; mark 6; again on Y E ; mark 4. The outside curve, if drawn, will touch 6 D N, and the 
 inside curve touch 4 V Y. 
 
 The proportions of every mould throughout the work are found by this method, and in order to avoid repeti¬ 
 tion, it must be understood. No. 7 shows the mould drawn. 
 
 • 
 
 No. 6 is in all respects the same as No. 4, with the single exception of the ordinate, which is drawn down 
 instead of up. The angle F N P S, is the same as F N P S, No. 4. This plan will be found very convenient, from 
 the fact that the drawing can be made on a much less board. Half the semi-ellipse is found, by producing the 
 quarter circle to cut the base line at Y. On each side of Y, set off’ half the width of the rail, which draw 
 parallel with the ordinate, to cut at 3 and J; then 3 and J are the width of the mould on the major axis; or in 
 other words, this gives a distance by which the focii are obtained for striking the semi-ellipse. Perhaps No. 7 will 
 better explain this, where the letters on the major axis, are the same as those on No 6. It will be noticed that 
 the face-mould is simply a portion of a semi-ellipse, the length of which has been obtained at No. 6. The stu¬ 
 dent is requested to make himself perfectly conversant with this, as nearly all the moulds in the book are drawn 
 on the same principle. 
 
 * This problem being the very basis of hand-railing, the pupil cannot do better, than to provide himself with a saw, and a block, 
 this may be of any length or size ; the sides make equal and the angles square, with this practise, by drawing pitches on two of its 
 sides in any direction; then find the section which the ends make, by the method shown at No. 4 ; prove it to be so by cutting the block, 
 and if an error or mistake is detected, try again, and again, until correctness is attained ; next find the bevels, prove these to be cor¬ 
 rect by the block. When this very simple and common-sense affair is mastered, the pupil may proceed with confidence and boldness 
 to draw the face-mould for any wreath. 
 
G 
 
 PLATE 3. 
 
 No. 1 is the ground-plan of a half pace or continued staircase; the elevation of the strings, landing and start¬ 
 ing are given, in order to show their connection with the trimmer that forms the face of the landing. 
 
 No. 2 exhibits the cylinder, and B B indicates the plank for the strings, which answers the double purpose of 
 string and carriage. 
 
 PLATE 4. 
 
 No. 1 is the ground-plan of a staircase with quarter-circles at the landing. The elevation of the strings 
 show their connection with the trimmer. The position of the last riser-landing, and the first riser-starting, re¬ 
 gulates the height of the level rail, yet the quarter-circle need not be limited to any particular radius, as it in no 
 way affects the position of the risers. At No. 4, the end view of the rail is seen, its lower side resting on the 
 corners of the steps ; the thickness of the level and raking rail indicated by A and B; the perpendiculars, 
 cutting at 2 2, show the centre of the rail and springing. This will also be the length of the face-mould, as 
 seen at No. 2, where 2 2 is the same. Make 2 3 equal to the radius on the ground-plan. On each side of 2, set 
 off half the width of the rail; draw the shank parallel with 2 2 ; find the width of the mould at 3, by the method 
 already given; draw the straight wood for the level rail, parallel with 2 3. The mould may be struck with either 
 the trammel or thread. 
 
 No. 3 is the section of the level rail, the plank cut square through; No 5 is the plan of the cylinders; B B 
 shows the string and carriage; A is the plank for the level string. It will be remembered that the same explanation 
 given for the wreath on Plate 2, Nos. 1 and 2, applies here also. 
 
TRIMMER 
 

TRIMMER 
 

 
 
 
 

 C 'foi, r !777.I Sir — -..dor- 
 
 R RidoL&lZ 
 
7 
 
 PLATE 5. 
 
 No. 1 is the ground-plan of a half-pace staircase ; the centre line of the rail given, and the fronts of the 
 risers in a position that will give the best effect to the rail and string. It would be difficult to fix upon any posi¬ 
 tive rule for the position of the risers, as they are depending on none; yet the author in his practice has adopted 
 the method laid down, which is to take half a step in the compasses, with this and 2 for a centre, intersect the 
 centre line at 3 3, from which draw the face of the risers, then set off the others. But in case the well-hole be 
 small, or so that the development of the circle equals a tread, the fronts of the risers and the springing will bo 
 on a line ; however, this we leave to the workman, to exercise his own judgment. 
 
 It will be noticed on the ground-plan, that 4 and 6 indicate the fronts of the risers ; and the height between 
 these is three risers ; or from 4 to the centre 2, is one riser and a half. This will be the height to set up for 
 the construction of the face-mould, which is found at No. 2, by drawing a base line, say II B V; make B Y 
 equal to L 2 ; draw the perpendiculars. From B set up to e, one riser and a half; draw e N parallel to B Y ; 
 with the pitch-board, draw HRN; from e, draw through the intersection at T; make 0 P equal to 0 e; draw 
 the ordinate P N 3 ; from 0 and e, draw lines parallel with it; through 0, draw J 2 indefinitely, and at right 
 angles to P N; make J 3 equal to II e or S 0 ; join 3 2; produce this line in order to find the length of the semi¬ 
 ellipse, which is obtained by producing the quarter-circle to cut the base at W ; on each side of W, set off half 
 the width of the rail (on the base); this draw parallel with P N, cutting the major axis at E and F. The face 
 mould is now easily found. 
 
 Let No. 3 be the board from which it is to be cut. The line P S 2, is the major axis, the same as 3 A 2, 
 No. 2. Square over P J, S 0, 2 e; make P J equal to P J, No. 2, and S 0 equal to L 2, No. 1, and 2 e equal 
 to e 2, No. 2; from S draw through J and e; draw H J T parallel with S e, and e II parallel to S J. 
 The tangents are now given ; these must be proved correct, for example, H J equals R T, No. 2, and II e 
 must equal e T. Complete the mould, by setting off half the width of the rail on each side of 0. Find the width 
 of the mould at J and e, (the method for this has been given in Plate 2); draw the shank parallel with J T; this 
 may be any length desired. At No. 2, take A F in the compasses ; with this distance, at No. 3, make 3 a centre, 
 and intersect the major axis on each side of S; points are thus given to fix the pins for striking the inside curve. 
 Take the outside of the rail on the minor axis for a centre, and intersect the major axis with a radius equal to 
 A E, No. 2 ; fix the pins, and strike the outside curve. 
 
 Make the centre joint e at right angles to e II; make the joint on the shank at right angles to T J; cut 
 out the mould and dress it to the lines. On the end of each joint square over the tangents; mark these on the 
 under side, the same as on the upper side. 
 
