CHAPTER XXVIII
SETTING OUT Tools—Transferring drawings to metal—Measurements—Various geometrical problems—Setting out inscriptions—Rectangular ring for small work. 
 
In this chapter are given a number of hints and rules which may be useful in the setting out of work. The tools required for work on paper are— 
1. A drawing board. This should be square at the corners, the sides should be absolutely straight and the surface level. The size must depend on the kind of work you are doing. 
2. A T-square. The head and blade of this tool are usually fastened together at right angles with screws. The angle between the two parts is liable to variation, so its accuracy should be tested occasionally. The working edge of the blade should be bevelled, so as not to throw a shadow on the work. The T-square should always be held firmly against the left-hand side of the drawing board when in use. Any number of horizontal, parallel lines can be drawn thus. Lines at right angles to these can be drawn either by the aid of a set square, which is held firmly against the T-square, itself held against the side of the drawing board; or the T-square itself may be gently slid down the board while the fingers rest upon it and hold the pencil which rules the line. With a little practice lines can be ruled in this way quite as accurately as by the aid of the set square. The T-sauare should not be turned so as to work from another edge of the drawing board. 
3. Two set squares. These are triangular pieces of wood, vulcanite or xylonite. Those having the angles of 60° and 45° are most generally useful. By sliding these tools along the T-squareto other positions any number of perpendicular or diagonal lines may be drawn. For sets of lines required at other angles,—place one of the squares on the paper so that its side points in the required direction; then put the T-square against it. Hold the T-square down and slide the other along it to the positions required for ruling the lines. If, however, much work has to be done at such an angle the paper maybe slewed round on the board and pinned in a fresh position, so that the lines may be ruled by the aid of the T-square alone. 
4. A set of mathematical instruments. 
5. A protractor, for setting out angles. 
6. Drawing pins. These should be driven in not quite at right angles to the board, so that some part of the heads touch the paper. They hold it better so. 
7. Paper, pencils and charcoal. The latter is very useful for roughing in large work. 

To transfer a drawing to metal. Put a sheet of carbon paper between the drawing and the metal and go over the outlines with a pointed tool. A knitting needle set in a handle, as the lead is set in a pencil, makes a useful tracing needle. Its point should be rubbed smooth. Another way is to use a mixture of virgin wax and whiting. Warm the metal and smear a very thin layer of the composition over it. Make a tracing of the drawing and turn it face downwards on to the white film left on the metal. Lay a piece of notepaper above and rub hard all over with the handle of a knife. 

To draw on metal, first roughen the surface with fine emery paper or pumice-stone and water, taking circular strokes. Pencil lines made in any direction will show on this surface. Erasions can be made with fine emery used as before. A pen and ink may be used, and faulty ink lines trued up with a knife point. 

The tools required in setting out work on metal are : A rule, preferably of steel. An accurate straight-edge, also of steel. A square;—this is made of two pieces of steel firmly fixed at right angles to each other. A pair of dividers or compasses with quadrant. A marking tool made from a length of § inch steel wire, ground to a sharp point. 

It is a good rule to take all measurements and angles from one central or base line. In careful work, measurements should be transferred from the rule to the work by means of the dividers. In doing so it is well to avoid the last inch on the rule. A measurement of an inch, say, taken from the extremity of the rule is likely to differ a little from one taken at another part. Not necessarily because the rule has become worn and rounded at the end, but because one point of the dividers rests on the end of the rule—some where, rather than in an accurately placed cut on the surface. 

In marking off successive measurements always add the length of the new section to the total of those which have gone before, and measure from the base to that total length. Greater accuracy is attained in this way than by that in which each successive measurement is carried on frosi the mark made for the last. 