 The application of the mould. Lay it on the .plank; mark by the edges ; then cut the plank square through; 
 face one side truly: No. 4 shows the piece cut, its thickness the same as the width of the rail; lay the mould on again, 
 and mark each joint; but before moving it, mark the piece so as to draw the tangents T II and J e on the face 
 of the stuff, the same as on the mould ; then make the joints truly, and at right angles to the face of the plank, also at 
 right angles to the tangents on the stuff: this may be done to a great nicety, by a proper application of the 
 square; for example, take the centre joint, place the stock of the square on its end, make the blade agree with 
 the tangent e J. For the other direction, make the blade of the square and the surface of the stuff to agree ; thus 
 the butt-joint is at right angles to both the tangent and surface of the plank. All the joints are made in this 
 manner. 
 
 On the end of each joint, square over the tangent lines T and e, make 0 in the centre of the stuff. The bevel 
 for the centre joint is found at No. 2. Take S for a centre; and for radius, a tangent curve to the produced line 
 e T; draw the circle to cut at K; join K R; in the angle is the bevel: with this, mark 3 3 on the end of the joint 
 No. 4. Square over 3 4; also square over the under side from 3. The spring-bevel for the joint on the shank is 
 found at No. 2 ; take 0 for a centre, and for a radius, a tangent curve to T N; draw the circle to cut at D; join 
 D e; in the angle the bevel is seen. With this mark the line 2 2 on the joint of the shank ; observe that 0 is 
 the centre of the stuff, through which the bevel lines are made ; with the square on the end of the joint, draw the 
 line 2 4; on the under side from 2 draw a similar line ; mark the square section of the rail on each joint, or in 
 other words, on each side of the bevel lines set off half the width of the rail, and from the centre 0, set oil' half 
 its thickness; P and S on the shank is half the width of the rail; from the joint, square up the line P P. The 
 application of the mould No. 3, is now very simple. Lay it on the piece, make the tangent II J T to agree with the tan¬ 
 gent 2 4; and H e to agree with 3 4 ; the outside edge will be on P P; now mark by the edge of the mould as 
 much of the plank as it covers ; mark the under side in the same manner ; cut off the slab P P at right 
 angles to the joint; also to the spring bevel P S; make 0 S at right angles with 2 2 ; from S, the end of the 
 joint, square up a line on the side of the wreath; on this mark a distance to equal J T No. 3 ; through 
 which mark the springing-line by the pitch-board. Cut off the superfluous wood ; in doing this, hold the plane or 
 saw in the same direction as the springing-line; or if the mould be tacked on, then its edge and the line marked 
 on the surface of the stuff is a perfect guide, in fact it is just the same as the oblique cut, because the edge of the 
 mould represents the plank. * 
 
 A guide is now required for the thickness, as it is understood that no falling moulds are used ; lay the mould 
 No. 3 on No. 4, and make e and e agree; also make T and T agree; then square over 6 G on both edges of the 
 wreath; on these mark the centre of the plank; on each side of which set off half the thickness of the rail; cut off 
 the slab on one side of the wreath, through the points indicating half the thickness of the rail; run on a gauge-line 
 for the thickness, and take the slab off the other side; remember, in putting the wreath together, that the line 3 3 
 
8 
 
 on each joint will be opposite, so that the two shants will he on their proper pitches. In order to avoid renetitioi 
 the application of the mould to the wreath-piece is the same in every case. As a general rule the plank for the 
 
 stuff re^hed ^ “ ““ ° f * he rail; th ° •* once shoLS Ihickn^f 
 
 It may be mentioned, that no parallel mould will produce a cylindrical line on the wreath-piece vet such 
 
 k.; 
 
 .A 
 
 PLATE 6. 
 
 « 
 
 No. 1 exhibits the plan of the stairs, starting from a level floor : the centre line of the rail given 
 Ihe face of the first riser commences at C. No. 2 is the elevation of the ramp-landing; No 3 shows the 
 level floor, w! h the tangents unfolded: that is to say, the distance between 2 and 8 is equal to four times A B, 
 ^ r °* !; 1 -f 1 ne p E B A 2, shows the centre of the rail and the centre of the plank, or the exact pitches of the 
 
 wreath as it stands over the plan. A mere examination of the plate clearly shows, that by simply Enfolding the 
 tangents on a plain surface,, and making the elevation of a step and riser, we have an unerring g P u fde for drawing 
 the centre of the rail, by which the heights are ascertained with the greatest nicety, so that it fs almost impossibffi 
 to make a mistake in the construction of any part of the wreath. The face mould No. 4 is found the samj as the 
 
 Ihfflno^ Sh ° rt e * planatl01 j for this > wdl be efficient. At No. 2, the centre of the level rail is raised above 
 t e flooi half a nsei this may be more or less, as circumstances require, but as a general rule, the under side 
 
 suit thelevll Tan d d e ing. f a nSer ^ ^ thlS 18 d ° ne in ° rder t0 W the lon S balusters on the steps, to 
 
 At No. 3, it must be observed that 2 2 and 8 C are the springing lines. Make 2 2 equal with 2 2 No 0 
 Draw - A parallel with the floor ; draw the under of the rail to rest on the corners of the steps indicated bv 'the 
 pitch-boaril; set off half its thickness, which draw parallel with the under side, to cut at Ejoin E A ^Tlm 
 clotted lines from 0 and B, cutting 3 and 4, give the height of the face-mould for the upper part of the wreath 
 ith the pitch-board, draw 3 6; from 4, draw through the intersection at S; make 0 5 equal to 0 4 • draw 
 the ordinate 5 b B; from 0 and 4, draw lines parallel with it; through 0, draw A D at right angles to A 5 • 
 make A B equal to 3 4; join B D. This line, we have already stated, is in all cases the major axis § From this * 
 the mould is easily obtained, without further drawing. Suppose B V D the edge of the bird from which the ? 
 mould is to be cut. Mark its edge at B V D; square these over on the face ; make B C to equal A 5 • make D 
 E to equal D 4; from V, draw through C and E; draw C II parallel with V E, and E ^parallel w “h Y C 
 These lines on the mould to be correct, C H must equal C E, No. 3, and H E must equal E B. Make Y J on 
 the minor axis equal to 0 4 ; on each side of J, set off half the width of the rail; draw the mould as usual and 
 make the joints on it at right angles to the tangents. The bevels are found the same as in Plate 5. That for 
 e centre joint E, w the angle 5 P 3; and that for the joint N, on the shank, is in the angle R0 4. It has 
 been mentioned, that in drawing the face-mould, that if a gauge-line is made on the face of the board to represent 
 the major axis, it will be found more convenient for striking the elliptic curves than working from the edge. 
 
 -vr o N °- 5 , ^® mould 1 fo A 1 * that part of the wreath which starts from the level floor; make A B to equa^l A B 
 
 ^mdd ^ d r B h C i eqU ^ A ?’ 0r j each Slde of A » set off half the width of the rail; find the width of the 
 
 mould at C, by the principle which has been given; add the straight wood for the shank: the bevel for this is 
 seen in the angle at No. 3; on the joint A, square over the tangent. This line, and the bevel line on the centre 
 
 near the movddNo !< 5 C ’ ^ ^ ° PP ° Slte wlien tbe wreath is in its position. The compasses will strike sufficiently 
 
* U- . 
 

 
 
 
 
 
 
 •% 
 
 
 
 
 
 
 
 
 
 
 
PITCH 30ARO 
 
 PI TCH 
 
 
 
 
 3 
 
 \ 
 
 * 
 
 - : ;Xi 
 
 - j__ 
 
 4 
 
 ■ 2 . 
 
 j — ^ 
 
9 
 
 PLAT E 7. 
 
 No 1 is the ground-plan for a rectangular staircase ; the risers are placed in such a position, that the shanks 
 of the 'wreath will be on the same pitch as that of the stairs; the centre line of the rail given: produce this, to 
 intersect at 2 ; make 2 3 and 2 4 equal to half a step ; from 3 and 4 draw the fronts of the risers, which form 
 the landing; set off the other risers ; draw the quarter-circle ; lay the rise of the pitch-board on the tangent 2 4 
 P; draw OP; let No. 2 be the board for the face-mould; any distance from its edge, make.a gauge line, say 
 T V; square over the line 0 N; make this to equal 0 3, No. 1 ; bisect 0 N at J; through J, draw H P parallel 
 with T Y. 
 
 At No. 1, take 0 P in the compasses ; with this distance take N, No. 2, for a centre ; intersect the line through 
 J, at H and P; from N, draw through H and P ; also from 0, the centre, draw through H and P ; make 0 3 
 equal to 0 3, No. 1; on each side of 3, set off half the width of the rail; find the width of the shanks at H and 
 P, by the methods which have been given ; the straight wood draw parallel with N P and N II; make the joints 
 A B at right angles to the tangents ; then with a trammel or straight-edge, strike the mould ; the shanks may be 
 any length desired; both pitches being alike, one bevel answers. This is found at No. 1 : take 4 for a centre, and 
 for radius, a tangent curve to P 0 ; draw to cut at R ; join R 0 ; and in the angle is the bevel. Mark the plank 
 and cut it square through ; face one side ; lay the mould on the stuff; mark the joints and tangents on its surface ; 
 make the joints, and apply the bevel by the principle already stated. 
 
 No. 3 exhibits the plan of a staircase, where the risers are placed without rule, method, or order. This is 
 purposely done to show, that it matters not what the position or plan may be ; we are guided by one unchange¬ 
 able principle, which has been given in the elementary lessons of this work, so that the plan before us presents 
 little or no difficulty in finding the face-mould. 
 
 At No. 3, it will be noticed that 2 and 6 are the faces of the risers, forming the landing; so that in a case 
 of this kind, it will be best to have the shanks of the wreath the same pitch as the stairs ; to do this a joint must 
 be made in the circle, say at 4 ; this being in the centre, one face-mould will answer for both pieces of the wreath; 
 through 4 draw the tangent at right angles to the joint, cutting 3 5 ; these tangents are unfolded at No. 4; the 
 figures 2 3 4 5 6 are the same as those on the ground-plan. Let 6 P be the first riser, starting from the landing ; 
 Avith the pitch-board draw the step and riser; below 2 draw a step and riser; from 3 4 5 draw perpendiculars ; 
 produce the upper pitch to cut at S, and the lower pitch to cut at II; join IT S ; then 8 is the centre joint. We 
 have now the elevation of the landing, and the steps which connect with it; also the pitch of the plank and rail 
 is given. 
 
 At No. 3, make 6 8 equal to 4 8, No. 4; with the pitch-board (the rise on 6 8,) draw 8 P; from P through 
 4 draw the ordinate ; from 5 and 6 draw lines parallel with P 4 ; draw V A at right angles to 6 E ; make E C 
 equal to 6 8; join C A; produce this line; from V, the centre, draw parallel to E C, cutting at D ; then is 
 D the centre of the semi-ellipse. At No. 5, draw the major axis, A B C D. The letters and distances are the 
 same as those at No. 3. From the letters on the major axis, square over the lines ; make A 4 equal to A 4, No. 
 3; make B S equal to S 5 ; make C P equal E 6, and D R equal to V 6 (the radius ;) join 4 S and S P ; this pro¬ 
 duce. We have now the tangents through the centre of the mould; these, to be correct, must equal those on the 
 elevation No. 4: for example, 4 S equals 8 S, and S P equals S P. On each side of R, set off half the 
 width of the rail; from D, the centre, draw a line through P ; find the width of the mould at P and 4 ; draw the 
 shank parallel with P S ; now strike the mould as previously stated ; make the joints at E and 4 at right angles 
 to the tangents. To find the bevels, observe at No. 3 that the line from C is drawn at right angles to C D, cut¬ 
 ting the line V D; take this distance and set it off from C to V, No. 5; then draw D J parallel with P S, and 
 D T parallel with S 4. With C for a centre, and for a radius, a tangent curve to 1) T, draw the circle to cut 
 c ; join o V ; in the angle is the bevel for the joint 4. The spring bevel for the shank : take centre C, and a tangent 
 radius to J 1) ; draw the circle to cut at N ; join N V ; in the angle is the bevel required. Cut the stuff square 
 through; make the joints at right angles to its surface, also at right angles to the tangents. 
 
 
10 
 
 PLAT E 8. 
 