To find the centre of a straight line with the compasses, Figs. 303, 304. Open them to a span of about half the length of the line. Place one leg at A and make a mark C on or across the line. Lift the compasses and place one leg at B. Make another mark D on the line. The centre is exactly half-way between C and D. It may be guessed, or the space of the compasses adjusted until marks made from either end of the line, as above described, are found to agree. It does not matter if the dividers are set to too great or to too small a span in the first instance. The method to be followed is the same in either case; 

The centre of any regular curve may be found in the same 
way, Fig. 305. 

To divide a given straight line into any number of equal parts, Fig. 306. If you cannot do so by measurement with the rule, proceed as follows. From one end of the line E F, draw another line, E G, of any length and at any angle. From E along the line E G, set off the required number of equal parts, say nine,—taking any convenient unit—inches on a foot rule,—for example. Join 9 and F. Then draw lines parallel to 9 F through each of the divisions, 8, 7, 6, etc., cutting the line E F. The line E F is now divided as required. 

To find the centre of any square, Fig. 307. Draw diagonals H K and I J. They will cross in the centre of the square. 

To find the centre of any circle, Figs. 308, 309. From any point in its circumference L, with a distance equal to about half the diameter of the circle for radius, describe a small arc, M. With the same radius from two other widely separated points in the circumference describe small arcs N and 0. The centre of the circle lies between the arcs M, N and 0 and may be guessed. Or, adjust the dividers until arcs struck from any point in the circumference all pass through one point. This will be the centre of the circle. It does not matter if the dividers are set to too great or to too small a span at first. 

To divide a circle into three or six parts, Fig. 310. Find the radius of the circle. This is the distance from the centre to the edge. From any point, P, in the circumference strike an arc of the same radius, cutting the circle in two places, Q and R. Either with Q as centre and Q R as radius describe an arc, cutting the circle in S; or draw a diameter passing through P and the centre to S. The circle is now divided into three equal parts in Q, R and S. To divide it into six, draw lines from Q and R through the centre, cutting the circle in T and V. Or, with P Q as radius and S as centre describe an arc, cutting the circle in T and V. Or, step the distance P Q round the circumference. 

To divide a circle into any number of equal parts, Fig. 311. Draw a diameter A B, to the circle. With A as centre, and A B as radius describe an arc. With B as centre and the same radius describe another arc, cutting the first in C. Divide A B into as many parts, say five, as you wish the circle divided into. Draw a line from 0 through the second division in all cases, whatever the number of parts may be, cutting the circle in D. Step the distance A D round the circle EFG. If AD,DE,EF,FG andGAare joined,a regular pentagon has been described in the circle. In the same way any regular polygon may be constructed. The pentagon has five sides. The hexagon six. The heptagon seven. The octagon eight. The nonagon nine. The deca gon ten. The undecagon eleven. The duodecagon twelve. 

To draw the given geometrical figures in the circles, Figs. 312, 313. Divide each circle into twice as many parts as there are foils. Let H be the centre of the circle. Find by trial the largest circle which can be inscribed in the space, H I J. Set out the distance from H to its centre on alternate radii and describe the other circles. 

To work this problem geometrically, Fig. 313. After dividing the circle into twelve parts, draw K L at right angles to H I, and complete the triangle H K L. Bisect the angle K L H. You do this by taking L as centre and striking the arc N M at any distance. From N and M with any radius strike two other arcs crossing each other in 0. Join 0 L, cutting H I in P. With P as centre and P I as radius inscribe a circle. It will fit exactly into the triangle H K L. With H as centre and H P as radius mark the centres of the other circles and complete the figure. 

Problems similar to those given above are often met with in setting out the bases of cups, chalices, bowls, etc. They may be dealt with in yet another way—by the use of the protractor. If you remember that the circumference of a circle is divided into 360 degrees, you have a very small sum to do to find out how many degrees must be allowed for each part of, say a nine, ten, twelve or fiftean sided figure. You have then but to set out with the protractor the correct number of degrees for each part. For other and more difficult problems Morris's Geometrical drawing for Art Students is probably the best book to turn to. 