 No. 1 is the ground-plan of a staircase, with winders round the quarter-circle ; the centre line of the rail 
 given; the upper part of the wreath to form its own ramp. Draw the tangents 2 3 4; these unfold atNo. 2, and which 
 AB4 represent; the perpendiculars from A and 4, indicate the springing lines, between which, make the ele¬ 
 vation of the winders and risers the same as they are on the tangent lines of the ground-plan. Take the pitch- 
 board, and draw a flyer on the upper and lower part of the elevation ; let the under side of the rail rest on the 
 corners of the flyers ; set off half its thickness; this is indicated on the upper part by 6 4 3, and on the lower 
 part by J N: it will be noticed that the upper pitch stops at 3, which is the angle of the tangents and the same 
 as on the ground-plan, so that here the plank must turn over, that is to say its surface must make two pitches, 
 one in the direction of 3 4 6, and the other 3 2. It may also be mentioned that 3 is a fixed point. The next 
 pitch from 3 is over the winders, so that to draw this is a matter easily determined : for example, the elevation 
 before us, shows that if the line through 2 were drawn below 2, the wreath at this part would approach 
 nearer the winders and shorten the ramp; if raised above 2, an opposite result must follow, so that we assume 
 for the pitch, 3 2 N ; this of course is entirely discretionary, and must be left to the judgment of the workman ; 
 yet the situation of the winders on the plan and elevation, may be considered a sufficient guide to draw it. 
 
 No. 3 is the construction for the face-mould. Let 2 3 equal 2 3, No. 1, and 2 A equal 2 A, No. 2 ; pro¬ 
 duce the line A P ; lay the rise of the pitch-board on the line P 3, and draw the pitch A B indefinitely ; from 
 
 2, draw through B, cutting the produced line A P ; make P V equal to P A ; from the intersection of the pro¬ 
 duced lines 2 B and A P, draw the ordinate through Y indefinitely; from P and A, draw lines parallel with the 
 ordinate; through P, draw 11 N at right angles with the ordinate ; make II J equal to 3 P ; join J N ; this is 
 the pitch, also the major axis. It will be noticed that we have drawn the ordinate down, which produces the 
 same result as if drawn up. Let No. 4 be the board for the face-mould, and the line JON the major 
 axis, the same as J 0 N, No. 3; square over the lines on the face of the board ; make J 2 equal with R Y, No. 
 
 3, and N 4 equal N A ; from 0, the centre of trammel, draw through 4 and 2; draw 4 3 parallel with 0 2, 
 and 2 3 parallel with 0 4 ; produce the lines 3 4 and 3 2. The tangents on the mould are now complete, and 
 their accuracy proved by 3 4 being equal to 3 4, No. 2, and 3 2 equals 3 2, No. 2. On the minor axis, set 
 off a distance to equal 3 4, No 1; on each side of this set off half the width of the rail; find the width of the 
 shank at 4, also at 2 ; draw the straight wood parallel with the tangents ; make 2 H equal with 2 H, No. 2 ; the 
 shank 4 P may be any length desired: the bevel for this is found at No. 3; let 3 be a centre, and for a radius, 
 a tangent to A B produced; draw the circle to cut at T; join T 2 ; in the angle is the bevel required. The bevel 
 for the joint H. Take P for a centre, and for a radius, a tangent curve to the produced line 2 B ; draw the 
 circle to cut at S ; join S A ; in the angle is seen the bevel. The mould draw as usual. The application and 
 every thing else connected with this plate, is in all respects the same as that which has been stated. It may be 
 noticed, that the length of the balusters can be obtained to a great nicety, from the fact that the centre of the 
 rail and the elevation of the winders present at one view the length of each baluster. The lower ramp: mark 
 the line H N on its side, and make the joint at right angles to this. 
 
 * 
 
PL. 8. 
 
11 
 
 PLATE 9. 
 
 « 
 
 No. 1 exhibits the ground-plan of a staircase, with winders round the semi-circle, the centre-line of the rail 
 given. On the plan it will be noticed that the winders commence at the springing. In large well-holes, no objec¬ 
 tion can be made to this, especially when the ends of the winders are equal or nearly so to those of the flyers. 
 In such cases the rail over the winders and flyers is made the same height; but in small well-holes a few of the 
 winders should be made to pass the springing, increasing their width at the ends, so that when the rail and string 
 are in position, both will present to the eye and hand a gentle and easy curve. The pupil will remember that 
 the wreath over winders, in small wells, must be raised a sufficient height, in order to afford a proper protection 
 against accident. 
 
 At No. 1 enclose the semi-circle by tangents; these unfold at No. 2; that is to say, make 2 3 4 5 6 to equal 
 the same numbers as those on the ground-plan; draw the dotted perpendiculars, then the lines from 2 and 6 will 
 represent the springing ; inside of these make the elevation of the winders the same as those on the tangent lines 
 of the ground-plan ; on the upper and lower part of this, set off one or two of the flyers indicated by the pitch- 
 boards ; draw the common pitch; from this set off half the thickness of the rail, which draw the upper part to 
 cut at E, so that E is a fixed point on which the plank turns to make the next pitch ; this may be either raised or 
 lowered, that is, from E to the ramp ; then assume E V W P Y to be the pitch. On each side of Y H set 
 off half the thickness of the rail, and form the ramp, the line 2 P being the springing; below this make the 
 joint on the ramp at right angles to H Y; the pitch over the winders has given the height for the upper part of 
 the wreath, its centre-joint being at V, so that by producing the dotted line through this, and drawing a line from 
 F, at right angles to the springing, intersecting at 5, we have the exact height, which is Y 5. At No. 3, is the 
 construction for the face-mould; make 5 6 equal to 5 6 on the plan, and 5 V equal to V 5 on the elevation : pro¬ 
 duce Y P 8 ; lay the rise of the pitch-board on the line 6 P, and draw the pitch V J indefinitely; from 5 draw 
 through J, cutting at 8; make P S to equal P Y; from 8, draw the ordinate through S ; from P and V, draw 
 lines parallel with 8 S ; through P, draw R A at right angles to 8 S ; make R B equal to 5 V ; join A B ; then is 
 A 0 B, the major axis. Let No. 4 be the board for the face-mould, and the line A 0 B the major axis, the same 
 as A 0 B, No. 3; square over the lines on its face, and make B F to equal Y A, No. 3, and A V to equal R S; from 
 0, (centre of the trammel,) draw lines through F and Y; then draw E V parallel with 0 F ; also draw F E parallel 
 with 0 V; produce E F for the shank : this completes the tangents on the mould, the correctness of which are 
 proved by F E Y being equal to F E V on the elevation; make 0 3 to equal K 6 on the ground-plan; on each 
 side of 3, set off half the width of the rail; find the width of the mould for the shank, also at the centre-joint, then 
 strike it as usual; make the joints at right angles to the tangents ; the bevels for these are found at No. 3. That for 
 the shank: take 6 for a centre, and for a radius, a tangent curve to the produced line V J, cutting below S; from 
 which draw to 5, and in the angle is the bevel required. 
 