To draw an ellipse, the length and breadth being given. Let A B and C D be the major and minor axes (the length and breadth). They are drawn in Fig. 314 crossing each other at right angles. 0 is the centre both of A B and C D. With radius A 0, and centre C describe an arc cutting A B in E and F. These two points are called the foci. Take three pins and stick them firmly in at the points C, E andF. Tieapieceofstringround thesethreepins running from C to E, E to F, and back to C again. Remove pin at C and replace it with a pencil. Move the point of the pencil round, keeping the string tightly stretched. The curve traced by the pencil point will be an ellipse. G and H show the position of the pencil at three different times on its journey. The dotted lines proceeding from G and H to E and F show the position of parts of the string at those 
times. 

Second method, Fig. 315. Set up the axes A B and C D as before. Take a piece of paper, or a long, flat ruler and make EFequaltoA0 andEGequaltoC 0. PlaceitsothatG may be on the major (longer) axis and F on the minor (shorter) axis. Then E will be a point on the curve. By shifting the paper, and always keeping G on the major and F on the minor axisanynumberofpointsonthe curvemay be obtained. Draw the curve through these points. 

In constructing narrow, deep vessels or those figures whoseshape approaches that of a truncated cone,a consider able saving in time may be effected if a seam up the side be permitted, for in raising a deep shape without a join a good deal of time is required. Almost any vessel of the typesshowninFigs. 316to318maybeconstructedbycutting a suitably shaped piece to form its sides, and another flat piece for the bottom. But the exact shape shown in the figures could not be obtained from any flat piece of metal. The nearest one can approach to it is shown by the dotted lines inside each figure. They represent part of a cone— a tapering tube. If a piece of metal were cut to such a shapeitcouldbealteredintothe form"required bysnarling and shaping. But remember that it is easier to expand parts of a shape to the correct size than to reduce them. So as a rule, draw the dotted lines just within the narrowest parts of the outline of the vessel. Experience only can guide you to choose the best position to place them. First draw the elevation of the vessel. Then, if its sides are not straight,markinthe dottedlinesasindicated. LetABCD, Fig. 319, be the elevation of the shape required. It would do, upside-down, for a bowl of the shape shown in 317. Produce the sides B A, C D till they meet in E. With E as centre and E A as radius describe an arc. With E as centre and E B as radius, another arc. Along the larger arc mark off F and G, making B F and C G each equal to B 0. Beyond G,markoffH,makingGH equalto oneseventhof BCor of CG. This distance can be easily guessed. The total distance F H is, therefore, 3^ times B C, see page 300. From F and H draw straight lines towards E, cutting the smaller arc in I and J. Then I F H J is the shape required. A piece of metal cut to that shape will curl up to form the sides of the vessel A B 0 D. The join up the side must be soldered and the metal snarled and hammered to the curved shape 
required. 

In setting out ornament on the four sides of an oblong box, usually made from one long strip of metal, do not forgetthatthelongandshort sidescomealternately. Thus: long, short, long, short. 

The stems of candlesticks and other objects are often made with a spiral twist or flute, Fig. 323. This twisting or fluting can be worked upon the piece of sheet metal which is to form the stem before it is bent round into cylindrical form and soldered. Suppose that the twisted stem is to be 6 inches high by 1 inch in diameter. Take a piece of sheet metal measuring 6 inches by 3| inches, Fig. 322. (The drawing has been made too wide in proportion, by mistake.) On the back of the metal you have now to set out the lines of the ridges which form the twist. They will afterwards be driven up by repousse work. Let us suppose that the ridges are to cross the stem as shown in Fig. 323. Divide the two long sides of the metal into nine equal parts. Draw a straight line from the top right-hand corner to the third mark down on the left-hand side. Now draw other lines parallel to the first through all the marks previously made. Put the work on pitch and drive up each line as a ridge on the other side of the metal. When this is done clean off the pitch and bend the sheet of metal round in cylindrical form, with the ridges to the outside. They will follow on at each side of the join quite accurately; some little care is necessary, however, in getting the edges to fit well enough beforesoldering. Afterthisyoumay fillthetubewithpitch; or if it is of brass or copper, with lead; and complete the modelling. It is dangerous to put molten lead into contact with silver,—there is so much danger that it may " burn " its way into the silver^ see page 40. The turn in this case will be a left-hand twist. To obtain a right-hand twist you have only to join the top left-hand corner to the third mark down on the right when you are marking the metal, and then to put the other lines parallel. To make a quicker twist you must join the top corner to the second or first mark down on the opposite edge, instead of to the third. The ridges will, however, be wider apart unless you reduce the space between the marks. For a slower twist join the top corner to the fourth, fifth or sixth mark opposite. The ridges will be closer together unless you make the marks further apart in this case. 