 The bevel for the centre joint Y (on the mould,) is found by taking P for a centre, and for a radius, a tangent 
 curve to J 8, cutting at E ; join E V; in the angle is the bevel. 
 
 To find the face mould for the lower part of the wreath: let No. 5 be the board for this. On its face square 
 over’aline, then any distance from its edge make a gauge-line for the major axis; let 0 be its centre ; make 0 W equal 
 to K 5, on the ground-plan ; bisect 0 W in N ; through this, draw P V parallel with the major axis. At No. 2, 
 take W Y in the compasses; with this distance, take W, No. 5, for a centre, and intersect the line through N at 
 V and P; from W, draw lines through V and P ; make 0 2 equal to K 6 on the ground-plan; on each side of 2, 
 set off half the width of the rail; draw the mould as usual; make P H equal to P II, No. 2 ; make the joints at 
 right angles to the tangents ; one bevel answers for both joints; this is found at No. 2, by drawing W Y parallel 
 with 3 4; take Y for a centre, and for a radius, a tangent curve to W V, to cut at D; join D W; and in the angle 
 is the bevel required. 
 
12 
 
 PLATE 10. 
 
 No. 1 exhibits the ground-plan of a staircase with winders in the quarter circle ; the centre line of rail 
 given ; it is required to have a joint in the wreath, the upper part to form its own ramp. 
 
 It will be recollected that we have already given a plan similar to this, but there the wreath and upper ramp 
 were in one piece, so that this plate will embody a principle by which the wreath can be made in any number of 
 pieces or joints. 
 
 Let No. 1 be the plan, and the joint at 6 ; through 6, draw the tangent K Y at right angles to the joint; the 
 quarter-circle is now enclosed by the tangents J K 6 Y 3. At No. 3, unfold these as usual; then make the eleva¬ 
 tion of the winders, and a square step at the upper and lower part. Draw the centre of the rail on the common 
 pitch, cutting at T ; remember, T is a fixed point. From T draw the pitch, cutting say S. Form the ramp ; make 
 its joint below the springing line W. Nowthe line through 2, cuttingat e, gives the height for the upper part of the 
 wreath. Then at No 1, make 3 e equal with 2 e, No. 3; take the pitch-board, with the rise on e 3, and draw the 
 pitch e II; from R, draw the ordinate through the centre of the joint; from Y and 3, draw lines parallel to this ; 
 from 0, the centre, draw a line at right angles with the ordinate; make h N, No. 2, equal to 3 e; join N C; 
 through 0, draw the major axis parallel with N C ; from 0, draw the minor axis at right angles to it; make 
 0 5 to equal to 0 J ; draw P T and Y 4 parallel with 0 5; at the intersection of the line from R, and the major axis, 
 draw a line parallel with 0 5; let the intersection and 2 equal C 6; make P T to equal W Y, and Y 4 to equal h 3; 
 join 2 T; from T draw through 4. This completes the tangents on the mould, and their proof is, that 4 T 2 
 equals 4 T 2, No. 3 ; from 0, draw a line through 4 ; on each side of 5, set off half the width of the rail. Find 
 the width of the shank: this draw parallel with 4 6 ; now strike the mould, and make the joints 2 and 6 at right 
 angles to the tangents. The bevels and their application have already been given. 
 
 No. 4 is the mould for the lower part of the wreath. Draw any line for the major axis; square over a line 
 for the minor; let 0 be the centre; strike the circle B S B, with the same radius as 0 J, No. 1; make the 
 chord B B equal to J 6, No. 1--; make the tangents J B B the same length as J K 6, No. 1; at No. 3, take J 2 
 in the compasses ; with this, and J, No 4, for centre, intersect the chord at W and 2 ; from J, draw a line through 
 W and 2, on each side of S; set off half the width of the rail; find the width of mould; draw the shank parallel to 
 W J ; make W V equal to W Y, No. 3; make the joints at right angles to the tangents. 
 
 The bevel for the joints is found by drawing the line 0 B 3; then, with J 2 for radius, and centre J, draw 
 the'circle to cut at 3 ; join 3 J ; take B for centre,^and for radius, a tangent circle to 3 J, cutting at P ; join P 0 ; and 
 in the angle is the bevel required for each joint. For striking this mould, a straight edge will be most convenient. 
 With this, any number of points may be given through which to trace the curve. 
 
 The face-moulds are now complete. It may be remarked in relation to this plate, that the principle given 
 for finding the face-moulds is such that can readily be applied to every position of hand-railing ; and we may add 
 that the elevation of the winders and centre line of the rail in this or any other case, at once gives the exact 
 length of the balusters. For example, suppose the under side of the rail drawn at No. 3, and the dotted line 
 cutting the joint 2, to be the centre of a baluster; also the riser line at 4, the centre of a short baluster. Then 
 it is clear that the distance between the top of the winder below 2, and the under side of the rail added to the 
 given length of the short baluster, is the required length. This is self-evident, for the reason that when the rail 
 is in its place, it retains the same position as it does in the elevation. 
 

 
 
 
 
 
 
 
 
 
PL. ||. 
 
PLATE 11. 
 
 No. 1 is the ground-plan of a staircase-landing, on a level floor, the centre line of rail given, the semi-circle 
 enclosed by the tangents H P R D E, These are unfolded at No. 2, indicated by the same letters, HP RDE. 
 It may be well to state that the elevation of the winders, flyers, and tangents, can be laid out on a narrow board, 
 by the same principle as that for a string; a glance at No. 2, will show this. There the winders, and one or two 
 of the flyers are given, the measurement of which is the same as those on the ground-plan. The dotted lines 
 from II and E indicate the springing. Make the under side of level rail, say, half a rise above the floor; set 
 off half its thickness; this draw to cut at D; at the lower part, let the under side of the rail rest on the common 
 pitch; set off half its thickness; this draw indefinitely : now D, as usual, is a fixed point, from which draw a line 
 to cut, say W, (remember that the rail from D may be raised or lowered as the judgment of the workman may think 
 proper); draw the ramp, and make the joint below the springing. The face moulds for this are extremely simple. 
 That for the upper part of the wreath is found at No. 3, by drawing a line for the major' axis, and squaring over 
 a line for the minor axis ; then make C D equal to C D, No. 2, and D E equal to D E No. 2 ; on each side of C, 
 set off half the width of the rail; find the width of the shank, to which add three or four inches of straight wood; 
 strike the mould as usual: one bevel will only be required; this is seen in the angle 4. 
 
 No. 5 shows the stuff cut square through and to a parallel width. The tangents DCS are the same as on 
 the mould ; the joints are made at right angles to these. The line 3 3 is made by the bevel 4 ; and on the centre 
 joint, the^line C 2 is made by a square. At No. 4 is the face-mould for the lower part of the wreath. The major 
 and mttfcr axes given : make 0 P equal to 0 P, No. 1; bisect 0 P, through which draw N K parallel with the major 
 axis, i At No. 2, take B C or B A in the compasses, with this and P, No. 4, for a centre, make an intersection at 
 N anu K ; from P draw through N and K; make 0 R equal 0 R, No. 1; on each side of R set off half the width 
 of the rail; find the width of the mould at each end; draw the shank parallel to P N ; make N V equal to A G, 
 No. 2 •,( draw the joints at right angles to the tangents; the mould strike as usual: one bevel answers for each 
 joint. This is found at No. 2, by drawing B L parallel with II P; take L for centre, and for a radius a tangent 
 curve to A B; draw the circle to cut at Y; join Y B; and in the angle is the bevel required. When the slab is 
 cut off the outside of the shank, the bevel 4 will give the springing line. 
 
 It must have been noticed in the letter-press description, that there is a sameness or similarity, so that the 
 illustration*of the two first plates nearly answers for all the rest. This clearly demonstrates the excellency of a 
 system that has for its basis simplicity and truth; but above all, its perfect adaptation to every possible position 
 of har^d-railing. 
 
 
 V 
 
14 
 
 PLATE 12. 
 
 No. 1 exhibits the plan of stairs starting with scroll winders and flyers, the centre line of rail given. The 
 tangents 1 2 3 4 5 enclose two quarter-circles of unequal radius. The joints made at 3 and 5, No. 2, exhibit the 
 tangents unfolded the same as those on the plan. Make the elevation of the winders and one flyer the same as on 
 the tangent lines of No. 1; let the under side of the rail rest on the pitch-board; set off half its thickness; this 
 draw to cut at K : draw the under side of the scroll, say three inches above the curtail step, (the line 1 2, &c., indi¬ 
 cates this:) set off half the thickness of the rail; then draw the next pitch cutting the perpendicular, say at J: 
 in relation to this pitch it has already been mentioned that the situation of the winders in the elevation is a suffi¬ 
 cient direction to draw it, yet some little judgment is required; for example, the joint A shows a part of the 
 easing in the eye of the scroll, but if desired, this can be made perfectly level, simply by drawing from J, a 
 line parallel with the curtail; but this would not have so good an effect, beside, the eye of the scroll would be 
 too high. To ascertain this height, add the distance between the curtail step and under side of the scroll to 
 the length of the front or short baluster. 
 
 These remarks are made to show the workman his complete control over the pitches and heights, but this 
 is a matter entirely of taste; not affecting the principle in any way. Draw J A; through A, make the joint at 
 right angles to A J. Then the height for the lower part of the wreath is A B, and the height for the upper part 
 F E. To describe in full the method for drawing the face-moulds and finding the bevels, would be a useless repeti¬ 
 tion of words that have already been gone over, so that a brief description will be sufficient. At No. 3, make H 
 D equal to F E, No. 4 ; with the pitch-board, draw D E produced; from H draw through E, cutting the produced line 
 D 0 ; make 0 6 equal to 0 D ; draw the ordinate through 6 ; from 0 and D, draw lines parallel with it; through 0, 
 draw 5 2 at right angles with the ordinate; make 5 4 equal to F 0 ; join 4 2, the major axis ; at No. 5, is the face- 
 mould the major axis indicated by 2 3 4, the same as No. 3. The mould is drawn and the bevels found as usual. 
 The tangents P K E equal P K E, No. 2. The lower face-mould for the wreath joining the scroll is found at No. 4. 
 Make C D equal to A B; the produced line D E is the same pitch as J A, and the line 2 3 4, the major axis. 
 The same is seen at No. 6, which is the face-mould, its tangents being D J E, and these equal A J E, No. 2. 
 
 The thickness of the block for the eye of the scroll is found by measuring from its under side to the upper cor¬ 
 ner of the joint. In making this joint, lay the pattern on the stuff, and mark on its face the line of the joint, the 
 same as 5 on the ground-plan; continue the line down the side the same as 5 A, on the elevation. On this set off 
 the distance from the under side to A. Set the bevel to the angle, its blade made to pass through A ; mark the 
 joint on the side; continue this line over the face, parallel with that made by the pattern ; cut off slab, and 
 work to the bevel and the line on the face. j 
 
 In sawing the block, make allowance for over wood. j 
 
 • V.- I 
 
 ' X * .-'-V r- i 
 
 9 # \, 4 . 
 
 -.•'w v X i 
 

 
 
 
 
 
 
 
15 
 
 PLATE 13. 
 
 No. 1 exhibits the ground-plan of a staircase on -which the risers are situated, so that the shank on the lower 
 half of the wreath must form a part of the ramp landing, and the shank on the upper half, made on a pitch to 
 suit the ramp over the winders. 
 
 In giving this plan, the object in view is, to show that it matters not how the risers are situated, all positions 
 being equally simple and easy. And in this case the face-moulds are obtained on precisely the same principles as 
 those which have already been laid down. It will be noticed at No. 1, that S is the last flyer-landing, and II the 
 first flyer above the winders; so that we have only to draw the tangents on the ground-plan, then unfold them, 
 as seen at No. 2 ; there ABODE are the same letters as those at No. 1. The pitch-board shows the position 
 of the last step and riser landing. The dotted line A J indicates the springing. Outside of this is the elevation 
 of the two winders and flyer, the same as on the plan. Inside, make the elevation of the winders and risers the 
 same as they are on the tangent lines which enclose the semi-circle. On the upper part, let the under side of the 
 straight rail rest on the corners of the flyer ; set oil' half its thickness ; this draw. The next pitch will be the 
 centre of the shank on the upper part of the wreath. This may be raised or lowered to suit the stairs. Take 
 any part of the centre-line on the common pitch, and draw to cut, say P ; from P draw to cut, say S; from S draw 
 to cut the centre of the rail on the common pitch landing. 
 
 The pitches and the centre-line of the wreath are now drawn. These have been discretionary so far as height 
 is concerned, yet the elevation has given a direction by which the length of each baluster may be obtained. 
 