To produce a similar twist on a tapering stem you must make the marks at each side of the curved shape, Fig. 320. This shape you set out just as you did that shown in Fig. 319, above. Then, with the compasses set to the distance L M you make an arc, M N. From the point, N, which you find by trial, and without altering the span of the compasses, you may reach one of the marks, 0, at the left-hand side of diagram. From N as centre you make a series of arcs cutting each one of the marks at the side of the diagram, reducing the span of the compasses each time, but always keeping N as the centre. If you had wished to produce a slower twist you could have joined L to the second, third, fourth or fifth mark down. The point N in this case would have been found much further to the right on the drawing. Set out in this way the spiral will be found accurate enough for practical purposes, though it is not geometrically 
correct. 

In setting out an inscription the first thing to do is to count the total number of letters in all the words, reckoning the spaces between words as letters,—for the space between two words may take up about the room of one extra letter. Then consider the space available in your design. It may be longenoughforthe inscriptionto gointo a fewlinesoflarge letters, or so narrow as to require numerous lines of lettering. Reckon out roughly how many letters will go into a line. To do this, lightly rule two parallel lines across the paper at a distance apart equal to the height of the letters you would like to use. You are trying to find out if there is room for letters of that size. Having ruled the lines, lightly sketch in part of the inscription to try how many letters are required to fill the line. It is only necessary to sketch in each letter very lightly before going on to the next. When the line is complete count up the number of letters you have worked into it, reckoning spaces between two words as letters, as before. Having found out how many letters will go in to one line,a simple calculation will show how many lines are required for the whole inscription. Measure up the available space to see if there is room for that number of lines with the necessary intervals between them. It may be that there is not room, and you must either use smaller letters, drawing the parallel lines, above mentioned, closer together; or you must compress the letters laterally, so as toget moreofthemintoaline. Ontheotherhandyoumay have room to spare, and can therefore enlarge the letters or spread them out more. One or two trials may be necessary before a suitably sized letter can be settled upon. In finding out how many letters a line will hold, it is not always necessary to draw a complete line of the inscription. A half or a quarter of a line may be all that it is necessary to fill, and the number of lines required reckoned from that. 

Proper names or dates should never be spaced so as to come partly ononeandpartly ona secondline,ifit canbepossibly avoided, nor should any unusual division of a word be made. The number of letters which can go into certain lines of the inscription may be thus affected, and any varia tion must be reckoned with in finally deciding on the size of letter to be used. In the chapter on Repousse work, page 131, there are given some further hints as to the spacing of lettering for execution by that process. 

In setting out small work—an engraved pattern or in scription, for example—some difficulty may be met with in firmly holding the work in such a manner that a set square can be used on it. It is a good plan to make a rectangular ringofironorbrass,Fig. 321,thetopand edgesofwhichare quite true and square. Fix this on the pitch bowl with its upper part projecting a little above the surface. Work can now be fastened down on the pitch within the rectangle in the usual way, and the square held against the ring while lines are being ruled. It is, of course, necessary to keep the working edges of the ring quite free from pitch.