 The face-mould for the upper part of the wreath is found from No. 5. Make 4 5 equal to 4 5, No. 2; make 
 5 6 equal to J P, No. 2; from 4, draw through 6, cutting the produced line, from 5; draw the ordinate as usual, 
 and the line J S, at right angles to it; make J P equal to 4 5; join P S ; then P 0 S is the major axis, and at 
 No. 6, this is indicated by the same letters. The mould draw in the usual manner. The tangents 6 Y II equal 4 
 P J, No. 2. 
 
 The mould for the lower part of the wreath is obtained from No. 3. Make 2 3 equal with 2 3, No. 2 ; draw 3 
 S parallel with 2 S, No. 2 ; from 2 draw through the intersection to cut the produced line from 3 ; draw the ordinate 
 as usual, and the line N D at right angles to it; make N Y equal with 2 3 ; join Y D ; then Y 0 D is the major 
 axis, and at No. 4 this is indicated by the same letters. The tangents J II Y equal 2 S 4, No. 2. The bevels 
 are found and applied as usual. 
 
16 
 
 PLATE 14. 
 
 - 1 f h * lts the P lan of a staircase starting with a scroll-step and winders, the joint extended beyond the 
 quaiter-circle, the wreath to form two ramps, one to connect with the eye of the scroll, the other over the win- 
 ders and flyers, its shank to be on the common pitch. The object of this plate is to show that we are not limited 
 to any particular part of the circle. 
 
 _ nt A h o 4 C r e X°^l d Nn°o tain f d 1 ^ SUa1 ' c At N °' ^ make J hc J ’°l nt on ar A P art of the circle, say 6 ; draw the tan¬ 
 gents 3 4 5b at No. 2, unfold these; from each figure draw the dotted perpendiculars ; make the elevation of 
 
 the winders and one flyer the same as those on the tangent lines of the plan; with the pitch-board, draw the under 
 side of the rail to rest on the angles of the step; set off half its thickness ; this draw to cut the perpendicular at 
 15 ; irom 15 draw the next pitch to cut, say D. ^ F 
 
 , m T ! ie f ace - mould . TCil J now be drawn the same as for a quarter-circle. The height is found by drawing a line 
 w £ A , , C ’ c . ut t in g the perpendicular at W and P; make W II equal with 2 3, No. 1; draw H 0 parallel to 
 W P; with the pitch-board draw P Y produced ; draw W Y, cutting the produced line P 0; make 0 4 equal to 
 0 P; make the tangents 4 5 6 equal to 4 5 6, No. 1; from 4, draw the ordinate; from 5 and 6, and 0 P^ draw 
 lines paiallel to it. Through 0, draw the base R 8, at right angles to the ordinate; make Y L equal to H 0 * 
 jom L Reproduce this to cut Iv. We have now the major axis; and at right angles to it, draw lines from R2L 
 F k make K E equal to 8 6, and F D equal to e 5 ; join D E; make L 0 equal to V 4, and R A equal R P- 
 
 2?pmSi a tn d n P-’ draW 1 D .? P arallel With 2 A and A B parallel with 2 C; produce B A for the shank; make 
 - 3 equal to 0 1 , on each side of o, set off half the width of the rail; find the width of the shank, also the width on 
 the major axis at K: strike the mould as usual; make the joint at right angles to E D. The bevel for this is 
 round by drawing L J parallel with E D, and producing the minor axis to cut at N, with 2 for a centre and for 
 radius a tangent curve to L J; draw the circle to cut at S ; join S N; and in the angle is the bevel required. 
 1 hat tor the shank: take II for a centre, and for radius, a tangent to the produced line, P Y ; draw the circle 
 to cut at 4; join 4 W; in the angle is the bevel. 
 
 To find the plane or pitch of the plank at the joint of the scroll: make D E, No. 2, equal to E D, No. 3- pro- 
 duce the line D E, and make the joint at right angles to it; on each side of this set off half the thickness of the 
 
 rail; from the upper corner of the joint, set off the thickness of the block for the eye; this will also be the under 
 side oi the scroll. 
 
 
PL. 14-. 
 

 

 ■ 
 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
17 
 
 PLATE 15. 
 
 On this plate a ground-plan is given, made up of various curves, the illustration of which will entirely exhaust 
 the subject of hand-railing, from the fact that nothing further remains.to be added. In the constructive principle, 
 it must have been observed, that everything was depending on tangents or straight lines. The methods taken 
 to demonstrate these, we think the most simple that perhaps could be devised. The language and terms used 
 are such as are generally known among workmen. 
 
 The plan before us presents no difficulty or change of system. The same principles which have been given 
 for finding the face-moulds will be adopted here: but to proceed with the drawing; let Nos. 1 and 3 be the ground- 
 plan, the position of the winders given, and the joints made at 1 3 5 7 9. Draw the tangents through the centre of 
 each joint: the meeting of these are at 2 4 6 8. 
 
 Unfold the tangents on a board-in the same manner as laying out a string; for example, suppose No. 1 to be 
 the face'of the board, and the line or margin of the plate its edge ; now set a bevel to any angle; apply this to 
 the edge of the board, and draw 12 3, which are equal to the length of the tangents 1 2 3 on the ground-plan; 
 proceed to unfold the remainder of the tangents on the board, the same as they are on the plan; then make the 
 elevation of the winders precisely the same as they are on the tangent lines of the plan ; next draw the floor or 
 landing, No. 3; also draw the top of the curtail-step. 
 
 The winders, tangents, floor and curtail-step are now spread out the same as on the plan. Complete the eleva¬ 
 tion by drawing the pitches for the rail. Commence at No. 2, by drawing the under side of the rail to rest on 
 the angles of the winders 3 and N; these are the elevation of those between 3 and 5 on the plan ; set off half the 
 thickness of the rail; this draw to cut the tangents T and J; above the floor, set off the centre of the level rail 
 indicated by 8 9 ; join 8 and T ; at the lower part of the elevation, the centre of rail having cut at J, deter¬ 
 mines this as a fixed point; from which must be drawn a pitch to suit the eye of the scroll; this must be a suffi¬ 
 cient height above the curtail, say six inches, that is, its under side; this, added to the length of a baluster, gives 
 the whole height when in position; so that we assume A for the joint, through which draw a line from J; the 
 centre of the rail, or the pitches which the plank makes, are now given, the joints indicated by A S P 5 9; these 
 when in position, stand over the joints 1 3 5 7 9 on the plan. 
 
 Now commence the face-mould for the wreath that stands over the winders, between 1 and 3 on the plan. 
 The height for this is given on the elevation at Fig. 5; from the centre of the joint A, draw a line parallel with 
 the steps, cutting the perpendicular 2 3; produce the line from J, cutting that from A in 2; then 2 on th*e per¬ 
 pendicular, and the centre of the joint S, is the height, and 2 2 the base. The face-mould is found at No. 4,’which 
 is the same as Fig. 3 on the plan; from the centre of the joints, draw the tangents, meeting at N; produce 2 N, 
 and make 2 2 equal with 2 2, Fig. 5; make 2 3, Fig. 4, equal with 2 S, Fig. 5; from 2, draw the ordinate 
 through the centre of the joint F ; from N and 2, draw lines parallel with the ordinate ; through 0, the centre, 
 draw H R, at right angles to the ordinate; make R W equal with 2 3, Fig. 4; join W H; at right angles to this, 
 draw lines from WKH; make II A equal to II F, and K J equal to L N, and. W S equal to R 2; join S J and 
 J A. These are the tangents through the centre of the mould, and their correctness proved by being equal to A 
 J S, Fig. 5. 
 
 The plan No. 4, having two curves of unequal radius, it will be more convenient to draw a few ordinates, and 
 trace the mould in the usual way, than to apply the trammel, or the thread. Make the joints A and S at right 
 angles to the tangents; the bevels for these are found by drawing W Y and W P parallel with the tangents on the 
 mould ; then draw a line, say e D, at right angles with W II; take e for a centre, and for a radius, a tangent 
 curve to W Y, cutting above 6, from which draw to D, and in the angle is the bevel for the joint A ; for the other 
 bevel, take centre e, and for radius, a tangent curve to W P, cutting at C ; join C D; in the angle is the bevel 
 for the joint S. 
 
 The next mould will be for the wreath that stand the winders between the joints 3 and 5 on the plan. At No. 
 5, draw a line for the major axis; let 0 be its centre ; through which draw the minor axis; make 0 e R equal to 
 0 S 4 on the plan; through e draw the dotted chord, parallel with the major axis ; make e 3 equal with S 3 on 
 the plan ; join R 3; make R P and R S equal to R P and R S, No. 2, (the elevation ;) from 0, the centre, set 
 off a distance on the minor axis, to equal 0 3 on the plan ; on each side of this, set off half the width of the 
 rail; find the width of the mould at S and P; then with the trammel or straight .edge, strike it as usual; make 
 the joints at right angles to the tangents P R and S R. To find the bevel for the joints : from 0, the centre, 
 draw a line through 3; take R for a centre, and S for a radius ; draw the circle to cut at N ; join N R ; take 3 
 for a centre, and for a radius, a tangent curve to N R, cutting at 2; join 2 0 ; and in the angle is the bevel for 
 the joints P and S. 
 
 The next mould will be for the Avreath that stands over the tangents 5 6 7 on the plan. The upper end of 
 this forms part of the ramp-landing. The height is found at Fig. 9, (the elevation.) From the centre of the joint 
 P, draw a line parallel with the steps cutting the perpendicular, 4 5; then 4 5 is the height; find the base by 
 drawing 4 5 parallel with P T; now make No. 6 the same as No. 1, (the plan;) the tangents Y H 4 make equal 
 with 5 6 7 on the plan; produce the tangent 4 H; draw 4 5 at right angles to it; make 4 5 and 4 4 equal with 
 4 5 and 4 4, Fig. 9; from 4, draw the ordinate through Y; from H and 4, draw lines parallel with the ordinate ; 
 from the centre, draw e N, at right angles to the ordinate ; make e R equaPwith 4 5, Fig. 6 ; join R N; produce 
 this, (the major axis); from CRD, draw lines at right angles to it; make C 0 equal to 0 5, the plan ; make 
 R P equal to e 4, and D T equal to N II; make the distance from the intersection to 5 equal with that and Y ; 
 join T 5 and T P; the correctness of these are proved by being equal to P T 5, Fig. 9; on each side of 0, set off 
 
18 
 
 • half the width of the rail; find the width of the mould at 5; then with the trammel or thread, strike it; the joints 
 P and 5 make at right angles to the tangents ; find the bevels by the same method as at Fig. 7. 
 
 The next and last mould will be for the wreath, which stands over the tangents 7 8 9 on the plan. The 
 position of this part of the wreath is seen on the elevation at No. 3. There its centre is indicated by the lines 
 5 8 9. The reason for calling particular attention to this, is when the wreath, or a portion of it is required 
 to fall level. In all such cases, the tangent on the plan is the ordinate, which No. 7 will explain. Make 
 its tangents V P 9 the same as 7 8 9 on the plan; make Y 5 equal with V 5, No. 3; join 5 P ; then is P 9 
 both tangent and ordinate; from Y, draw a line parallel with it; make A B equal to V 5; from 9, draw 
 through A ; we have now the major axis; from 6, the centre, draw a line parallel to Y B, cutting at N ; from N 
 A 9, draw lines at right angles with the major axis: then make N R, (the minor axis,) equal to 6 V; make A 5 
 equal to B Y, and 9 8 equal to 9 P; join .5 8 9; these tangents are equal to those on the elevation at No. 3; the 
 joint 5 make at right angles to 5 8; on each side of R, set off half the width of the rail; find the width of the 
 mould at the joint 9 ; then strike it by any of the methods which have been stated. The bevel for the joint 9, is 
 seen in the angle at S. Find the bevel for the joint 5 by the same principle as those found for the joints at 
 Fig. 7. The face-moulds are now complete, and we conclude with the remark that all the drawings and descrip¬ 
 tion which have been given, amount but to the simple fact of finding the length of straight lines in space, to stand 
 over straight lines which have been given on a plain surface. 
 
 To make this perfectly understood, that which we have just done will convey the idea. Suppose the joint A 
 on the mould, Fig. 7, to rest on the joint 1, the ground-plan; then let A J on the mould, make the same pitch as 
 A J on the elevation, No. 1; now it is evident that J and S, on the mould, stand over 2 and 3, on the plan; t 
 again take the mould, Fig. 5, place the joint S against the joint S of the mould, Fig. 7 ; then will S R P. on Fig. 
 
 5, stand over 3 4 5 on the plan. Again, take the mould, Fig. 2 ; place the joint P against P, No. 5 ; then will 
 P T 5, on Fig. 2, stand over 5 6 7, on the plan, and so on with Fig. 8. It may be stated, that if the plan con¬ 
 tains five, ten, or fifteen winders more than what is here given, the mould No. 5 answers for any additional number 
 of pieces to stand over five winders: Note. —If the plan be elliptical, or its representative that is struck by centres, 
 the face-moulds are found on the same principle as laid down in this plate. 
 
 / 
 
 f 
 
 *